Teleologism Full Stop: a General Theory of Ability, Agency, Obligation, and Justification

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2016 Teleologism Full Stop: A General Theory of Ability, Agency, Obligation, and Justification

Hebert, Ryan

Hebert, R. (2016). Teleologism Full Stop: A General Theory of Ability, Agency, Obligation, and Justification (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/27992 http://hdl.handle.net/11023/2916 doctoral thesis

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Teleologism Full Stop:

A General Theory of Ability, Agency, Obligation, and Justiﬁcation

Ryan Hebert

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE

DEGREE OF DOCTOR OF PHILOSOPHY

GRADUATE PROGRAM IN PHILOSOPHY

CALGARY, ALBERTA

April, 2016

©Ryan Hebert 2016 ABSTRACT

Deontic modals are the topic of my dissertation. All deontic modals, yes, but justification in particular, and epistemic justification even more specifically. Deontic modals operate upon performances—they appraise performances. Positively appraised, a performance is appropriate, decent, justifiable, right, permissible, or proper; negatively appraised, inappropriate, indecent, unjustifiable, wrong, impermissible, or improper. Belief and knowledge and performances in exactly the same sense that action and intention are performances: all are products of powers that are in some sense responsive to reasons. The principal difference is the direction of fit between mind and world. Knowledge and belief the product of cognitive powers aimed at adapting mind to world, action and intention the product of conative powers aimed at adapting world to mind. All are normatively evaluable and the characteristic normative appraisal of each is deontic. Epistemology, ethics, and rational choice all investigate the nature of deontic modals, differing only insofar as the central aims are epistemic, moral, or prudential in nature. In this sense, the general theory of deontic modals is the parent to epistemology, ethics, and rational choice. My project is to develop and defend a schematic theory of justification. I achieve this end by developing and defending a general theory of deontic modalities. Riffing on two pithy turns of phrase, the deontic theory may be tersely sloganized: value first and one must do the best one can. It is a teleological theory that defines all deontic concepts from the theoretically foundational notions of ability and value. Roughly, a belief is epistemically justifiable if, and only if, it is part of an epistemically optimific belief set the agent is able to have. Roughly, an act is morally justifiably if, and only if, it is part of a morally optimific action set the agent is able to perform. My pet interest is in the former. The resultant framework is enormously fruitful, especially in epistemology.

ii ACKNOWLEDGEMENTS

I have richly benefited from the talent and insight of many friends and colleagues over the years. It is my distinct honor and pleasure to recognize these individuals. I owe Jeremy Fantl a huge debt of gratitude for his encouragement, patience, and support. He is an excellent mentor and a wonderful advisor. When he originally agreed to be my advisor, I promised a project very different—and far, far less complicated—than the one I ended up with. Jeremy would have been fully within his rights to complain or suggest that take my research elsewhere, but he never did. Instead he used his encyclopedic knowledge to direct me to engage with interesting issues in accessible ways. I am not confident that I succeeded in living up to the direction, but I am thankful for his diligence, his faithfulness, and the abundance of helpful advice, both professional and personal. I also owe Ish Haji a huge debt of gratitude. He often played the role of surrogate advisor, with all the annoyances and burdens that it entails. He is a brilliant, incisive critic with a prescient ability to cut the core. Whenever I sit down to do philosophy, I imagine Ish as my interlocutor and I am better for it. He taught me how to do philosophy with clarity, grace, and rigor. I am thankful for his example. I want to thank Richard Zach for his instruction and understanding. I have been his teaching assistant and his student. I learned firsthand that he is a meticulous logician that generously donates time to painstakingly answer the fumbling questions of confused students. I learned much about formal methods under his tutelage. I could not have asked for a better committee. Many thanks to you all. My work also benefited immensely from an epistemology study group at the University of Calgary. Audrey Delamont and Caleb Lee occupied the trying role of copy editors for many early drafts of chapters. Their commentary helped to me to refine ideas and present them far more clearly. The many hours spent discussing difficult topics was an endless

iii iv source of enjoyment. More importantly, both have been marked inﬂuences upon my life. Simply put, each is the kind of person I want to be. Audrey is a better, more steadfast friend than I deserve. Caleb is the warmest, most upright person I have ever met. Words fail to express my personal thanks. Finally, I wish to recognize and thank my mother, Amy Schihl, for her boundless love, support, and good humor. DEDICATION

I dedicate this work to my mother, Amy Schihl.

v TABLE OF CONTENTS

Abstract ii

Acknowledgements iii

Dedication v

Table of Contents vi

List of Figures xi

List of Tables xiii

List of Nomenclature xv

I Introduction1

1 Ability and Normative Appraisal2 1.1 Introduction...... 2 1.2 Normative Appraisals...... 4 1.3 Knowledge and Epistemic Justification...... 7 1.4 Justification and Justifiers...... 13 1.5 Teleologism and Deontic Modals...... 16 1.6 Structure of the Dissertation...... 18

II Formal Foundations 20

2 What We Can Do 21 2.1 Introduction...... 21 2.2 A Structural Taxonomy of Praxeo-Abilitives...... 23

vi 2.2.1 Capabilities, General Abilities, and Speciﬁc Abilities...... 24 2.2.2 Simple and Competent Abilities...... 25 2.2.3 Nonperformative and Performative Abilities...... 28 2.2.4 The Structural Taxonomy...... 29 2.3 Adequacy Desiderata for Praxeo-Abilitive Logics...... 31 2.3.1 Mele’s Constraint...... 31 2.3.2 Kenny’s Constraint...... 33 2.4 The WWCD Framework...... 38 2.4.1 WWCD Foundations: Theory of World...... 38 2.4.2 WWCD Assumptions, Frames, and Models...... 47 2.4.3 WWCD Semantics...... 54 Normal Boolean Connectives...... 55 Normal Tense Modalities...... 56 Normal Abilitive Modalities...... 56 Normal Praxeological Modalities...... 57 The Theory of Alternality...... 61 Normal Reasons Modalities...... 63 The Theory of Intentional Action and Knowledge...... 70 Nonnormal Semantics...... 72 2.4.4 WWCD Syntax...... 72 Proof Rules...... 73 Axiom Schemata...... 77 Interaction Theorems...... 79 2.5 Adequacy Desiderata Satisﬁed...... 83 2.5.1 Satisfying Mele’s Constraint...... 84 Variations on the Abilitive Index...... 84 Variations on the Praxeological Index...... 85 Generating the Characteristic Praxeo-Abilitive Compounds..... 87 2.5.2 Satisfying Kenny’s Constraint...... 89 2.6 Conclusion...... 92

3 Doing the Best We Can 93 3.1 Introduction...... 93 3.2 The Structure of Praxeo-Deontives...... 95 3.2.1 Primary Deontic Statuses...... 96 3.2.2 Normative Language: Axiological and Deontic...... 98 3.2.3 Deontic Language: ‘Must’ and ‘Ought’...... 99 3.2.4 A Structural Taxonomy...... 102 3.3 Adequacy Desiderata for Praxeo-Deontic Logics...... 103 3.3.1 Meinong’s Constraint...... 103 3.3.2 Marcus’s Constraint...... 103 3.3.3 Urmson’s Constraint...... 106 3.4 The DBWC Framework...... 114 3.4.1 DBWC Assumptions, Frames, and Models...... 114 3.4.2 DBWC Semantics...... 118

vii Normal Primitive Deontic Modalities...... 118 Normal Primary Deontic Modalities...... 121 Normal Subsidiary Deontic Modalities...... 123 3.4.3 DBWC Syntax...... 125 Proof Meta-Rules...... 125 Axiom Meta-Schemata...... 126 Interaction Theorems...... 127 3.5 Adequacy Desiderata Satisﬁed...... 132 3.5.1 Satisfying Meinong’s Constraint...... 132 3.5.2 Satisfying Marcus’s Constraint...... 133 3.5.3 Satisfying Urmson’s Constraint...... 134 3.6 Conclusion...... 136

III Philosophical Theory 138

4 Deontic Justification 139 4.1 Introduction...... 139 4.2 The Schematic DBWC Theory of Deontic Justification...... 141 4.2.1 Morphic and Praxistic Justification...... 141 4.2.2 Two Conceptions of Deontic Justification...... 145 4.2.3 The Justification Meta-Norm...... 147 4.2.4 Justification Principles...... 150 4.3 Justification and Ability...... 156 4.4 Justification and Deontic Conflicts...... 159 4.4.1 Deontic Dilemmas...... 159 The First Syntactic Argument...... 160 The Second Syntactic Argument...... 161 4.4.2 Deontic Disagreements...... 162 4.5 Justification and Deontic Holism...... 166 4.6 Justification and the Paradoxes of Agglomeration...... 167 4.6.1 The Lottery Paradox...... 167 4.6.2 The Preface Paradox...... 170 4.7 Conclusion...... 171

5 Value-First Epistemology 172 5.1 Introduction...... 172 5.2 Against Objections to Teleological Deontism...... 174 5.2.1 Doxastic Voluntarism Objection...... 174 5.2.2 Isolation Objection...... 177 5.2.3 No Positive Obligations Objection...... 181 5.3 Disarming Counterfactual Worries About Knowledge...... 186 5.3.1 A Closer Look at the Formal Features of Knowledge...... 187 5.3.2 Knowledge of Necessity...... 188 5.3.3 Justiﬁcationally Unsafe Belief...... 190

viii 5.4 Schematic Argument for Unhinged Justiﬁcation...... 197 5.4.1 Objections to the Fourth Premise...... 199 5.4.2 Objections to the Fifth Premise...... 202 5.4.3 Brute Objections to the Conclusion...... 205 5.4.4 A Corollary for Epistemic Norms...... 206 5.5 Speculative DBWC Refutation of Skepticism...... 207 5.5.1 Sketching the Strategy...... 208 5.5.2 A Defense of Epistemically Justiﬁed Belief...... 209 5.5.3 Extending the Defense to Knowledge...... 214 5.6 Conclusion...... 216

Bibliography 217

IV Appendices 237

A Elementary Mathematical Concepts 238 A.1 A Sprinkle of Elementary Set Theory...... 238 A.2 A Sprinkle of Elementary Order Theory...... 242

B Modal Logic Crash Course 243 B.1 The Base Language ℒ ...... 243 B.2 Relational Structures...... 245 B.3 Neighborhood Structures...... 249 B.4 From Neighborhood Structures to Relational Structures...... 254 B.5 Counterpossible Relational Structures...... 255

LIST OF FIGURES

2.1 Praxeo-Abilitive Hierarchy...... 30 2.2 Determinism vs. Indeterminism (in Branching Tree Structures)...... 42 2.3 Lattice of Nonpraxeological Interactions...... 80 2.4 Lattice of Praxeological Interactions...... 80

3.1 Alethic Square of Opposition...... 96 3.2 Deontic Square of Opposition...... 97 3.3 Lattice of Deontic Interactions...... 127

LIST OF TABLES

2.1 Possible Praxeo-Abilitive Compounds...... 29 2.2 Unacceptable Kenny Axiom Schemata...... 34 2.3 Branching Tree Semantics: Atoms and Booleans ...... 44 2.4 Branching Tree Semantics: Tense Modalities ...... 44 2.5 Branching Tree Inference Rules ...... 45 2.6 Branching Tree Axiom Schemata (Shared) ...... 46 2.7 Branching Tree Axiom Schemata (Unshared) ...... 46 2.8 WWCD Normal Semantics: Atoms and Booleans ...... 55 2.9 WWCD Normal Semantics: Discharger ...... 55 2.10 WWCD Normal Semantics: Tense Modalities ...... 56 2.11 WWCD Normal Semantics: Abilitive Modalities ...... 56 2.12 WWCD Normal Semantics: Monadic Praxeological Modalities ...... 58 2.13 WWCD Normal Semantics: Schematic Dyadic Praxeological Modalities .... 60 2.14 WWCD Normal Semantics: Dyadic Praxeological Modalities ...... 60 2.15 WWCD Normal Semantics: Schematic Alternality ...... 61 2.16 WWCD Normal Semantics: Reasons Modalities (First Formulation) ...... 64 2.17 WWCD Normal Semantics: Reasons Modalities (Second Formulation) ..... 65 2.18 WWCD Normal Semantics: Discharged Reasons Modalities ...... 69 2.19 WWCD Normal Semantics: Derived Monadic Praxeological Modalities ..... 70 2.20 WWCD Normal Semantics: Derived Dyadic Praxeological Modalities ...... 72 2.21 WWCD Nonnormal Semantics ...... 72 2.22 WWCD Inference Rules ...... 73 2.23 WWCD Axiom Schemata ...... 78 2.24 WWCD Reasons-Wise Axiom Meta-Schemata ...... 79 2.25 Unacceptable Kenny Axiom Schemata...... 89 2.26 WWCD Variants of Unacceptable Kenny Axiom Schemata (for Intentional Action)...... 90 2.27 WWCD Variants of Unacceptable Kenny Axiom Schemata (Generalized).. 90

3.1 DBWC Normal Semantics: Primitive Deontic Modality ...... 119

xiii 3.2 DBWC Normal Semantics: Discharged Primitive Deontic Modality ...... 120 3.3 DBWC Normal Semantics: Primary Deontic Modalities ...... 121 3.4 DBWC Normal Semantics: Discharged Primary Deontic Modalities ...... 123 3.5 DBWC Normal Semantics: Subsidiary Deontic Modalities ...... 123 3.6 DBWC Normal Semantics: Discharged Subsidiary Deontic Modalities ..... 125 3.7 DBWC Inference Meta-Rules ...... 125 3.8 DBWC Axiom Meta-Schemata ...... 126 3.9 DBWC Normal Semantics: The Evaluative ‘Ought’ ...... 133

4.1 DBWC Justiﬁcation Principle Theorems...... 153 4.2 First Syntactic Argument...... 161 4.3 Second Syntactic Argument...... 162 4.4 A Formal Variant of the Lottery Paradox...... 168 4.5 A Formal Variant of the Preface Paradox...... 170

5.1 Doxastic Voluntarism Objection...... 174 5.2 Isolation Objection...... 177 5.3 No Positive Obligations Objection...... 181 5.4 Schematic Argument for Unhinged Justification...... 199 5.5 Schematic Closure-Based Argument for Justificational Skepticism..... 209 5.6 The DBWC Refutation of Justificational Skepticism...... 212 5.7 Schematic Closure-Based Argument for Knowledge Skepticism...... 214

xiv LIST OF NOMENCLATURE

Notation/Symbol Definition/Meaning/Interpretation , ¨, ¨¨, … Agents p, q, … Propositions or propositional constants Atom A set of atomic formulas, including ⊤ and ⊥ , , , … Well-formed formulas of a formal language Φ The set of all well-formed formulas of a formal language Ψ A set of well-formed formulas of a formal language M Model D Domain (of possible moments ) , ¨, ¨¨, … Possible moments

 Set of all possible histories h, h¨, h¨¨, … Possible histories

Histories Set of all histories passing through the moment Pair Set of all moment/history pairs

 Partition of D (subdomain of possible world-moments) w, w¨, w¨¨, … Possible world-moments

 Set of all possible world-histories ¨ ¨¨ Possible world-histories hw, hw, hw, … Continued on next page. . .

xv xvi

Notation/Symbol Definition/Meaning/Interpretation

Historiesw Set of all world-histories passing through the world-moment w Pair Set of all world-moment/world-history pairs  Partition of D (subdomain of possible mind-moments) m, m¨, m¨¨, … Possible mind-moments

 Set of all possible mind-histories ¨ ¨¨ Possible mind-histories hm, hm, hm, …

Historiesm Set of all mind-histories passing through the mind-moment m Pair Set of all mind-moment/mind-history pairs ⩽ Historical ordering relation over D

 The set of the possible times t, t¨, t¨¨, … Possible times Λ Sortal function operating under some parameterization to sort elements of domain D into contextual subsets , ¨, ¨¨, … Parameterizations of Λ over domain D ℜ Binary accessibility relation mapping elements of a set to other elements of a set

 Neighborhood function mapping elements to a set of neighborhoods

≾r r-reasons-wise ordering relation over the domain

≾v v-value-wise ordering relation over the domain ∗ r-value-wise ordering relation over sets of performative formu- ≾v las ℑ Normal interpretation function mapping propositional constants to elements of domain D

ℑ− Nonnormal interpretation function mapping a subset of well- formed formulas to elements of the domain ⊨ Semantic consequence relation ⊢ Syntactic consequence relation Part I

Introduction CHAPTER 1

ABILITY AND NORMATIVE APPRAISAL

Abstract

I adumbrate my dissertation project.

1.1 Introduction

bility is the fulcrum upon which action and knowledge are leveraged. Action theory A broadly construed is the branch of philosophy that studies action, intention, and the brand of normative appraisal attendant to conation. Epistemology broadly construed is the branch of philosophy that studies knowledge, belief, and the brand of normative appraisal attendant to cognition. Following Timothy Williamson (2000), it is tempting to say that action and knowledge are the central relations between mind and world:

Knowledge and action are the central relations between mind and world. In action, world is adapted to mind. In knowledge, mind is adapted to world. When world is maladapted to mind, there is a residue of desire. When mind is maladapted to world, there is a residue of belief. Desire aspires to action; belief aspires to knowledge. The point of desire is action; the point of belief is knowledge (2000: 1).

Crudely, action is the well-arrangement of world to fit mind and knowledge is the well- arrangement of mind to fit world. Conative powers all aim for the achievement of mind- to-world fit. Cognitive powers all aim for the achievement of world-to-mind fit. So understood, the conative powers possessed by an agent properly aim at action and the cognitive powers possessed by an agent properly aim at knowledge.

2 1.1. Introduction 3

Agents are richly endowed with powers, conative and cognitive, and have the capacity for both action and knowledge, both intention and belief. On my view, an agent is an embodiment of intelligence, where intelligence is a special complex of reasons-responsive powers. In this regard, most human beings number among agents, but are not the only possible agents. Nonhuman animals, groups, institutions, and even software might qualify. Insofar as they are products of an agent’s powers whose end is the adjudication between mind and world, all of action, belief, intention, and knowledge—and indeed many other things—are performances. All are performances in the sense that they are special arrangements arising within, or are issued from, an agent’s intelligent sensitivity to the environment. Factors both intrinsic and extrinsic to the agent contribute to the success or failure of a performance. Action and knowledge—intention and belief—are possible, when they are, because the agent is sufficiently well-adapted for the world as it is; impossible, when they are, because the agent is insufficiently well-adapted for the world as it is. Performativity is the interactivity of powers and reasons, where ‘power’ is the name given to those intra-agent factors, ‘reasons’ the name given to those extra-agent factors, their relation such that powers function to take reasons as inputs to output performances. Apart from being successful or unsuccessful, performances are normatively appraisable. Deontic appraisals are the normative appraisal of performance. When positively appraised, a performance is appropriate, apt, correct, justifiable, permissible, proper, right, or warranted; negatively appraised, inappropriate, inapt, incorrect, unjustifiable, impermissible, improper, wrong, or unwarranted. Roughly, a performance has positive deontic status if, and only if, the performance is the nondeviant product of powers responding to good reasons; negative deontic status if, and only if, the performance is the nondeviant product of powers responding to bad reasons. Deviant or otherwise ill-formed performances are inapt targets of deontic appraisal; they lack any deontic status. So, too, are agents normatively appraisable. Hypological appraisals are the desert- sensitive normative appraisal of agents.1 When positively appraised, an agent deserves approbation, credit, or praise; negatively appraised, an agent deserves disapprobation, criticism, or blame. An agent’s being rational, reasonable, or responsible is evocative of an agent’s having positive hypological status; irrational, unreasonable, or irresponsible evocative of negative hypological status. Roughly, an agent has positive hypological status if, and only if, the agent performs for apparently good reasons; negative hypological status if, and only if, the agent performs for apparently bad reasons. Just as there is a difference between appearance and actuality, there is a difference between the apparent

1 Michael Zimmerman draws the term from the Greek ύπόλογος, meaning “held accountable or liable” (2002: 554). Hypological appraisals are sometimes called responsibility appraisals. Ability and Normative Appraisal 4

and actual quality of an agent’s reasons. The apparent goodness or badness of reasons in virtue of which an agent deserves credit or criticism might be merely apparent. It need not track their reality. In point of fact, hypological appraisals do not track deontic appraisals for fallible agents: it is possible for an agent to deserve credit for an objectively impermissible performance and it is possible for an agent to deserve criticism for an objectively permissible performance. This is because fallible agents do not have privileged access to the actual quality of reasons. Rather, they must make due with mere appearances, which but imperfectly track reality. Such are the thematic ties, as I see them, between abilities, reasons, Deontic appraisals, and hypological appraisals. As will become clear, not everyone agrees. I intend to put hypological appraisals aside. Deontic appraisals are the topic of my dissertation. All deontic appraisals, yes, but justification in particular, and epistemic justification even more specifically. Ultimately, my goal for this dissertation is to defend three theses:

∙ Thesis1: Epistemic justiﬁcation is a deontic modal.

∙ Thesis2: All epistemic modals are a deontic modals.

∙ Thesis3: All deontic modals are teleological.

The ﬁrst thesis is the main object of interest and the other two are subsidiary theses that I hope to make plausible by indirect means. The purpose of this introductory chapter is to explicate and situate my main thesis.

1.2 Normative Appraisals

In this section, I identify and typify the four principal classes of normative appraisal. As far as I can tell, the taxonomy is exhaustive, at least in the sense that any remaining normative statuses can represent compositions of the four principles types. The dialectical aim of this section is to articulate terminology that will help to frame the dissertation project as a whole. There are exactly four sui generis types of normative appraisal: aretaic, axiological, deontic, and hypological. All are distinguishable in terms of target and content. To the best of my knowledge, the classes are completely exhaustive.2 All other normative appraisals are compositions of elements belonging to one or more of the four classes. Aretaic appraisals are the normative appraisal of an agent’s character. Positively appraised, a character is virtuous; negatively appraised, vicious. Individual virtues and vices

2 See Michael Zimmerman (1996, 2002, 2006b) and Ishtiyque Haji (1998, 2002, 2009, 2012, 2014). 1.2. Normative Appraisals 5

are clusters of dispositions contributing to the overall evaluation of an agent’s character. Virtuousness or viciousness might be the accidental product of nature and upbringing or they might be the cultivated product of self-directed education and habituation. All this is to say that aretaic appraisals evaluate character for its virtuous and vicious qualities simpliciter, not its origins, not whether the agent is responsible for their character, not whether virtues and vices are fairly or justly distributed, and not whether character traits are epistemologically, morally, or prudentially relevant. All and only aretaic appraisals target character for virtue and vice content. Axiological appraisals are the normative appraisal of states of affairs. Positively appraised, a state of affairs is good or valuable; negatively appraised, bad, evil, or disvaluable. An axiology is a theory of value; it identifies what is valuable and disvaluable and in virtue of what. The taxa of possible values are complex and beyond the scope of the present project. All and only axiological appraisals target states of affairs for value and disvalue content. Deontic appraisals are the normative appraisal of performance concerning right and wrong. The family of deontic concepts includes the obligatory, permissible, impermissible, omissible, and the optional, but not only these five. Insofar as the performing of a performance is a state of affairs, there is possible overlap between axiological and deontic appraisals. However the two do not have the same extension. First, many states of affairs are not apt targets of deontic appraisal because they are not performances. As such, some valuable states of affairs are not permissible performances and some disvaluable states of affairs are not impermissible performances. Second, some permissible performances are not valuable. Broadly, necessary evils are those cases where all available alternatives unavoidably result in disvalue such that the permissible options realize the least amount of disvalue. Third, some impermissible performances are not disvaluable. Broadly, insufficient goods are those cases where all available alternatives unavoidably result in value but some options are nonetheless impermissible because they are comparatively realize too little value. All and only deontic appraisals target performances for permissibility or impermissibility content. Hypological appraisals are the normative appraisal of agents concerning the desert of credit and criticism. As Ishtiyque Haji (1998) notes, it is important to distinguish an agent’s actual deservingness of credit or criticism from the first-, second-, or third- personal perspective in which one is justified in praising or blaming the agent. Hypological appraisals exclusively concern the former. Deontic appraisals cover whether acts of crediting or criticizing are justifiable for agents. It is in principle possible for it to be unjustifiable for anyone to give an agent what they deserve, especially since that which Ability and Normative Appraisal 6

justifies our crediting or criticizing an agent does not supervene upon that in virtue of which an agent deserves credit or criticism. All and only hypological appraisals target agents for responsibility or irresponsibility content. A helpful mnemonic for distinguishing between normative appraisals is consider their role in traditional normative ethics. Virtue-theoretic accounts define the truth-conditions of deontic appraisals in terms of aretaic appraisals.3 Roughly, the right act is the one a virtuous agent would perform; or, it is the act that best exemplifies the operative virtues. Teleological and value-theoretic accounts define the truth-conditions of deontic appraisals in terms of axiological appraisals.4 Roughly, the right act is the one that optimally or satisfactorily realizes value. Deontologism rejects deontic reductionism and holds that the truth-conditions of deontic appraisals stand for themselves.5 Roughly, the right act is the one an agent has most duty to perform; or, it is the act that best accords with moral law. Many more normative concepts are composite than not. I have already introduced the examples of necessary evil and insufficient good, both of which are constituted by axiological and deontic features. Necessary evil is the permissibly disvaluable. Insuffi- cient good is the impermissibly valuable. Supererogation and suberogation are tripartite compound normative statuses. Paul McNamara (1996a, 1996b, 1996c, 2011a, 2011b) and Terry Horgan and Mark Timmons (2010) argue that supererogatory performances have three constitutive features:

∙ Axiological: The supererogatory thing is better than at least some of its permissible alternatives.

∙ Deontic: The supererogatory thing is optional. ∙ Hypological: In doing what is supererogatory, the agent deserves credit/praise; in refraining from doing what is supererogatory, the agent does not deserve criticism/blame.

By the same token, suberogatory performances have three constitutive features:

∙ Axiological: The suberogatory thing is worse than at least some of its permissible alternatives.

∙ Deontic: The suberogatory thing is optional. ∙ Hypological: In doing what is suberogatory, the agent deserves criticism/blame; in refraining from doing what is supererogatory, the agent does not deserve credit/praise.

3 See Gary Watson (1993), Rosalind Hursthouse (1999) and Michael Slote (2001, 2002). 4 See G. E. Moore (1903, 1912), Fred Feldman (1986), and Michael Zimmerman (1996, 2008). 5 See Immanuel Kant (1788), W. D. Ross (1930), and Christine Korsgaard (1996). 1.3. Knowledge and Epistemic Justiﬁcation 7

I’ll discuss supererogation and suberogation in more detail in later chapters. Presently, my goal is not to classify the possible arrangements of normative compounds. It is merely to note that they enjoy genuine pretheoretic life and are analyzable in terms of the four sui generis classes of normative appraisal.

1.3 Knowledge and Epistemic Justiﬁcation

The topic of my dissertation is epistemic justification. What is epistemic justification? Why does it matter? Well, that’s precisely the crux of the problem. No one can say exactly. Roughly, epistemic justification is the most crucial knowledge-conducive normative status attributable to doxastic attitudes. It is the well-supportedness of belief by good evidence, good reasons, or some such thing that is, paraphrasing Richard Swinburne, “indicative of truth” (2001: 1). Epistemic justification is important at least insofar as knowledge or evidentially well-supported beliefs are important, but maybe it matters for other reasons too. Admittedly, none of this is terribly informative, but little more can be said without gross violations of theoretical neutrality. According to a long and venerable tradition reaching at least as far back as Plato (Theaetetus, 200d–201d), epistemic justification is the prime, indeed only, factor that distinguishes knowledge from mere true belief:

Socrates. The art of the greatest representatives of wisdom—the men called orators and lawyers. These men, I take it, use their art to produce conviction not by teaching people, but by making them judge whatever they themselves choose. Or do you think there are any teachers so clever that within the short time allowed by the clock they can teach adequately the truth of what happened to people who have been robbed or assaulted, in a case where there are no eye-witnesses? Theaetetus. No, I don’t think they possibly could; but they might be able to persuade them. Socrates. And by “persuading them” you mean “causing them to judge”, don’t you? Theaetetus. Of course. Socrates. Then suppose a jury as been justly persuaded of some matter which only an eye-witness could know, and which cannot otherwise be known; suppose that they come to their decision upon hearsay, forming a true judgment: then they have decided the case without knowledge, but, granted they did their job well, being correctly persuaded? Ability and Normative Appraisal 8

Theaetetus. Yes, certainly. Socrates. But, my dear lad, they couldn’t have done that if true judgment is the same thing as knowledge; in that case the best juryman in the world couldn’t form a correct judgment without knowledge. So it seems they must be diﬀerent things. Theaetetus. Oh, yes, Socrates, that’s just what I once heard a man say; I had forgotten, but now it’s coming back to me. He said that it is true judgment with an account that is knowledge; true judgment without an account falls outside knowledge. And he said that the things of which there is no account are not knowable (yes, he actually called them that), while those which have an account are knowable.

True belief is attainable by mere lucky guess. Knowledge requires something more. It requires that the belief is supported by good grounds—something that relevantly favors or probabilifies the content of belief. The aforementioned Platonic passage suggests that knowledge is justified true belief. While it does not account for what justification is, the Platonic orthodoxy at least elegantly describes its functional role as the knowledge- conducive ingredient distinguishing knowledge from mere true belief. Edmund Gettier (1963) exploded Platonic orthodoxy. He, and many others since, showed that justified true belief is not sufficient for knowledge. The functional role played by epistemic justification has since become unclear and, consequently, the prospects of a functional definition dim. The loss of the functional account supplied by Platonic orthodoxy would not be cause for concern were it were supplanted by a general account of what epistemic justification is, but epistemology has made little headway on that front. Quoting William Alston (1985), Paul Silva, Jr. (2015a) summarizes the state of the literature:

Nearly three decades ago, William Alston observed that despite the prominence of epistemic justification epistemological debates “it is usually not at all clear just what an epistemologist means by ‘justified’, just what concept the term is used to express” (1985: 81). Things have, I think, changed little. Many epistemologists proceed as if we all knew just what we were talking about in talking about justification, or at least that further clarification would be of little benefit. This does not necessarily mean epistemologists have been talking past each other, for justification is typically taken to be that normative quality whose presence makes (or at least marks) the difference between unGettierized true belief and knowledge. Although acknowledging this functional role of 1.3. Knowledge and Epistemic Justification 9

justification can help fix the reference of the term ‘justification’, it leaves much to be desired for it tells us nothing about justification’s relation to our inventory of normative statuses (2015a: 1).

About the only thing for which there is anything resembling consensus is the thought that only justified beliefs instantiate knowledge and epistemic justification is a normative appraisal of some kind or another.6 Alvin Goldman, for example, says that ‘justification’ “is an evaluative term, a term of appraisal” (1979: 1). William Alston (1985) agrees:

[‘Justiﬁcation’] is an evaluative concept, in a broad sense in which this is contrasted with “factual”. To say that is justiﬁed in believing that p is to imply that there is something all right, satisfactory, in accord with the way things should be, about the fact that believes that p. It is to accord ’s believing a positive evaluative status (1985: 58).

As does William Lycan (1985):

The key notions of epistemology are normative through and through. ‘Justiﬁca- tion’, ‘warrant’, ‘rationality’, and the like are matters of what one ought or ought not believe. Epistemic obligation and permission seem to be sui generis—in particular, they do not coincide with moral obligation and permission—but they are as fully evaluative as their moral counterparts (1985: 137).

And, again, Alvin Goldman (1986):

[T]erms like ‘justified’ and ‘unjustified’, ‘warranted’ and ‘unwarranted’, ‘well- grounded’ and ‘ill-grounded’, ‘reasonable’ and ‘unreasonable’, ‘rational’ and ‘irrational’, when applied to beliefs and other doxastic attitudes, typically express epistemic evaluations. They are used to grade a belief along some evaluative epistemic dimension (1986: 20). Calling a belief justified implies that it is a proper doxastic attitude. These notions have a strong deontic flavor. . . They are naturally captured in the language of ‘permission’ and ‘prohibition’. . . (1986: 59).

6 In addition to those cited below, see John Dreher (1974), Roderick Firth (1978), Catherine Lowy (1978), Earl Conee (1980), Alvin Goldman (1988), Hilary Kornblith (1983, 1993, 2001), Kent Bach (1985), Mylan Engel, Jr. (1992), Robert Audi (1993, 2001), Robert Fogelin (1994), Linda Zagzebski (1994, 1996, 2003), Richard Fumerton (1995), John Pollock and Joseph Cruz (1999), Susan Haack (2001), Bruce Russell (2001), Matthias Steup (2001, 2003), Richard Swinburne (2001), Wayne Riggs (2002, 2008), John Greco (2003, 2007, 2010), Jonathan Kvanvig (2003), Ernest Sosa (2007, 2011), Jeremy Fantl and Matthew McGrath (2009), Stephen Grimm (2009), and Duncan Pritchard, Alan Millar, and Adrian Haddock (2010), Clayton Littlejohn (2012), Kieran Setiya (2012), Ralph Wedgwood (2012), and Selim Berker (2013a, 2013b). Ability and Normative Appraisal 10

And Roderick Chisholm (1989):

The term ‘justify,’ in its application to a belief, is a term of epistemic appraisal: it is used to say something about the reasonableness of that belief. So, too, are such terms as ‘evident’, ‘gratuitous’, ‘certain’, and ‘probable’. And ‘reasonable’ itself may be a term of epistemic appraisal (1989: 8).

And Alvin Plantinga (1993):

[T]here is obviously something normative or evaluative about warrant. To attribute warrant to a belief is to appraise that belief, and to appraise it favorably; and we use such terms as ‘warranted’, ‘justification’, ‘justified’, and the like as “terms of epistemic appraisal”. To say that a belief is warranted or justified for a person is to evaluate it or him (or both) positively; his holding that belief in his circumstances is right, or proper, or acceptable, or approvable, or up to standard. We evaluate a person’s beliefs (more exactly, her believings) as warranted, or justified, or rational, or reasonable, contrasting them with beliefs that are unwarranted, unjustified, irrational, unreasonable (1993: 3).

And Richard Feldman (2001, 2008):

Our talk about epistemic matters parallels our talk about ethical matters in noteworthy ways. Among the ethical judgments we make are judgments that a person ought to perform a certain action, that someone should not do a certain thing, that people have obligations to act in some ways, that they are permitted or required to do certain things, that they have a right to do one thing and a duty to do another, and that sometimes they deserve praise or blame for what they have done. We make seemingly analogous judgments about beliefs and believers (2001: 77). The evaluations of beliefs that I take to be paradigmatically epistemic depend primarily on the relation of the beliefs to their sources or their bases. It is difficult to find a theoretically neutral way to describe the sort of evaluation I have in mind, but perhaps the following will do. We can assess beliefs in terms of whether they are epistemically proper responses to the information the believer had to go on when forming the belief. No doubt there are difficult questions about how to understand the idea of an epistemically proper response to information and how to specify the information the believer had to go on when forming the belief. Some will interpret the proper response relation in 1.3. Knowledge and Epistemic Justification 11

reliabilist terms while others will favor alternative interpretations. For present purposes, it does not matter which interpretation is adopted. Some may hold that what the person has to go on in forming the belief is limited to those things the person is aware of and knows to be relevant to the content of the belief. Others may think that more falls into what the proper response is a response to. Again, these diﬀerences do not matter for present purposes. Reliabilists, proper functionalists, evidentialists of various stripes, and others, all agree that there is some notion of a proper response to information (or evidence or stimuli), and that paradigmatic epistemic evaluations are about this. A belief is favorably evaluated when it is a proper response and unfavorably evaluated when it is an improper response (2008: 347).

So, too, do many, many others agree that epistemic justification is a positive normative appraisal attributable to doxastic attitudes. After that, almost nothing resembling a general theory of epistemic justification exists in print except for a few scattered, undeveloped suggestions. If we take seriously the thought that epistemic justification is a normative appraisal, what kind exactly? Is it aretaic, axiological, deontic, hypological, or some composition of several? It is immediately obvious that justification is not a species of aretaic or hypological appraisal. Neither aptly targets performances. So, if there is aretaic or hypological content embedded in epistemic justification, it must be because it is a composite normative status. This leaves only the possibility that epistemic justification axiological, deontic, or composite normative appraisal. Epistemology is not the only normative discipline interested in the normative status denoted by justificatory locutions. Normative ethics is interested in moral justification (and cognates). An ethicist might ask: is this act morally justifiable for the agent to perform? Under what conditions are actions morally justifiable? Rational choice is interested in prudential justification (and cognates). A rational choice theorist might ask: is this act prudentially justifiable for the agent to perform? Under what conditions are actions prudentially justifiable? And so forth. Plausibly, epistemic, moral, and prudential justification are all exemplars of a single normative status, justification (‘justifiable’, ‘justified’, and cognates), in principle attributable to any performance. If so, then the core structural features of justification as such is shared across all the relevant normative domains. If justification is a species of axiological appraisal, it is for all; if a species of deontic appraisal, it is for all; if composite, it is for all. I assume as much, anyway. I know of no good reason to suppose otherwise. It is on this basis that I reject the suggestion that epistemic justification is axiological. Neither Ability and Normative Appraisal 12

moral justification nor prudential justification are axiological. Morally horrific acts are in principle justifiable when they are instances of necessary evil. During the World War II, the American Armed Forces ultimately decided to drop two atomic bombs on Japan because they saw no other way to minimize the carnage that would otherwise inevitably ensue from ground invasion. While I doubt that any right-minded person could sensibly argue that the murder of some 200,000 civilians realized an iota of moral value, the horrific act could be justifiable provided that every other option would have resulted in a far greater magnitude of destruction and suffering. Plenty of other examples are possible, both moral and prudential. The general point is that the justificatory status attributable to performances is not tantamount to value and does not require the realization of value. I will return to this point shortly, especially as it pertains to epistemic matters. Wishing to avoid the headache of experimenting with various normative compositions, I will conjecture that epistemic justification is a species of deontic appraisal. In fact, I think all justificatory statuses ascribed to performances (e.g., doings, believings, intendings, knowings) are deontic—and only deontic. By no means am I the first to endorse a deontic conception of epistemic justification, but the so-called deontological conception is associated with sloppiness that I wish to explicitly disavow. Carl Ginet (1975) states the view as follows:

One is justified in being confident that p if, and only if, it is not the case that one ought not to be confident that p: one could not be justly reproached for being confident that p (1975: 27).

In similar fashion, Matthias Steup (2003) describes deontological justiﬁcation as follows:

An act that is morally justified is an act that is morally permissible, an act for which one cannot be justly blamed, or an act the agent was not obliged to refrain from performing. I conceive of epistemic justification in an analogous way. A belief that is epistemically justified is a belief that is epistemically permissible, a belief for which the subject cannot be justly blamed, or a belief the subject is not obliged to drop (2003: 312).

As I have already indicated, the four types of normative appraisals are sui generis and logically independent. Insofar as the deontological conception of justification treats it as a species of deontic appraisal, Ginet, Steup, and many others engaged in the topic, either for or against the view, equivocate between classes of normative appraisal. By endoring a deontic conception, I postulate that the justificatory statuses typifying performances in no way bear any conceptual relation to aretaic, axiology, or hypological 1.4. Justification and Justifiers 13

statuses. In particular, I disavow any purported connection between a belief’s being epistemically justifiable and the agent’s being creditworthy, excusable, praiseworthy, rational, reasonable, responsible, or unworthy of blame or criticism. My project concerns all and only epistemic justification conceptualized as a pure deontic modal. Attempts to appropriate normative concepts beyond this narrowly specified domain shall be regarded as non sequiturs. It is on this basis that I am entitled to ignore much of the existing literature discussing the so-called deontological conception.

1.4 Justiﬁcation and Justiﬁers

In this section, I acknowledge the ambiguity of ‘justification’ and clarify the object of interest. In the course of clarification, I raise some concerns for a recently proposed composite conception of epistemic justification. The purpose of these worries is to help motivate the preference for a deontic conception of epistemic justification. Paul Silva, Jr. (2015a) denies a pure deontic conception. He argues that justification is a composite normative status. In his view, a belief is epistemically justified if, and only if, it is both epistemically permissible and epistemically good. He offers both negative and positive arguments for his thesis. Both arguments hinge upon all of the following theses, which are taken as adequacy desiderata of sorts:

∙ Doxasticism: Justiﬁcation can apply to beliefs.

∙ Comparativism: Justiﬁcation comes in degrees; one can have more or less justiﬁcation to believe that p.

∙ Goodness Entailment: To have justiﬁcation to believe that p is to stand in a valuable position with respect to believing that p, at least to the extent that having justiﬁcation to believe that p entails that believing that p is an epistemically good thing to do.

∙ Permission Entailment: Justiﬁcation is permission-entailing in the sense that has justiﬁcation to believe that p only if it is permissible for to believe that p.

Summarizing, the positive argument is that all rival noncomposite views are false because they fail to satisfy all of the adequacy desiderata. In particular, the deontic conception is false because it fails Comparativism and Goodness Entailment (2015a: 6–7; 18). The positive argument is that the compound deontic-axiological conception is true because it satisﬁes all four adequacy desiderata (2015a: 10–12). I am moved by neither argument. Silva suggests that the compound deontic-axiological conception satisﬁes Comparativism is because goodness is degreed (2015a: 11). But this Ability and Normative Appraisal 14

claim doesn’t follow. Nothing about the concept of goodness necessitates that it is degreed. Every theory of value has a nondegreed counterpart. Binaried hedonism accords moral value 1 all and only to an agent’s being pleased; moral value −1 all and only to an agent’s being in pain. Binaried knowledge primitivism accords epistemic value 1 all and only to an agent’s belief being an instance of knowledge; epistemic value −1 all and only to an agent’s belief failure to instantiate knowledge. Binaried veritism accords epistemic value 1 all and only to true belief; epistemic value −1 all and only to false belief. Generalizing, binaried axiologies do not accord degrees of value. Maybe binaried axiologies are implausible, but that’s beside the point. The issue is whether it follows from the mere fact that a composite deontic-axiological conception invokes goodness that its resultant conception of justification is degreed. The answer is no. As an aside, the composite deontic-axiological conception potentially has undesirable entailments. Monistic knowledge primitivism is at least prima facie as a theory of epistemic value. It can, for instance, be motivated by appeal to the Meno problem.7 But pairing knowledge primitivism with Silva’s conception entails that a belief is justifiable only if it is knowledge.8 Pairing veritism with Silva’s conception entails that a belief is justifiable only if it is true.9 Generalizing, pairing the composite deontic-axiological conception of epistemic justification with any monistic axiology entails that justification is that epistemic value-conferring factor (plus more besides). Pairing it with a pluralistic axiology entails that justification is all the epistemic value-conferring factors (plus more besides). My point is that independently plausible epistemic axiologies have potentially bad entailments when paired with the composite deontic-axiological conception. This is a consequence of the Goodness Entailment. Ultimately, I reject both Comparativism and Goodness Entailment. I think they are mainly motivated by a category mistake conflating justification-conferrers and justification- bearers. ‘Justification’ (and each cognate) is polysemous, equally well denoting that which justifies and that which is justified. Justifiers confer justificatory status upon that which is justified because they are literal good-makers. Very roughly, a belief has the status ‘justifiable’ or ‘unjustifiable’ in virtue of the availability of relevant justifiers that could typically make the belief good from an epistemic point of view; ‘justified’ or ‘unjustified’ in virtue of the appropriate deployment of the relevant justifiers. Justifiers are quantitative, justification proper qualitative. Comparativism is false because justification proper is qualitative. Just as one cannot

7 See Pritchard, Millar, and Haddock (2010) for discussion. 8 See Jonathan Sutton (2007) for a statement and defense of this view. 9 See Clayton Littlejohn (2012) for a statement and defense of this view. 1.4. Justiﬁcation and Justiﬁers 15

be knowier, a belief cannot be justifiedier. Just as one can know better, a belief is more or better justifiable or justified, but only in virtue of the quantity and quality of epistemic grounds that justify. The exact nature of the relation is unclear, but the fact that “one can have more justification while having fewer grounds” is, pace Silva, not inherently problematic (2015a: 7). Goodness Entailing is objectionable on a number of points. First, it is false for moral and prudential justification. Yet epistemic justification has identical structural features. Second, it is potentially problematic for epistemic closure principles. There are a number theories of value such that goodness isn’t closed over entailment, known entailment, or competent deduction. If not, then epistemic justification won’t be closed on any of these theories of value, contrary to consensus. As such, the desideratum robs a theory of its ability to guarantee valid closure principles. Third, it has potentially skeptical consequences. Skeptics purport to show that many of our theoretical beliefs lack any epistemically interesting good-making properties. This is especially salient when considering the lottery puzzle.10 I am inclined toward agreement. But if skeptics are right on this point, then the absence of epistemic goodness is grounds enough to deny justification—and, by implication, knowledge. Fourth, epistemic justification is applicable to doxastic attitudes apart from belief. Withholdings are epistemically justifiable. Yet it is false that justifiable withholdings realize epistemic value. Rather they are justifiable because they relevantly avoid the realization of epistemic disvalue. To repeat, the prima facie plausibility of Silva’s adequacy desiderata is in part motivated by an equivocation between justifiers and justification proper. As I see it, justifiers are axiological entities, justifications deontic entities, and the exact nature of their relation altogether unclear. In the course of my dissertation, I will argue that beliefs can be justified even in the absence of justifiers; that, in other words, a belief can be permissibly held without being epistemically good. I will also argue that epistemically justifiable beliefs will tend to be those that realize epistemic value. The tendency is a possible source of the axiological implicature of justificatory locutions, and if it is, then it could well serve as an error theory for the admitted intuitive plausibility afforded to the Goodness Entailing desideratum. The dialectical upshot is this. Justification proper is the topic of my dissertation. I have no interest in justifiers or the theory thereof, which I take to belong solely to the axiological domain. Nonetheless it is plausible that there is some sort of relation between justifiers and justification proper. But if beliefs are justified in virtue of that which justifies,

10 See Jonathan Vogel (1990) and John Hawthorne (2004) for discussion. I cover this issue in more detail in the ﬁnal chapter. Ability and Normative Appraisal 16

where the former is a deontic notion and the latter an axiological notion, it seems that we have arrived at teleologism, the view that deontic appraisals are deﬁnable from axiological appraisals.

1.5 Teleologism and Deontic Modals

My first, and main, thesis is that epistemic justification is a deontic modal; it is the status of a performance’s being obligatory or permissible from an epistemic point of view. Consequently, a belief is epistemically justifiable if, and only if, the belief is epistemically obligatory or epistemically permissible. Though my present sympathies run in favor of permissibility, I don’t intend to settle between justification-as-obligation or justification- as-permission in this dissertation. I acknowledge that it is not enough for me to merely argue that justification is a deontic modal. In order for the view to be informative, a fully general theory of deontic modals is required. In this sense, I am obliged to espouse a deontic theory. Methodologically, I aim to make the case for deontism by sketching a deontic theory of justification and investigating its benefits. I wish to develop but one fully general deontic theory and pair it with deontism to derive a schematic theory of justification. I want to recognize from the onset that there are many possible ways the project could go from here. I invite anyone who does not share my philosophical persuasion to try the project for themselves. Dialectically, I hope that my attempt may be considered a suitable blueprint for how future research might be directed. I am a teleologist. It is my view that all deontic modals are definable from a special class of axiological appraisals. More specifically, I am student of the Massachusetts school, a family of teleological theories that analyze deontic modalities from the more fundamental notions of ability and goodness. In slogan form: one must do the best one can. Fred Feldman (1975, 1986) presents the foundational framework, but some of his students make interesting contributions to the framework and indeed the school as a whole, including Michael Zimmerman (1996) and Paul McNamara (1996a, 1996b).11 Massachusettsian school is but one among many in a very large field, but I think it is the indisputable champion. I won’t attempt to defend that conviction here. Plenty of ink has already been spent in defense of the Massachusettsian school and everything I would wish to say has already been better articulated by Feldman, Zimmerman, McNamara, and others. I humbly suggest that interested readers consult the originals. For my part, I develop a new Massachusettsian theory of deontic modals named Doing

11 See Chapter2, footnote2 for additional citations. 1.5. Teleologism and Deontic Modals 17

the Best We Can (DBWC) in homage to F. Feldman (1986). DBWC is an enormously fruitful schematic teleological theory of deontic modals. Among other things, epistemic modals are features of the framework. Epistemic justification is a deontic status attributable to a doxastic attitude. Knowledge is modalized justified true belief; or, belief whose justification tracks truth. Both are elements expressly understood through the deontic machinery. In this sense, I take the plausibility of the DBWC framework to indirectly corroborate my second thesis. By developing and defending the framework, my third thesis is indirectly supported. Having said all that, I take my greatest accomplishment to be DBWC itself, not its attendant theory of deontic justification or its relation to the first two theses. DBWC augments and improves Massachusettsian theory in a number of significant and interesting ways. Most deontic theories, formal and substantial, lack anything like a theory of ability or action, and so in principle cannot attach deontic operators to performances. The original Massachusettsian frameworks exhibit this shortcoming and I think it damning. If nothing comporting to performativity is accommodated by a deontic theory, then in no sense is it a genuine deontic theory, because deontic appraisals are the normative appraisal of performance. In fact, the absence of a theory of performativity is the source of at least two additionally related problems. Firstly, in the original Massachusettsian frameworks, deontic modals operate upon true propositions that are abilitively accessible to agents, where the abilitive accessibility relation is a theoretical primitive expressing a weak ‘can do’. It follows that agents can see to the occurrence of any proposition true in any abilitively accessible world. But that’s crazy. Most things true at a possible world fall well beyond any given agent’s ken. It is false that anyone sees to every ⊤, or that 2 + 2 = 4, or that E = mc2, or that the sun rises, or that the radioactive particle decays, or that lottery ticket #355,947,602,111 is the winner, or any number of other things. Performances are special in ways that mere true propositions are not. The upshot is that, absent a theory of performativity, deontic theory cannot properly distinguish between the agent and the world. Secondly, in the original Massachusettsian frameworks, it is possible for agents to have absurd obligations. Failing to distinguish between the agent and the world, it follows that the frameworks predict that the best states of the world are obligatory, even if their occurrence is purely accidental or far beyond any agent’s ken. By holding an eligible lottery ticket, it is obligatory for an agent to win the lottery because the best accessible worlds are just those where the agent wins. By having able hands, it is obligatory for an agent to open a safe or vault they don’t know how to open if its opening results in a far better world. And so, too, does it follow that all lotteryesque states of the world are obligatory for an Ability and Normative Appraisal 18

agent to bring about if the agent would relevantly enjoy far more value than otherwise possible, even if it isn’t in any way up to the agent that the world turns out that way and in no way could the agent know how to make the world that way. The upshot is that, absent a theory of performativity, deontic theory cannot properly distinguish between idyllic states of the world and the things actually requirable of an agent. DBWC is an extension of a novel schematic theory of ability. My deontic theory obviates these all these theoretical hazards because performativity is given pride of place.

1.6 Structure of the Dissertation

The goal of this dissertation is to address a lacuna. Epistemic justification is a central topic in epistemology, but the discipline lacks a general theory of justification proper. There are plenty of views about the nature and structure of justifiers, but very little about what in general it is for a belief—or, indeed, any performance—to be justified or justifiable proper, epistemically or otherwise. The absence of general theory is the lacuna; it is my problem set. My contribution to the discipline is a bridge across the gap. During the course of constructing the bridge, I respond to very few objections. The very fact of the lacuna explains the dearth of objections worthy of consideration. The substance of the dissertation is carved up into four chapters. Chapter2 presents What We Can Do (WWCD), a formal theory—a modal logic—of ability, action, belief, intention, knowledge, and reasons founded upon counterpossible branching tree structures. In broad outline, its job is to provide a solid foundation for understanding the scope and limits of performativity. Prepare yourself, reader; it’s a slog. Chapter3 covers DBWC, the deontic extension of WWCD. It is the crown chapter that defines a wide array of deontic modals from special value-wise orderings over the domain of possible states of world. It inherits all the complexity of WWCD. In broad outline, the job of the chapter is to provide an abstract theory for understanding the array of deontic modals applicable in different normative domains, including epistemology and ethics. Perhaps its most interesting feature is that it mathematically regiments the relationship between ability, performativity, deontic modals, and reasons-wise modals. Chapter4 sketches the schematic DBWC theory of deontic justification. More specifically, it distinguishes between potential and actual justification under two competing deontic conceptions, namely justification-as-permission and justification-as-obligation. The job of the chapter is to highlight the main points of the formalism and apply them to a number of issues. The theory validates a slew of justification principles, including versions of single- and multi-premise closure. It also falls out of the framework that justification 1.6. Structure of the Dissertation 19

requires ability. A belief cannot be epistemically justified, for instance, unless the agent is able to have the belief. Deontic conflicts are ruled out. As such, moral dilemmas and rational disagreement are impossible by the theory’s lights. So, too, are the lottery and preface paradoxes deflated. Chapter5 elucidates and defends the schematic DBWC theory of epistemic justification. It instantiates the general theory sketched in the previous chapter in the epistemological domain. I call upon the full complement of theoretical resources enabled by the DBWC framework to rebut the three most popular objections to deontism. I also disarm some counterfactual worries about the DBWC theory of knowledge. But the real heart of the chapter is the defense of justificationally unhinged belief—viz., permissibly held beliefs that fail to realize any epistemic value. Justificationally unhinged belief is philosophically important and for two reasons. First, it falsifies the letter of all existing theories of epistemic justification. Second, it grounds a refutation of skepticism. Skeptics argue, rightly to my mind, our ordinary beliefs entail antiskeptical commitments that lack any of the common sense good-making properties enjoyed by our ordinary beliefs. But by accepting the possibility of unhinged justification (and ipso facto denying the requirement that only good doxastic attitudes are justifiable), the skeptic’s prime contentions can be conceded without threat to the possibility of justified belief or knowledge. Part II

Formal Foundations CHAPTER 2

WHAT WE CAN DO

Abstract

I develop a general formal theory of performativity called What We Can Do (WWCD) using counterpossible branching tree structures. WWCD is a polymodal framework accounting for action, belief, intention, knowledge, reasons, and the abilities for all. The philosophical upshot is that a robust theory of performativity can be built out of relatively modest theoretical primitives, namely powers and reasons.

2.1 Introduction

gents are intelligent things endowed with an array of powers, both cognitive and A conative, that enable them to navigate the world that they inhabit. Human beings are in this sense agents, but it is doubtful that only humans are agents. Cognitive powers aim for the adaptation of mind to fit world, conative powers the adaptation of world to fit mind. Belief is the manifestation of cognitive powers to represent the world as it is, intention the manifestation of conative powers to represent the world as it is wished to be. Knowledge is the paradigmatic exemplar of cognitive achievement, the special class of belief that succeeds in its aspirations. Intentional action is the paradigmatic exemplar of conative achievement, a special class of intention that succeeds in its aspirations. The theory of ability is the common root from which action theory and epistemology sprout. To unify the disciplines, we must return to the source. In this chapter, I lay out a unifying formal theory—a modal logic—of ability, action, belief, intention, knowledge, and reasons. All are conceptualized through the lens of an agent’s suite of powers, both cognitive and conative. Because interdisciplinary unification under a single formalism

21 What We Can Do 22

is a diﬃcult task, I am obliged to recruit the assistance of philosophical theory, both substantive and formal. My main sources of insight and inspiration are as follows:

∙ The substantive literature pertaining to ability and know how.1 I borrow much from Alfred Mele (2003, 2005) in particular.

∙ The Massachusetts school, a family of teleological theories that analyze deontic modalities from the more fundamental notions of ability and goodness using a Chisholmian methodology.2 In slogan form: one must do the best one can. I am most inﬂuenced by Fred Feldman (1986), Michael Zimmerman (1996), and Paul McNamara (2011a).

∙ Various praxeological logics, especially stit theory as developed by Nuel Belnap, Michael Perloﬀ, and Ming Xu (2001) and John Horty (2001).3

My aim is to fuse all these elements together into a general praxeo-abilitive theory. In short, I attempt to capture the truth-conditions of performativity using counterpossible branching tree structures, especially as it relates to believings, doings, intendings, and knowings. The result is a sophisticated framework called What We Can Do (WWCD). The structure of this chapter is as follows. In Section 2.2, I highlight the phenomena of interest and sketch a coarse-grained taxonomy of quasi-theoreticized praxeo-abilitive concepts. In Section 2.3, I motivate two adequacy desiderata for any praxeo-abilitive logic worth its salt. In Section 2.4, I expound the philosophical foundations, formal semantics, and axiomatization for the WWCD framework. In Section 2.5, I argue that WWCD satisﬁes the adequacy desiderata. Finally, in Section 2.6, I conclude by summarizing the ﬁndings of the chapter.

1 For more on the ‘can’ of ability, see J. L. Austin (1961), A. M. Honoré (1964), Anthony Kenny (1975, 1976), Angelika Kratzer (1977, 1981, 2012), Fred Feldman (1975, 1986), David Lewis (1979, 1979), Peter van Inwagen (1983), Mark Brown (1988, 1990, 1992), Tomis Kapitan (1996), Michael Zimmerman (1996), Ann Whittle (2010), Berislav Marušić (2012), and John Maier (2014a, 2014b). The abilitive ‘can’ sometimes denotes know how. For more on procedural knowledge, see Gilbert Ryle (1945, 1949), Jane Roland (1958), David Carr (1979, 1981), David Lewis (1990), Jason Stanley and Timothy Williamson (2001), Katherine Hawley (2003), Alva Noë (2005), Jeremy Fantl (2009, 2012, 2014), Eprhraim Glick (2011, 2012), and Jason Stanley (2011), and Ralph Wedgwood (2013). 2 For the foundational texts, see Fred Feldman (1975, 1986). For revisions or variations, see Fred Feldman (1990, 1993, 1997, 1998, 2000, 2004, 2006, 2012), Ishtiyaque Haji (1998, 2002, 2009, 2012, 2013), Paul McNamara (1996a, 1996b, 1996c, 2000, 2004, 2011a, 2011b), and Michael Zimmerman (1995, 1996, 1997, 2001, 2002, 2004, 2006c, 2006a, 2008). For important texts exemplifying the Chisholmian method, see Roderick Chisholm (1964, 1974, 1989). 3 See especially G. H. von Wright (1951b, 1963), Stig Kanger (1972), Ingmar Pörn (1974, 1977, 1989), Krister Segerberg (1973, 1992), Mark Brown (1988, 1990, 1992), Nuel Belnap (1991), Filipe Santos and Jose Carmo (1996), Dag Elgesem (1997), Lennart Åqvist (1999), Paul McNamara (2000, 2004), Nuel Belnap, Michael Perloﬀ, and Ming Xu (2001), and John Horty (2001). 2.2. A Structural Taxonomy of Praxeo-Abilitives 23

2.2 A Structural Taxonomy of Praxeo-Abilitives

In this section, I offer a coarse-grained 12-fold taxonomy of quasi-theoreticized praxeo- abilitive concepts. The concepts are quasi-theoretical in the sense that they are my attempts to lift something philosophically substantive out of the sludge of messy intuitions evoked by examples. They are not entirely pretheoretic because they are not handmaidens to raw intuition and represent effort toward theory. They are not entirely theoretic because they are the skeletal frame upon which substantive theory must hang. My method is to appeal to examples to illustrate a number of logically independent conceptual distinctions. The quasi-theoretical concepts are generated from the interaction of these distinctions. Ultimately, the objects of interest fit the praxeo-abilitive compound form ‘can ’, where the blank can be filled out by any of the praxeological modals ‘be’, ‘believe’, ‘do’, ‘intend’, ‘intentionally do’, ‘know’, and so forth. The canonical praxeo-abilitive form is as follows:

Agent can at time t that at time t¨.

The compounds is built up out of two components, namely the relevant abilitive auxiliary and the relevant praxeological auxiliary. The former takes the latter as its propositional object and the latter takes a proposition—or, rather, a well-formed formula—as its object. This structure can be made visually more perspicuous:

Abilitive Index ©®ª Agent can at time t that at time t¨. «¯¬ Praxeological Index

The abilitive index of a praxeo-abilitive compound functions to ascribe some abilitive sense of ‘can’—whether ability or mere abilitive consistency—to the agent. The praxeological index is the compliment of the abilitive index and functions to describe the nature of the agent’s powers at stake. If cognitive powers, then ‘believe’ or ‘know’; if conative powers, then ‘do’ or ‘intend’. Broadly, a praxeo-abilitive molecular compound describes a way the agent can be. If, for example, the proposition that the window is broken is taken as the complement of the praxeological index, then the praxeological index taken alone says that the agent (believes/brings it about/intends/knows) that the window is broken and the whole praxeo-abilitive compound says that the agent can that the window is broken. It is literally true that something is believable, doable, intendable, or knowable for an agent if, and only if, the agent has the relevant ability to believe, do, intend, or know. What We Can Do 24

2.2.1 Capabilities, General Abilities, and Speciﬁc Abilities

There is a distinction between capabilities, general abilities, and specific abilities. To the best of my knowledge, J. L. Austin (1961) and A. M. Honoré (1964) are the first to draw the distinction between general and specific abilities in its most current form. The threefold distinction is perhaps easiest to see by appeal to examples:

Example 2.1. Janine is prematurely born baby suﬀering from blindness as a result of cortical visual impairment. After a thorough medical examination, it is found that Janine is completely neurotypical and will develop into a healthy person. Though she is temporarily blind because her visual systems are presently underdeveloped, and she therefore lacks any ability to see in the present instant, she has the capability to see because her innate visual powers are intact and will soon come into their own.

Example 2.2. Frédérick is a virtuoso pianist. One day he boards an airplane, and there is no piano aboard the plane. Though Frédérick is, in a general sense, able to play the piano because he retains his prodigious skill, he is, in a speciﬁc sense, unable to play the piano because he lacks any actual opportunity to play while aboard the plane.

Example 2.3. Dana owns an extremely reliable home safe. Its dial runs from 1 to 100 and requires an ordered sequence of four digits to open. Dana knows how to open the safe in general because she knows the combination and, moreover, can easily input the combination now because she is standing next to it (and nothing will interrupt her if she tries).

In all of the above examples, the agent has the relevant capability, but only Janine has a capability absent any corresponding general ability or specific ability. Capabilities are the weakest abilitive notion that holds fixed only the agent’s suite of powers and ignores considerations about the agent’s environment. Capabilities are defined primarily through the abilitive index. Every abilitive operator is defined by appeal to a domain of quantification. Roughly, an agent can perform something just in case the agent performs that thing in some of the relevant moments. Capabilities quantify over all abilitively accessible moments. It is false that Janine manifests her visual powers in any possible moment temporally co-occurring with the present, but there are accessible future moments where her visual powers are manifested. These future moments are those in which her organs have developed enough to allow her to see. Frédérick and Dana both have the relevant general abilities, but only Frédérick has a general ability absent any corresponding specific ability. General abilities are a middling abilitive notion that holds fixed the agent’s suite of powers as well as the temporal index 2.2. A Structural Taxonomy of Praxeo-Abilitives 25

corresponding to the agent’s present. The only thing that stops Frédérick from playing a piano is the absence of any local opportunity—he, more specifically, lacks a piano to play. As before, general abilities are defined primarily through the abilitive index, quantifying over all and only temporally co-occurring abilitively accessible moments. In a word, an agent has a general ability just in case they manifest the relevant powers in a possible moment constitutive of a hypothetical opportunity. Were a piano present and he so inclined to play, Frédérick would play the piano. Dana has the specific ability to open the safe. She has both the general ability to open the safe and a local opportunity to manifest that ability. Specific abilities are the most restrictive abilitive notion that holds fixed the agent’s suite of powers as well as the prevailing circumstances of the agent’s present. Frédérick lacks the specific ability not because he doesn’t have the skills, but because he lacks any local opportunity to play the piano. Dana has everything she needs (in terms of both skill and environment) and so has the specific ability to open the safe. As twice before, specific abilities are defined primarily through the abilitive index, quantifying over all and only nearby temporally co-occurring abilitively accessible moments. In a word, an agent has a specific ability just in case they manifest the relevant powers in a possible moment constitutive of a local opportunity. Were she so inclined to open the safe, Dana would open the safe. These three senses of ability are logically related. Every specific ability implies some corresponding general ability, and every general ability implies some corresponding capability. The converse of all these implications fail. Capability does not imply general ability, and general ability does not imply specific ability.

2.2.2 Simple and Competent Abilities

Mele (2003) persuasively argues for the distinction between simple, intentional, freedom- level, ensurance-level, and promise-level abilities to do things. My complaint is not that these are not legitimate abilitive notions, but that they cut across several conceptually independent distinctions. Mele doesn’t purport to oﬀer a general taxonomy, but that is precisely the aim of this section. All this is to indicate to the reader that I look to Mele for insight, but intend to do violence to the lines he has drawn. There is a distinction between simple and what I shall call competent ability. The diﬀerence is perhaps easiest to illustrate by appeal to examples:

Example 2.4. Yvonne is working class poor who tries to make an honest living as a waitress. One night, late after work, she is spending time with her friend who impulsively plays lottery. On a whim, Yvonne decides to buy a ticket too. As it turns out, Yvonne What We Can Do 26

becomes the next lottery winner when the numbers on her ticket are called.

Example 2.5. Bill is at a baseball game. During the seventh-inning stretch, a random seat is called to the ﬁeld to play a game. If the participant can hit a home run before they are struck out, they win a million dollar prize. As it so happens, Bill’s seat is called and he is invited to play the game. He is a truly awful player and has never managed to hit a single ball in his life, but miraculously makes the once-in-a-lifetime hit on the very ﬁrst pitch. He wins the prize by scoring a home run.

Example 2.6. Joanna is at the same baseball game as Bill and her seat is called right after Bill’s and she is invited to play the game. Joanna is an excellent baseball player, arguably better than anyone living, but hitting a home run is still a tall order. Even worse, a strong opposing wind just blew in that’s sure to rob the ball of much of its forward momentum. Joanna manages to hit several foul balls before she ﬁnally makes the fateful hit. Despite the wind, she wins the prize by scoring a home run.

Example 2.7. Ted is a high school student sitting attentively at his desk while the teacher takes attendance. When his name is called, he dutifully raises his hand and loudly declares, “Here!” He has always done this and is one of the very few students in his distract who has never missed a single day of school.

In all of the above examples, the agent has the relevant simple ability. Yvonne has the simple ability to win the lottery. Bill and Joanna each have the simple ability to hit the ball and indeed the simple ability to hit a home run. Ted has the simple ability to raise his hand. Simple abilities comport to the “ordinary sense of ‘able’ according to which agents are able to do whatever they do. In this sense of ‘able’, an agent’s having A-ed at a time is conceptually sufficient for her having been able to A then” (Mele 2003: 447–448). Mele frames the description in terms of doings, but the notion of a simple performance is capacious, including beings, believings, intendings, and knowings. It is false that Yvonne does anything to make herself a lottery winner, but she is a winner nonetheless. Ordinary testimonial knowledge is simple in this sense because it lacks the modal robustness constitutive of competent knowledge.4 Simple abilities are defined primarily through the praxeological index; that is, a simple ability is any ability filling out the abilitive index that takes as its object a simple praxeological operator. Every praxeological operator is defined by appeal to a domain of quantification. Roughly, an agent is a certain way just in case something is true of the agent in all of the relevant possible moments; and, similarly, an agent does something just

4 Compare with Jennifer Lackey (2007). 2.2. A Structural Taxonomy of Praxeo-Abilitives 27

in case something is true because of the agent in all of the relevant abilitive possibilities. Simple praxeological modals quantify all and only over those possible moments in which the agent is, believes, does, intends, et cetera, that thing. If Yvonne had a one in a million chance of winning the lottery, there are at least a million possible moments in the domain to which she has abilitive access, at least one for each possible lottery ticket number. The praxeological modal for Yvonne’s simply being such that she wins the lottery quantifies all and only over those possibilities at which her number is called. The praxeological operators for Bill’s and Joanna’s simply doing such that they hit home runs quantifies all and only over those abilitively possible moments at which the ball sails well beyond the field; and, the operator for Ted’s simply doing such that he raises his hand quantifies all and only those abilitively possible moments at which his hand is raised. Competent ability is simple ability and more besides. As before, competent abilities are defined primarily through the praxeological index; that is, a competent ability is any ability that takes as its object a competent praxeological operator. Competent praxeological modals quantify over a larger portion of the domain than their simple counterparts. Which parts and much exactly is likely a matter of context and remains an open question. Whatever the details, competent ability is indicative of expertise—it is the sort of ability had by masters but lacked by amateurs. Let the domain be parameterized by some context, and it is clear that Yvonne lacks the competent ability to win the lottery and that Bill lacks the competent ability to hit the ball. These agents lack the relevant competent abilities because it is false that they succeed in all of the relevant abilitively possible moments.5 In point of fact, they fail in nearly all the abilitively possible moments. By contrast, Joanna might lack the competent ability to hit a home run, but she doesn’t lack the competent ability to hit the ball. Ted has the competent ability to raise his hand. Both succeed in all of the relevantly parameterized abilitively possible moments. If, for example, the relevant possibilities are only those in which the agent tries under normal conditions, then an ability is competent when the agent succeeds in all possible moments where the agent tries and the conditions are normal.6 The logical relation between these two kinds of ability is, I hope, evident. Competent ability implies simple ability (because competent praxeological modals imply simple

5 This is a crude simpliﬁcation that some might deem objectionably strict. It might be instead suggested that, roughly, an agent has a competent ability to be or do something just in case the agent is successful in an appropriate proportion of the relevant possibilities. If, for example, the magic proportion in this case is 9∕10, then competent ability requires that an agent is successful in 90% of the relevant possibilities. In truth, this accords well enough with what I have said. Parameterize the domain with the magic proportion such that we deﬁne some number of nth percentile subsets of the domain. Competent ability is success at every possible moment belonging to one of these nth percentile subsets. 6 Compare with Ernest Sosa (2015), especially the discussion of the SSS structure of competences. What We Can Do 28

praxeological modals), but simple ability does not imply competent ability.

2.2.3 Nonperformative and Performative Abilities

Everything I’ve said thus far to distinguish some of the various species of ability and action fails to do justice to agents (qua embodiments of intelligence). Though it is an abuse of language, rocks and other inanimate objects can be said to have capabilities, general abilities, and specific abilities as well as simple and competent abilities. Glass is fragile and fragility is associated with what can be called the competent ability to break. A glass can be said to have the general simple ability to not shatter if it could be pushed to the ground and fail to shatter. A broken glass, in turn, can be said to have manifested its specific competent ability to shatter when it falls to the ground and nondeviantly shatters. My point is that the substance of these distinctions could just as well be captured with the vocabulary of dispositional powers. Though I count this a happy thing, it does raise important questions. Where does intelligence fit in? What distinguishes an ability proper from the sort of dispositional powers attributable to nonagents like rocks and shards of glass? Plausibly, an ability proper is performative. Insofar as an agent is an endowment of intelligence, and intelligence is just some sophisticated complex of reasons-responsive powers, agency is constituted by a complex of reasons-responsive powers. A performance proper is any activity or passivity outputted by a reasons-responsive power. The difference between nonperformative abilities and performative abilities is the difference between, for example, mere beings or mere doings and beings-for-reasons or doings-for-reasons. Under the current regime, mere beings, mere doings, and all other mere manifestations of powers are not inherently performative, which is to say that an agent’s reasons do not play a role in the truth-conditions of the relevant praxeological modal. Glass is merely such that it is fragile. It cannot have reasons. Janine is merely such that she is a lottery winner. It false that her winning is the manifestation of some reasons-responsive power that she exercises to win. Bill merely does such that he hits a home run. It is false that his hitting the home run is the manifestion of some reasons-responsive power that he exercises to hit the ball. I have not said that Janine lacks reasons to win the lottery or that Bill lacks reasons to hit the ball. Maybe they do, maybe they don’t. Rather, I have said that their reasons have not played the appropriate role in the explanation of their successes. Mere beings and mere doings are mere performances in the sense that they are unconditioned on any reasons. Broadly, nonperformative praxeological modals are unconditioned on reasons had by an agent. In contrast, beings-for-reasons and doings-for-reasons are performances proper. A 2.2. A Structural Taxonomy of Praxeo-Abilitives 29

performance proper is a performance-for-reasons. A performative ability is an ability to properly perform. When an agent forms a particular belief as a result of the evidence that the agent has, the agent is a certain way—namely, in having a certain belief—for reasons. When an agent decides to do something after a course of deliberation about the pros and cons, the agent does something—namely, make a certain decision—for reasons. So understood, only creatures endowed with powers to respond to reasons can have performative abilities. Performances proper require reasons because they are an agent’s response to reasons. Broadly, performative praxeological modals are conditioned on reasons had by an agent. Applying the intuitive distinction, nonperformative abilities are deﬁned primarily through the praxeological index; that is, a nonperformative ability is any ability ﬁlling out the abilitive index that takes as its object a nonperformative praxeological operator. A performative ability takes a performative praxeological operator as its object. A praxeological operator is performative just in case it conditions upon some of the agent’s reasons; otherwise, it is nonperformative. Summing the logical relations, performative ability implies nonperformative ability (because performative praxeological modals imply nonperformative praxeological modals). Obviously, being-for-reasons has as a trivial consequence being and doing-for-reasons has as a trivial consequence doing. However, the converse implications fail. Nonperformative ability does not imply performative ability (because nonperformative praxeological modals don’t imply performative praxeological modals).

2.2.4 The Structural Taxonomy

The logical space is characterized by the interaction of these distinctions. I employ a tabular method, where each distinction arrayed on a table and the number of resulting possible positions are counted. Table 2.1 displays the twelve possible positions for each praxeological modal and therefore the maximum possible praxeo-abilitive compounds for each ‘can ’ construct. Figure 2.1 arranges this information hierarchically.

Table 2.1: Possible Praxeo-Abilitive Compounds

— Nonperformative — — Performative — Simple Competent Simple Competent Capability 1 4 7 10 General Ability 2 5 8 11 Specific Ability 3 6 9 12 What We Can Do 30 Capability General Ability Simple Specific Ability Nonperformative Capability ∗ Note: Competent General ahdarw niaemtra implication. material indicate arrows Dashed Ability iue2.1: Figure rxoAiiieMdlCompounds Modal Praxeo-Abilitive Specific Ability rxoAiiieHierarchy Praxeo-Abilitive Capability General Ability Simple Specific Ability Performative Capability Competent General Ability Specific Ability 2.3. Adequacy Desiderata for Praxeo-Abilitive Logics 31

2.3 Adequacy Desiderata for Praxeo-Abilitive Logics

In this section, I postulate and motivate two important desiderata for any philosophically adequate praxeo-abilitive logic. The joint satisfaction of the desiderata is a necessary, but not suﬃcient, condition for theoretical adequacy. To be clear, my goal is not to evaluate the merits of competing abilitive logics, nor do I intend to expend much ink to situate WWCD among them. Nevertheless I aim to make plausible the suggestion that, at least to the best of my knowledge, WWCD alone satisﬁes the adequacy desiderata.

2.3.1 Mele’s Constraint

The 12-fold taxonomy of praxeo-abilitive molecular constructions suggests an important desideratum for an adequate logic of ability:

∙ Mele’s Constraint: An adequate logic of ability must be able to characterize and distinguish the twelve possible interpretations for each applicable praxeo-abilitive molecular compound.

The praxeo-abilitive molecular compounds of present interest are actionability (‘can do’), believability (‘can believe’), intendability (‘can intend’), and knowability (‘can know’), but there might be others worth including. The desideratum is dubbed Mele’s Constraint in recognition of the present influence of Mele’s work. Because there are genuine and important differences between the various kinds of abilitive and praxeological modals, especially when compounded into a multimodal molecule, an adequate praxeo-abilitive logic respects the differences. All things being equal, then, a praxeo-abilitive logic is inadequate to the extent that it fails to satisfy Mele’s Constraint. In my view, Mele’s Constraint effectively rules out all the competition. There is a lacuna that WWCD aims to rectify in the philosophical logic literature, so it might be informative to at least gesture in the direction of the lacuna. The treatment of ability varies wildly among logicians. Some authors appeal to a single unanalyzed normal possibility operator to represent some praxeo-abilitive compound (usually a morally interesting version of ‘can do’).7 Others use a single but obviously unacceptable normal possibility operator. Examples run the gamut. Walter Carnielli and Marcelo Coniglio (2014) and John Horty (2014) represent ability with alethic possibility.8

7 For examples of this variety of sin, see Anthony Kenny (1975, 1976) and Lou Goble (2009). Kenny’s sin is somewhat pardonable because he argues against the possibility of an adequate praxeo-abilitive logic. 8 These authors are not explicitly concerned with the logic of ability, but they do claim to represent some version of what I shall call Kant’s Law, the principle stating that obligation to do something implies What We Can Do 32

Dale Jacquette (1991) represents ability with nomic possibility. There is no need to pause to cast aspersions at any such treatment; the faults are plain enough. Some logicians correctly analyze ability ascriptions as multimodal compounds, but still appeal to an unacceptable normal possibility operator to represent ability. Nuel Belnap, Michael Perloff, and Ming Xu (2001) and John Horty (2001) are perhaps the most famous examples. In both cases, they use a stit action operator for ‘do’ and a historical possibility operator for ‘can’. This treatment faces at least two independent difficulties. The first issue is that historical possibility is a bad proxy for ability: it is both too inclusive and too exclusive. Too inclusive because some things are historically possible but not within an agent’s power (at least for competent abilities). Too exclusive because some things are within an agent’s power but not historically possible (at least for capabilities and general abilities). The second issue is that the entire stit framework is founded upon indeterministic semantics. While the formalism is not strictly speaking indeterministic, the assumption of indeterminism plays a central role in the theory of action and ability.9 However, there is no good reason why ascribing the ability to be causally responsible for something should entail indeterminism. After all, inanimate objects have such abilities too. Yet this is what the paradigmatic stit analysis of action and ability entails. To be clear, my complaint is that the theory of ability should be as metaphysically neutral as possible. I’ll say more about metaphysical neutrality in the next section. Fortunately, there better existing treatments of ability. Mark Brown (1992) and Paul McNamara (2000) likewise correctly analyze ‘can do’ as a multimodal compound, where ‘do’ is denoted by some action operator and ‘can’ is denoted by an ability operator roughly corresponding to its being within the agent’s power. Dag Elgesem (1997) and Wayne Wobcke (1998) offer special single operator treatments that are similarly excellent.10 It is especially happy that Elgesem and Wobcke embed a notion of opportunity in their analyses of ability. As far as I can tell, and though each is not without its faults, these four treatments rank among the best modal logics of ability. While I reject a number of the axiom schemata validated in each of the aforementioned systems, I wish instead to register a general complaint. It is that none have the theoretical resources to respect any of the quasi-theoretic distinctions set out earlier. As evidenced by

ability to do that thing, whose formal counterpart roughly states that deontic necessity implies abilitive possibility. These authors represent the consequent of this deontic principle with an alethic possibility operator or, equivalently, by noting consistency among the relevant class of well-formed formulas. This is a categorically mistaken representation of the principle. 9 See footnote 13 for details. 10 Brown (1988, 1990) oﬀers a nonnormal single operator treatment for abilities. In the later cited paper, Brown shows that this is logically equivalent to multimodal compounds of normal operators. 2.3. Adequacy Desiderata for Praxeo-Abilitive Logics 33

their own words, Kenny and Brown are exclusively interested in competent ‘can do’:

To say that I am able to hit the bullseye at dart is not merely to say that I can try and may succeed, but to say that my success is (at least) reliable and (perhaps) reproducible. Kenny holds that “abilities are inherently general; there are no genuine abilities which are abilities to do things only on one particular occasion” (1975: 135). Thus Kenny holds out for reproducibility. This may seem like a strong constraint. Even if opportunity only knocks once, I may be able to act on it, and may be culpable for doing so, or for failing to do so. But, whether or not we disagree with Kenny about this, we must at least hold that nothing will count as a (morally relevant) ability unless it is reliable. Chance accomplishments do not establish morally relevant abilities. There are such things as accidents, happy and otherwise, for which no one is held responsible (Brown 1988: 1–2).

While McNamara, Elgesem, and Wobcke develop interestingly nuanced formalisms, they all ultimately fall prey to the complaint that the focus is exclusively upon ‘can do’ without distinguishing between simple and competent ability. From the perspective of the quest for a general praxeo-abilitive logic, the problems only multiply from here. There is no hint of any other praxeo-abilitive molecular compound in any of these systems. Nor is there anything in any of these frameworks to distinguish between nonperformative or performative abilities despite the fact that it is clear that these authors aim to capture something very much akin to performative abilities. I leave it to the reader to investigate each of these systems to observe the role that reasons had by the agent play in the truth- conditions of any of the praxeo-abilitive compounds. Expect disappointment. In sum, I know of no framework that satisﬁes Mele’s Constraint. As a consequence, I know of no logic with the requisite expressive power to felicitously characterize the intuitive data. A perfunctory survey of the action theory, moral responsibility, ethics, and epistemology literatures shows that there is demand for a general theory of ability.

2.3.2 Kenny’s Constraint

Kenny (1975, 1976) famously argues that a modal logic of ability is impossible. Though Kenny is demonstrably mistaken, it is usually conceded by logicians—and in this I agree— that there are unacceptable axiom schemata for any modal logic of ability.

Let ⧆ abbreviate the multimodal praxeo-abilitive ‘can do’ compound, where the

formula ⧆ means that the agent is able to intentionally bring it about that . Kenny contends that the following should not be theorems in any praxeo-abilitive logic: What We Can Do 34

Table 2.2: Unacceptable Kenny Axiom Schemata

Axiom Name Axiom Schema

4 ⧆ ⧆ ⧆ → ⧆

T ⧆ → ⧆

C ⧆ ⧆ ( ∨ ) → ( ⧆ ∨ ⧆ )

Schema 4 ⧆ translates to the claim that if the agent is able to intentionally bring it about that the agent is able to intentionally bring it about that , then the agent is able to intentionally bring it about that ; or, if the agent can acquire the ability to see to it that , then the agent can see to it that . Here is what Kenny says against the schema:

An interpretation of [4 ⧆ ] on the lines suggested would be ‘If I can bring it about that I can bring it about that I am speaking German, then I can bring it about that I am speaking German’ or, equivalently, ‘If I can acquire the ability to speak German, I can speak German’. This is clearly false. If, when applying for a post in a German department, I am asked whether I can speak German, it would hardly be proper for me to reply “yes”, starting from the premise that I can acquire the ability to speak German (say by attending courses for three

years) and reasoning with the aid of [4 ⧆ ] and modus ponens. Hence [4 ⧆ ] ought not to be a law of the logic of ability (1976: 213).

Extrapolating, I take Kenny to mean that there is a difference between capabilities, general abilities, and potential abilities. Capabilities are exercisable powers. General abilities are capabilities exercisable in hypothetical opportunities. Potental abilities are higher-order general abilities to have or acquire lower-order general abilities. The counterexample is intended to show the difference between potential abilities and general abilities. While I think the lesson is sound, Kenny’s actual counterexamples fail because Kenny incorrectly identifies the relevant temporal indices. Luckily, tweaked cases can be easily produced. Consider a rephrased version of the canonical ‘can do’ form:

can at time t bring it about that at time t¨.

In the rephrased form, is the propositional object of the praxeo-abilitive compound. Correctly embedded, potential ability ascriptions have the following form:

can at time t bring it about that ( can at time t¨ bring it about that at time t¨¨).

Though temporal indices are annoyingly multiplied, they can be safely dropped when context makes them clear. Consider the following pair of sentences, where all the temporal indices are ﬁxed to now: 2.3. Adequacy Desiderata for Praxeo-Abilitive Logics 35

Kenny can now bring it about that Kenny speaks German now.

Kenny can now bring it about that (Kenny can now bring it about that Kenny speaks German now).

A genuine counterexample to 4 ⧆ is a case in Kenny has the potential ability but lacks the corresponding general ability. Here are two such cases:

Example 2.8. Kenny applies for a job in the German department, where the appointment requires the general ability to speak German. He cannot utter a single syllable of German, but God owes him a favor. Being omnipotent, God can instantaneously grant Kenny the general ability to speak German and would happily do so if Kenny asked Him to do such a thing. Though Kenny now lacks the general ability to speak German now, he now has the potential to speak German now because he can beneﬁt from a miracle at whim. Example 2.9. Kenny applies for a job in the German department, where the appointment requires the general ability to speak German. He cannot utter a single syllable of German, but he has a magic pill. If consumed, the pill instantaneously rewrites the subject’s cognitive architecture in such a way so as to impart artiﬁcial memories of several years of immersive German lessons. Though Kenny now lacks the general ability to speak German now, he now has the potential to speak German now because he has the magic pill and can ingest it at whim.

As variations on a theme, Example 3.8 and Example 3.9 suggest that 4 ⧆ fails because, as it is for every compound praxeo-abilitive notion, it is possible to merely possess a potential ability; that is, it is possible for an agent to have a potential ability without its being exercised or manifested so as to acquire the corresponding general ability. It

seems, then, that 4 ⧆ is tantamount to the claim that every potential ability is manifested such that the agent has the corresponding general ability, which is patently absurd. To be clear, the problem pertains to the manifested/unmanifested distinction, a distinction that applies to every praxeo-abilitive notion. Consequently, 4 should not be a theorem for any praxeo-abilitive logic for any praxeo-abilitive modality.

Schema T ⧆ translates to the claim that if is true, then the agent is able to see to it that ; or, whatever is the case is such that it is within the agent’s power. Here is what Kenny says against the schema:

A hopeless darts player may, once in a lifetime, hit the bull, but be unable to repeat the performance because he does not have the ability to hit the bull. I What We Can Do 36

cannot spell ‘seize’: I am never sure whether it is an exception to the rule about ‘i’ before ‘e’; I just guess, and ﬁfty times out of a hundred I get it right. On

each such occasion we have a counterexample to [T ⧆ ]: it is the case that I am spelling ‘seize’ correctly but it is not the case that I can spell ‘seize’ correctly (1976: 214).

I have no objections. T ⧆ is tantamount to the claim that whatever is the case is such that the agent is able to intentionally bring it about that it occurs, which is absurd. There is a diﬀerence between what is actual and what the agent is able to do. Further examples push the point. It is the case that it is the case that E = mc2, and it is the case that the sun rises, and it is the case (for some particle) that the radioactive particle decays, but no one is able to be an agent or a subject of any of these things. All except the last are examples of facts inexorably true for anyone. By deﬁnition, the inexorable rules out the possession of any ability with respect to it. The last is an example of a fact incidentally true for anyone. The problem with T ⧆ , then, is that it makes it impossible to distinguish between agent-independent facts and agent-dependent facts. Since agent-independent facts (e.g., inexorable truths) are possible, T ⧆ must be false. Consequently, T should not be a theorem of any praxeo-abilitive logic for any praxeo-abilitive modality.

Finally, schema C ⧆ translates to the claim that ability distributes over disjunction; that is, if the agent is able to intentionally bring it about that ( ∨ ), then the agent is able to intentionally bring it about that or the agent is able to intentionally bring it about that . Here is what Kenny says against the schema:

If we are careful in interpreting [C ⧆ ] we see that it does not express a logical law. Given a pack of cards, I have the ability to pick out on request a card which is either black or red; but I don’t have the ability to pick out a red card on request nor the ability to pick out a black card on request. That is to say, the following [. . . ] is true:

I can bring it about that either I am picking a red or I am picking a black

but the following [. . . ] is false:

Either I can bring it about that I am picking a red or I can bring it about that I am picking a black.

Similar counterexamples can be constructed in connection with any other discriminatory skill (e.g., one may have suﬃcient skill at darts to be quite sure 2.3. Adequacy Desiderata for Praxeo-Abilitive Logics 37

of hitting the board, and yet not be at all sure of obeying either the command “Hit the top half of the dartboard” or the command “Hit the bottom half of the dartboard”) (1976: 215–216).

I take Kenny to mean that there are acts such that the act can be given a number of logically equivalent disjunctive descriptions, and that the agent can possess sufficient skill to count as being able to perform the disjunctive act as a whole without being so skillful as to count as being able to ensure of any particular member of the disjunction that it occurs. For example, what it is to hit a dart board at all is to hit either its top half or its bottom half; or, to hit either its top quarter, right quarter, bottom quarter, or left quarter; et cetera. Moreover, what it is to pick a card from a deck at all is to pick either a red card or a black card; or, to pick either a club, diamond, heart, or spade; et cetera. Every ability, amateurish or masterful, is only so discriminating. On a sufficiently fine-grained description of a disjunctive act, not even the expert is able to ensure of any particular

member of the disjunction that it occurs. However, C ⧆ is tantamount to the claim that, on any description of a disjunctive act, if the agent is able to perform the act as a whole, then the agent is able to ensure that some particular disjunct occurs, which is absurd. Kenny can easily and reliably bring it about that he picks a card from the deck, but it is doubtful that he can easily and reliably bring it about that he specifically picks the Queen of Hearts (or any one of unique 52 cards in the deck). His success is ultimately a matter of luck. Consequently, M should not be a theorem of any praxeo-abilitive logic for any competent praxeo-abilitive modality. These reflections can be briefly summarized as the following desideratum:

∙ Kenny’s Constraint: An adequate logic of ability must not have axiom schemata 4 or T as theorems for any praxeo-abilitive modal compound, and it must not have axiom schema C for any competent praxeo-abilitive modal compound.

The desideratum is dubbed Kenny’s Constraint for obvious reasons. All things being equal, a praxeo-abilitive logic is inadequate to the extent that it fails to satisfy Kenny’s Constraint. What We Can Do 38

2.4 The WWCD Framework

WWCD is a modal logic of ability and performance founded upon branching tree structures. In this section, I present WWCD’s foundational theory of world and specify WWCD’s frames, models, semantics, and syntax. I deﬁne an array of modal operators designed to approximate a spectrum of intuitive ability and inability concepts.

2.4.1 WWCD Foundations: Theory of World Agents are embedded in the world, sometimes being enabled and other times being disabled by the world. Following this natural thought, I found the formal theory of ability upon the formal theory of the world. The formal theory of world that I ultimately settle upon is a branching tree framework. Given what the world is like at a moment, how many physically possible futures are there? As observed by Peter van Inwagen (1983), the answer to this question depends upon whether the world is deterministic or indeterministic.

Determinism . . . is the thesis that there is at any instant exactly one physically possible future. There must, of course, be at least one physically possible future; if there is more than one, if at some instant there are two or more ways in which the world could go on, then indeterminism is true (1983: 3).

More precisely, determinism is the thesis that all the laws of nature plus all the facts about the universe at moment in time entail all the facts about the universe for every moment of history. Indeterminism is the denial of determinism. It is the thesis that there exists at least one fact about the universe true at some moment in history such that it is not entailed by the conjunction of the laws and the past. Is the world deterministic or indeterministic? While an important and interesting question, both for its own right and its implications, the answer is ultimately irrelevant for the general theory of ability: agents have powers of some kind regardless of determinism or indeterminism. If certain powers either require or preclude determinism, then the eﬀects of determinism on the expression of ability should be highlighted in a pairwise study of agents in deterministic settings and their counterparts in indeterministic settings. My point is that the general theory of ability should be developed within a framework that is consistent with both determinism and indeterminism. The demand for metaphysical neutrality is a fundamental selection criterion for a theory of world. If the theory of world cannot adequately represent both determinism and indeterminism, then it fails as an adequate foundation for the theory of ability. 2.4. The WWCD Framework 39

I recognize that there are many ways to proceed from here. My selection criterion does not pick out a unique theory of world. I will try the experiment of building a theory of ability up from one possible foundation and leave its evaluation to others. One popular program for researching agency is stit11 theory, which is founded upon a logic of branching time.12 The theory of branching time is a philosophical reinterpretation of branching tree structures, where branching trees represent indeterminism. In fact, some of the stit operators are deﬁned in such a way as to require indeterminism. And while the pioneers of stit theory tend to locate indeterminism at the core of the philosophical enterprise, I think it important to observe that branching tree structures are strictly speaking consistent with both determinism and indeterminism.13 Allow me to explain.

11 The acronym ‘stit’ stands for ‘sees to it that’. The canonical form of a stit formula is:

[ stit: ], translating to the claim that agent sees to it that . There is a plurality of different stit operators. 12 Nuel Belnap, Michael Perloff, and Ming Xu (2001) has become the locus classicus of contemporary stit theory, but Nuel Belnap and Michael Perloff (1988), Nuel Belnap (1992), John Horty and Nuel Belnap (1995), and John Horty (2001) all make important contributions. Arthur Prior (1967) and Richmond Thomason (1970, 1984) are credited in these works for developing the theory of branching time upon which stit theory is founded. 13 Compare with Belnap et. al. (2001: 203–209). Summing the flavor of the formalism, and the background commitments that guide them, Belnap. et. al. have this to say:

[W]e are not determinists, even though the denial of determinism is not a postulate of this book. But more than that, on the theory oﬀered here, if anyone could ever see to anything, then determinism is false. So even though we do not lay down indeterminism as a postulate, since we believe that sometimes people have choices, we are indeterminists. Accordingly we think that any theory (of anything) should be compatible with at least a little indeterminism (2001: 204).

Belnap et. al. define three stit operators. The achievement stit and the deliberative stit both require indeterminism, but the Chellas stit doesn’t. However, pride of place is given to the deliberative stit. It is for this reason that Belnap et. al. endorse an agency incompatibilism akin to that of Helen Steward (2012). Agency incompatibilism is the view that agency requires indeterminism. It entails that sentences that ascribe agency, or describe actions, likewise require indeterminism. In a word, all agentive constructions are quite literally false if determinism is true. By implication, persons embedded in derterministic environments cannot in any sense be ascribed agency. I find agency incompatibilism implausible. It is troubling that linguistic competence could somehow hinge upon esoteric metaphysics. Yet agency incompatibilism entails that everyone is radically mistaken when they deploy ordinary agentives (e.g., “He made dinner,” “She hit the ball,” “They built a bridge”) in deterministic contexts. It is no less troubling that basic proficiency with natural language agentives suffices for a proof of indeterminism. By thanking someone for making dinner, and complimenting them on the excellence of the meal, it is in no way mysterious that I—correctly—ascribe to them the action of having made dinner. (Many times I have said, “Thanks for making dinner! It was amazing!” And many times have I heard in reply the implicit admission of agency, “You’re welcome! I’m so glad you enjoyed it.”) Nevertheless I don’t, and I shouldn’t, take myself, or my agreeing interlocutors, to thereby demonstrate, implicitly or explicitly, the falsity of determinism. In sum, I find objectionable the idea that ordinary agency depend on matters so far removed from the tests of everyday life as to make agency metaphysically exotic in ways totally unlike any other human What We Can Do 40

Let ℒBT be the language of branching trees extending the language of propositional logic ℒ.14 The set of all atoms, Atom, is composed of propositional constants, ⊤ (tautology), and ⊥ (contradiction). All other well-formed formulas are deﬁned recursively.

ℒBT ∶= Atom | ( → ) | □ | ⊡ | ℙ | F | S

Besides the propositional constants and Booleans molecules of ℒ, the language ℒBT has ﬁve tense modalities, respectively, for omnipresent tense, counterfactual present tense, past tense, future tense, and settledness. The formulas □, ℙ, F , and S respectively read that is always true, is counterfactually true, was true, will be true, and is settled true. The ﬁrst modality approximates alethic necessity and the last approximates determinacy. More of these details shortly.

Definition 2.4.1. A branching tree frame is an ordered set

F = ⟨D, ⩽⟩ where each element is deﬁned as follows:

∙ D = {, ¨, ¨¨, …} is the nonempty domain of all possible moments. A possible moment is a coarse-grained point describing a way the world as a whole might be.

∙ ⩽ is a partial temporal ordering over D. The irreﬂexive dual of ⩽ is <. Both are temporal ordering relations representing the ﬂow of history.

The concept of a history plays a central role in branching tree structures. Every history, h, is a set of moments that are temporally ordered representing the natural unfolding of events over time. The course of history h is represented by the ⩽-wise ordering of moments ∈ h. Let  = {h, h¨, h¨¨, …} be the set of all histories.

Definition 2.4.2. A history, h, is a maximal nonstrict totally ordered subset of D. The following conditions hold for all histories h ⊆ D: ∙ Subset: h ⊆ D. ∙ Nonstrict Total Ordering: h is ordered such that it is reﬂexive, transitive, asymmetrical, and comparable.

performance. I do not, for instance, take on deep metaphysical commitments by praising schoolchildren for what they know. The same should go for ascribing action (qua causal responsibility), especially in ordinary contexts. 14 See AppendixB for more about language of propositional logic ℒ. 2.4. The WWCD Framework 41

∙ Maximality: There is no h¨ ⊆ D such that h ⊊ h¨ and h¨ is a nonstrict totally ordered subset of D.

If the set Histories = {h ∶ ∈ h} denotes the set of histories passing through , then

determinism entails that Histories is a singleton and indeterminism entails that Histories contains at least two histories. It is possible to augment branching tree structures with what I’ll call the theory of times. The theory of times represents the intuitive idea that every moments has a temporal index corresponding to the time at which the moment occurs. Every time, t, is an equivalence class, a set whose members are moments originating from any number of different histories are contemporaneous. The set of all times,  = {t, t¨, t¨¨, …}, is an ordered partition of the domain such that every possible moment is a member of exactly one t ∈  and all times are strictly totally ordered by temporal sequence. While Nuel Belnap, Michael Perloff, and Ming Xu (2001) avail themselves to a thusly augmented branching tree frames to define one stit operator, they have reservations.15 It is important to these theorists that it be made clear that the theory of times is a generally inessential primitive of branching tree structures and particularly inessential for stit theory as a whole. However, I presently include the theory of times because an adequate theory ability requires of its foundational theory of world that it incorporates a theory of times. The aim of providing an adequate foundation for a theory of ability suggests a second amendment. The distinctions between abilities sometimes requires quantification over smaller or larger swaths of modal space contained in a time. Whereas capabilities quantify over moments across many times and general abilities quantify over moments at a single time, specific abilities quantify over a subset of moments at a single time, namely moments that are sufficiently similar with respect to the actual opportunities enjoyed by the agent at the relevant moment in the relevant history. The upshot is that branching tree structures need a mechanism for sorting possible moments into proper subsets of the domain, histories, or times in order to achieve the variable domain of quantification over which the spectrum of intuitive ability concepts range.

Definition 2.4.3. A branching tree frame is an ordered set

F = ⟨D, ⩽,  , Λ⟩ where each element is deﬁned as follows:

15 See (2001: 35–36; 140–141; 194–196) for the postulation and use times, which they call the theory of instants. See (2001: 195–196) for the motivational worry about justifying times and see (2001: 197) for the conceptual worry about whether “one can make sense of ’same time’ across diﬀerent worlds”. What We Can Do 42

∙ D = {, ¨, ¨¨, …} is the nonempty domain of all possible moments. A possible moment is a coarse-grained point describing a way the world as a whole might be.

∙ ⩽ is a partial temporal ordering over D. The irreﬂexive dual of ⩽ is <. Both are temporal ordering relations representing the ﬂow of history.

∙  = {t, t¨, t¨¨, …} is a strictly totally ordered partition of the domain into equivalence classes mapping the natural numbers. Every ∈ D is a member of exactly one time, t ∈  , and every time is a nonempty set of contemporaneous moments such that any two nonidentical , ¨ ∈ t are members of nonidentical histories. If ≈ is an equivalence ≈ ¨ ¨ relation, the notation  means that and occur at the same time, which is true if , ¨ ∈ t for some t ∈  .

¨ ¨¨ ∙ Λ = {, , , …} is a primitive sortal function operating under some parametrization,

, of the domain that maps moments/history pairs into sets . Every represents a set

of facts constitutive of a context such that (, h) ∈ if, and only if, (, h) agrees with

respect to the facts represented by . Every ⊆ D is an equivalence class containing all and only the possible moment/history pairs satisfying . If ≈ is an equivalence relation, ¨ ¨ ¨ ¨ the notation (, h) ≈ ( , h ) means that (, h) and ( , h ) are equally -wise similar, which ¨ ¨ is true if (, h), ( , h ) ∈ for some ∈ Λ.

Every parameterization of the domain, , is some set of facts or factors held constant in virtue of which the similarity of moments is assessed; it’s the stuﬀ that makes up a context of utterance. The sortal function, Λ, sorts moment/history pairs into equivalence classes according to whether is satisﬁed or not.

Figure 2.2: Determinism vs. Indeterminism (in Branching Tree Structures)

h1 h2 h3 h4 h5 h1 h2 h3 h4 h5 t3 t3

t2 t2 2 2

t1 t1 1 1

(a) determinstic history (b) indeterministic history 2.4. The WWCD Framework 43

Branching tree structures are so-named because they result in treelike depictions of possible histories. Figure 2.2 depicts deterministic and indeterministic histories using branching tree structures. Each node represents a possible moment belonging to the

domain. The y-axis represents the different times t1, t2, t3, … ∈  and a moment’s temporal index—its membership in a time—is represented horizontally. The dotted lines between nodes represents the upward flow of time connecting moments into a history. Possible histories are labeled at the terminus of historically connected moments. Deterministic histories consist of a single branch extending upwardly from root to tip, past to future. Indeterministic histories consist of many branches extending upwardly from the single root of a shared past. Subfigure 2.3(a) depicts five histories in a deterministic setting, which is why e.g. Histories = Histories = {h }. Subfigure 2.3(b) depicts five histories with a 1 2 1 shared past in an indeterministic setting, which is why e.g. Histories = {h , h , h , h , h } 1 1 2 3 4 5 but Histories = {h , h , h }. 2 1 2 3

Definition 2.4.4. A branching tree model is an ordered set

M = ⟨F, ℑ⟩ where each element is deﬁned as follows:

∙ F = ⟨D, ⩽,  , Λ⟩ is a branching tree frame. ∙ ℑ ∶ Atom × Pair ↦ {1, 0} is an interpretation function assigning truth-values to atoms at moment/history pairs, for all moment/history pairs belonging to P air ⊆ D ×  (where

(, h) ∈ Pair only if ∈ h) and all atoms, Atom, belonging to the language ℒBT .

A branching tree model is a branching tree frame plus an interpretation function. In branching tree models, formulas are evaluated at moment/history pairs, which is to say that the truth and falsity are double indexed to moments and histories. The double index requirement for alethic evaluation suggests a sensible modification to the definitions of satisfiability, validity at a point, and validity in a frame.

Definition 2.4.5. A well-formed formula ∈ ℒBT is satisﬁable at a moment/history pair, (, h), in a branching tree model, M, if M, (, h) ⊨ for some (, h) ∈ Pair.

Definition 2.4.6. A well-formed formula ∈ ℒBT is valid at a moment/history pair, (, h), in a branching tree frame, F, denoted F, (, h) ⊨ , if is satisﬁed at (, h) in every model, M, based on F. What We Can Do 44

Definition 2.4.7. A well-formed formula ∈ ℒBT is valid in a branching tree frame, F, denoted F ⊨ , if is valid at every moment/history pair (, h) ∈ F.

With these deﬁnitions in mind, Table 2.3 displays the semantics for atoms and Booleans, which behave as expected at moment/history pairs.

Table 2.3: Branching Tree Semantics: Atoms and Booleans

Operator Definition M, (, h) ⊨ ℑ(, (, h)) = 1 M, (, h) ⊨ ¬ ℑ(, (, h)) = 0 M, (, h) ⊨ ∨ M, (, h) ⊨ or M, (, h) ⊨ M, (, h) ⊨ ∧ M, (, h) ⊨ and M, (, h) ⊨ M, (, h) ⊨ → M, (, h) ⊨ ¬ or M, (, h) ⊨ M, (, h) ⊨ ↔ M, (, h) ⊨ → and M, (, h) ⊨ →

As I previously mentioned, ℒBT contains ﬁve modalities for tense, the semantics of which are displayed on Table 2.4. Intuitively, □ is a tenseless (or: omnipresent) modality, where the formula □ is true at a moment/history pair, (, h), if, and only if, is true at every moment/history pair, (¨, h¨), belonging to Pair. It can just as well be read as alethic necessity. ⊡ is a counterfactual present tense modality inspired by the notion of counterfactual necessity of David Lewis (1973). The formula ⊡ is true at a moment/history pair, (, h), if, and only if, is true at every (¨, h¨) ∈ Pair such that and ¨ belong to the same similarity class (given parameterization ). The idea is that ⊡ is localized necessity; or, truth across all proximal moment/history pairs. ℙ is the past tense modality, where the formula ℙ is true at a moment/history pair, (, h), if, and only if, is true at some moment (¨, h) occurring before . F is the future tense modality, where the formula F is true at (, h) if, and only if, is true at some ¨ ∈ h occurring after . Finally, S is the settledness modality, where S corresponds to the idea that no matter how history unfolds relative to the relevant moment, is true. The formula S is true at the (, h) if, and only if, is true at every moment/history pair, (, h¨), such that occurs in h¨.

Table 2.4: Branching Tree Semantics: Tense Modalities

Operator Definition M, (, h) ⊨ □ M, (¨, h¨) ⊨ for all (¨, h¨) ∈ Pair ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ M, (, h) ⊨ ⊡ M, ( , h ) ⊨ for all ( , h ) ∈ Pair such that ( , h ) ≈ ( , h ) M, (, h) ⊨ ℙ M, (¨, h) ⊨ for some ¨ ∈ h such that ¨ < M, (, h) ⊨ F M, (¨, h) ⊨ for some ¨ ∈ h such that < ¨ ¨ ¨ M, (, h) ⊨ S M, (, h ) ⊨ for all h ∈ Histories 2.4. The WWCD Framework 45

Philosophically speaking, the settledness modality provides yet another fruitful way for distinguishing between deterministic and indeterministic histories. The thrust of determinism is that the laws and the past completely settle all the facts for all times. Oﬃcially, if h is a deterministic history, then all truths are settled true and all falsehoods are settled false at every moment ∈ h. By contrast, the thrust of indeterminism is that the laws and the past don’t completely settle all the facts for all times. If h is an indeterministic history, then there exists at least one formula neither settled true nor settled false at some moment ∈ h.

The language ℒBT is closed under a number of inference rules and contains a number of axiom schemata. To avoid the unnecessary multiplication of tables, let ■ be a symbolic variable ranging over all of the tense modalities □, ⊡, ℙ, F , and S such that ■ can equally understood to mean any of □, ⊡, ℙ, F , or S. The convention is admittedly somewhat misleading, and I must beg for indulgence, because the past and future tense operators, ℙ and F , are far closer to notions of possibility rather than notions of necessity.

Keeping the shorthand in mind, Table 2.5 displays some inference rules that close ℒBT . Table 2.5: Branching Tree Inference Rules

Rule Name Rule Schema

TC 1, … , n ⊢ , for any tautological consequence of 1, … , n RN■ If ⊢ , then ⊢ ■ RM■ If ⊢ → , then ⊢ ■ → ■ RR■ If ⊢ ( ∧ ) → , then ⊢ ■( ∧ ) → ■ RE■ If ⊢ ↔ , then ⊢ ■ ↔ ■

Two brief remarks of clariﬁcation. The rule TC is a generalization of all propositional inference rules.16 In English, it can be interpreted to mean that the conclusion is provable

from the premises 1, … , n (provided, obviously, that is a tautological consequence of

1, … , n). RN■ is the rule of necessitation stating that if is provable from the empty set of premises, then ■ is likewise provable.

Clariﬁcations aside, Table 2.6 displays some shared axiom schemata contained in ℒBT

and Table 2.7 displays some unshared axiom schemata contained in ℒBT . An important observation. The validity of 4⊡ marks at point of contrast with Lewisian similarity semantics because the analogous version of axiom schema 4 fails.17 It fails for Lewisian semantics because proximity is not transitive: if moment ¨ is nearby moment

16 See Chellas (1980: 15–16; 45–46) for discussion. 17 See (1973: 26–31; 48–56) for the Lewisian account of counterfactuals. Let ∼ be a binary proximity relation between moments such that the notation ∼ ¨ means that ¨ is a nearby . Roughly, if ⊡ is counterfactual necessity, ⊡ is true at moment if, and only if, is true at every moment, ¨, such that ∼ ¨. What We Can Do 46

Table 2.6: Branching Tree Axiom Schemata (Shared)

Axiom Name Axiom Schema N■ ■⊤ M■ ■( ∧ ) → (■ ∧ ■ ) C■ (■ ∧ ■ ) → ■( ∧ ) R■ ■( ∧ ) ↔ (■ ∧ ■ ) K■ ■( → ) → (■ → ■ ) T■ ■ →

Table 2.7: Branching Tree Axiom Schemata (Unshared)

Axiom Name Axiom Schema 4□ □ → □□ 4⊡ ⊡ → ⊡⊡ 4ℙF ℙ → Fℙ 4Fℙ F → ℙF 4S S → SS

, and moment ¨¨ is nearby moment ¨, it does not thereby follow that ¨¨ is nearby .18 However, 4⊡ is validity in branching tree structures crucially because proximity is treated as an equivalence class relative to a parameterization of the domain and is therefore ¨ ¨ ¨ ¨ ¨¨ ¨¨ ¨¨ ¨¨ transitive: if (, h) ≈ ( , h ) and ( , h ) ≈ ( , h ), then (, h) ≈ ( , h ). Intuitively,

moments are members of if, and only if, all the relevant formulas constitutive of are ¨ ¨ true at the moment/history pair. If (, h) ≈ ( , h ), they agree on all the facts constitutive ¨ ¨ of ; and if (, h) ≈ ( , h ), they too agree on all the facts constitutive of ; so, (, h) and ¨¨ ¨¨ ¨¨ ¨¨ ( , h ) must likewise agree on all the facts constitutive of , in which case (, h) ≈ ( , h ). By way of conclusion, I think it worth recapitulating all the important formalism constitutive of the theory of branching tree structures. All the crucial theoretical cogs that work in tandem are as follows:

∙ F = ⟨D, ⩽,  , Λ⟩ is a branching tree frame, where D is the domain of possible moments, ⩽ is the temporal ordering relation over D,  = {t, t¨, t¨¨, …} is the ordered partition of D into times such that every time, t, is a primitive nonempty equivalence class, and ¨ ¨¨ Λ = {, , , …} is a sortal function mapping moments/history pairs into sets

representative of -wise similarity such that every is a nonempty equivalence class.

∙ M = ⟨F, ℑ⟩ is a branching tree model, where F is a branching tree frame and ℑ is

18 Let ∼ be a binary proximity relation between moments such that the notation ∼ ¨ means that ¨ is a nearby . Very roughly, the Lewisian countermodel to ⊡ → ⊡⊡ is the case in which ⊡ is true at because ∈ , ¨ and ∼ ¨, but ⊡ is false at ¨ because ∉ ¨¨ and ¨ ∼ ¨¨ and ∼ ¨¨. 2.4. The WWCD Framework 47

an interpretation function assigning truth-values to atoms at moment/history pairs belonging to the set Pair. ∙ h is a maximal nonstrict totally ordered subset of D called a history.

∙  = {h, h¨, h¨¨, …} is the set of all histories.

∙ Histories = {h ∶ ∈ h} is the set of all histories of which is an element.

My overall point is that branching tree structures are not inherently metaphysically biased. Both determinism and indeterminism can be felicitously represented. While it is not a unique advantage of tree structures, it is an important one. To be clear, branching tree structures are the foundation for my theory of ability. I have no principled defense of my theoretical choice apart from the fact that it adequately serves my philosophical needs and it is already a well-studied formalism. I simultaneously lack any principled objection to other possible foundations for a theory of ability provided that they are likewise metaphysically neutral.

2.4.2 WWCD Assumptions, Frames, and Models

WWCD is a language extending ℒBT , which is itself an extension of ℒ. In addition to all

the elements of ℒBT , all of the following are well-formed WWCD formulas:

x Φ ∶= … | ▣ | [] | [ ] | [] | [ ] | ■

ℒBT has ﬁve primitive modal operators. WWCD adds to that sum six more, resulting in the total of eleven primitive modal operators. The last is a reasons-wise modality expressing what it is that reasons favor. Reasons-wise modals generally operate upon praxeological modals or formulas built up from praxeological compounds. (■x is a variable that ranges over praxeological modals. I’ll discuss it in more detail later.)

Definition 2.4.8. A WWCD frame is an ordered set

F = ⟨D, , , ⩽,  , Λ, ℜ, i, … , n, ≾r⟩ extending a branching tree frame, where each element is deﬁned as follows:

∙ D = {, ¨, ¨¨, …} is the nonempty domain of all possible moments, both normal and nonnormal.

∙  = {w, w¨, w¨¨, …} is the partition of the domain containing all normal moments called world-moments. A possible world-moment is a possible way the world as a whole could in fact be. What We Can Do 48

∙  = D −  = {m, m¨, m¨¨, …} is the partition of the domain containing all nonnormal moments called mind-moments. A possible mind-moment is a possible way that the world could be imagined or represented, either cognitively or informationally, either exhaustively or only partially.

∙ ⩽ is a partial ordering relation over D such that each of  and  is independently partially ordered. The irreﬂexive dual of ⩽ is <. Both are temporal ordering relations representing the ﬂow of history.

¨ ¨¨ ∙ Λ = {, , , …} is a primitive sortal function operating under some parametrization,

, of the domain that maps moments/history pairs into sets . Every represents a set

of facts constitutive of a context such that (, h) ∈ if, and only if, (, h) agrees with

∙ ℜ ⊆ Pair × Pair is a binary reﬂexive accessibility relation that relates one possible world-moment/world-history pair to another possible world-moment/world-history pair. The notation (w, h)ℜ(w¨, h¨) expresses that (w¨, h¨) is accessible from (w, h), which is true if ((w, h), (w¨, h¨)) ∈ ℜ. Every agent is assigned an abilitive accessibility relation for the total suite of powers had by the agent.

∙  ∶ D ↦ P (P (Pair)) is a neighborhood function mapping elements of Pair into a set of

set of subsets of Pair. Every agent is assigned a set of neighborhood functions i, … , n

for the various subsuites of powers i, … , n had by the agent. j(, h) is the set of all subsuite j powers neighborhoods centered on the moment/history pair (, h).

∙ about is a nifty neighborhood function representing the subsuite of powers essential for an agent’s being subject to things.

∙ assent is a neighborhood function representing the subsuite of powers essential for an agent’s having beliefs about things. 2.4. The WWCD Framework 49

∙ cause is a consistent T-constrained quasiﬁlter neighborhood function representing the subsuite of powers essential for an agent’s being causally responsible for things.

∙ intend is a neighborhood function representing the subsuite of powers essential for an agent’s having intentions to do things.

∙ ≾r is a partial normative ordering relation over Pair such that each of Pair and Pair

are nonstrictly totally ordered. The irreﬂexive dual of ≾r is ≺r. Both are normative

ordering relations representing the overall normative weight. Every ≾r-wise ordering over Pair is indexed to an agent, some set of normative criteria, r, constitutive of reasons, and a moment/history pair.

Philosophically speaking, WWCD innovates branching tree structures by adding agents to the theory of world. As I envision them, agents are deeply imperfect, both cognitively and informationally, and it is this imperfection that is the ultimate motivation for many theoretical inclusions. WWCD is a counterpossible framework.19 In branching tree structures, the domain is made up of normal moments. In WWCD, the domain is made up of both normal and nonnormal moments. The domain is partitioned by interpretation: normal moments are invoked to represent the ways the world could in fact be and nonnormal moments are invoked to represent the ways an agent could mentally model the world. I call normal moments ‘world-moments’ because they are possible world states and nonnormal moments ‘mind-moments’ because they are possible mind states. Whereas D is the domain of all possible moments,  is the subdomain of all world-moments and  is the subdomain is all possible mind-moments. At bottom, mind-moments provide an elegant means for the formalism to approximate the cognitive limitations that creatures like us actually face. The inclusion of nonnormal moments has cascading consequences. I’ll cover the consequences as they become germane, but the discussion some of these consequences will have to wait until WWCD models are deﬁned.

19 Normal moments are both consistent and maximal, whereas nonnormal moments need neither be consistent nor maximal. Saul Kripke (1963, 1965) distinguishes between the two and provides model theory for normal and nonnormal modal systems. Normal modal frameworks are often unsuitable for studying nonideal agents. Jaakko Hintikka (1962) is the locus classicus normal modal framework for epistemic and doxastic logic. Hintikka’s original framework has been roundly criticized for the implication that the agents in the system are logically omniscient: they believe/know all the logical consequences of what they believe/know. Obviously no human being is logically omniscient. Nonnormal systems are appealing because they oﬀer better representations of creatures like us. See Hintikka (1975), Veikko Rantala (1975, 1982), Nicholas Rescher and Robert Brandom (1980), Heinrich Wansing (1990), Timothy Williamson (1993, 2013), Ronald Fagin et. al. (1995), Graham Priest (2008), and Giacomo Sillari (2008) for discussion of nonnormal systems and additional citations, especially as it pertains to epistemic and doxastic logics. See Francesco Berto (2013) for an overview on counterpossibles. What We Can Do 50

The relation, ⩽, is a partial temporal ordering over the domain, D, which is partitioned into the subdomain of world-moments, , and the subdomain of mind-moments, . More speciﬁcally, ⩽ imposes two distinct partial temporal suborderings over the domain, one for the world subdomain and one for the mind subdomain. Branching tree structures have a singular concept of a history owing to the fact that its domain is made up entirely of world-moments. WWCD is not, and so demands dual deﬁnitions of histories.

Definition 2.4.9. A world-history, hw, is a maximal nonstrict totally ordered subset of . All world-histories are members of the partition  ⊊ , where  is the set of all histories. The set Historiesw = {hw ∶ w ∈ hw} contains all the world-histories passing through world-moment w. The set Pair ⊆  ×  contains all world-history/world-  moment pairs such that (w, hw) ∈ Pair only if w ∈ hw. The set ⊆ Pair is the -wise parameterization of Pair.

Definition 2.4.10. A mind-history, hm, is a maximal nonstrict totally ordered subset of . All mind-histories are members of the partition  ⊊ , where  is the set of all histories. The set Historiesm = {hm ∶ m ∈ hm} contains all the mind-histories passing through mind-moment m. The set Pair ⊆  ×  ⊊ Pair contains all mind-  history/mind-moment pairs such that (m, hm) ∈ Pair only if m ∈ hm. The set ⊆ Pair is the -wise parameterization of Pair.

Definition 2.4.11. A history, h, any world-history or mind-history. The set  contains all histories, where  is the partition of all world-histories and  is the partition of all mind-histories. The set Histories = {h ∶ ∈ h} ⊊ Pair contains all the histories passing through moment . The set P air is the set of all moment/history pairs, where Pair is the partition of all world-moment/world-history pairs and Pair is the partition of all   mind-moment/mind-history pairs. A set ⊆ Pair is any or .

A world-history is a history exclusively made up of world-moments. A mind-history is a history exclusively made up of mind-moments. The twain never meet. The notation invented for branching tree structures is retained as a means of generalizing over all moments and histories, normal and nonnormal. There are no interesting changes to the embedded theory of times.  = {t, t¨, t¨¨, …} is a strictly totally ordered partition of the domain into times where every time, t, is a nonempty set of contemporaneous moments and every possible moment is a member of exactly one time. A time may be simultaneously populated by world-moments and mind-moments, as is the case when the agent has mental representations of the world 2.4. The WWCD Framework 51 while existing in it. Neither are there any interesting changes to the embedded theory of context. Λ remains a sortal function that sorts moment/history pairs into various equivalence classes according to whether or not is satisfied, for any parameterization . At least in principle, no constraints are imposed upon the behavior of the sortal function: depending on the , some -wise similarity equivalence classes might be populated solely by world-moments, some populated solely by mind-moments, and some mixed. WWCD is a formal theory of ability. Informally, a person is able to be the agent or subject of something if, and only if, it is abilitively possible for the agent to relevantly do or relevantly be that thing. If Lily is able to ride a bike, for example, there are abilitively accessible world-moment/world-history pairs at which Lily rides a bike. Broadly, the spectrum of intuitive ability concepts are defined from abilitively accessible world-pairs belonging to variously parameterized subsets of the domain. The accessibility relation, ℜ, interpreted as mapping of the idea that any agent is endowed with an array of powers that the agent could in fact actualize, exercise, or otherwise manifest in the world. This is why ℜ is defined over world-moment/world-history pairs alone. The possession of visual powers means that, in a vision-favoring environment, the agent could visualize objects within the agent’s visual field. The possession of cognitive powers means that, in a cognition-favoring environment, the agent could form or sustain propositional attitudes. The possession of intentional powers means that, in a choice-favoring environment, the agent could make certain decisions. And so on. I assume that an agent has a whole array of powers, some passive (such as those involved with various doxastic, emotive, or perceptual states) and others active (such as those involved with practical deliberation). All powers ¨ ¨ are lumped together in a suite such that the notation (w, hw)ℜ(w , hw) roughly means that ¨ ¨ there is some possible world-pair, (w , hw), that is in some sense a continuation of the total

suite of powers possessed by the agent at (w, hw).

Assumption 2.4.1. The WWCD accessibility relation, ℜ, is ﬁnite for each agent.

I impose the mathematically unjustifiable constraint upon ℜ that every agent has access to a finite number of world-moment/world-history pairs. Intuitively, the constraint approximates an agent’s mortal finitude. It suggests that no agent is immortal; or, that no agent is an endless font of ability. This makes explicit my intention to deploy WWCD as a general theory of agents relevantly like us. Without the constraint, WWCD is a questionable foundation for a deontic theory. I discuss the constraint in detail shortly. Whereas an agent’s total suite of powers is represented by the accessibility relation, ℜ, an agent’s various subsuites of powers are each represented by some corresponding What We Can Do 52

neighborhood function. By default, WWCD has only four neighborhood functions.

∙ about represents agent’s powers to be a subject of something. It is used to deﬁne [], the modality expressing an agent’s being a certain way.

∙ assent represents agent’s powers to believe something. It is used to deﬁne [ ], the modality expressing an agent’s belief.

∙ cause represents agent’s powers to be a cause of something. It is used to deﬁne [], the modality expressing an agent’s causal responsibility.

∙ intend represents agent’s powers to intend something. It is used to deﬁne [ ], the modality expressing an agent’s intention.

At least in principle, enriching what WWCD can say about ability is simply a matter of adding neighborhood functions to represent certain other powers. I leave it to the curiosity of others to explore the possibilities.

Definition 2.4.12. The neighborhood function, , is consistent if, and only if, both (, h) ≠ {ç} and {ç} ∉ (, h).

Definition 2.4.13. The neighborhood function, , is a quasiﬁlter if, and only if,  is closed under supersets and closed under intersections. The following conditions hold for all quasiﬁlter neighborhood functions in WWCD: ∙ Closed Under Supersets: If X ∩ Y ∈ (, h), then X ∈ (, h) and Y ∈ (, h). ∙ Closed Under Intersections: If X ∈ (, h) and Y ∈ (, h), then X ∩ Y ∈ (, h).

Definition 2.4.14. The neighborhood function, , is T-constrained if, and only if, it is the case that if X ∈ (, h), then (, h) ∈ X.

Some neighborhood functions have constraints imposed upon them, some don’t. In

particular, about and cause are consistent T-constrained quasiﬁlters, but assent and intend are free from constraint. Philosophically speaking, the praxeological modalities deﬁned by appeal to neighborhood functions are theoretical proxies for intuitive concepts of performances. Constraints are imposed upon neighborhood functions to ensure that the relevant modality’s behavior conforms to the intuitive phenomenon.

Finally, the relation, ≾r, is a partial normative ordering over the domain, which is, again, partitioned into the subdomain of world-moments, , and the subdomain of mind-

moments, . More speciﬁcally, ≾r imposes two distinct nonstrict normative suborderings over the domain, one for the world subdomain and one for the mind subdomain. While all 2.4. The WWCD Framework 53

world-moments are ≾r-wise comparable and all mind-moments are ≾r-wise comparable, the two normative suborderings are not intercomparable.

Every ≾r-wise ordering over Pair is indexed to an agent, a set of normative criteria, r, and a moment/history pair. Intuitively, the normative criteria, r, is a nonempty set of reasons, external (i.e., reasons that there are) or internal (i.e., reasons the agent has),

such that ≾r orders moment/history pairs according to how overall favorable the possible pairs are from the perspective of r relative to an agent at a moment in a history. As ¨ ¨ such, (, h) ≾r ( , h ) expresses the idea that (, h) is at least as overall r-reasons-wise ¨ ¨ ¨ ¨ preferable as ( , h ) for an agent at a moment/history and (, h) ≺r ( , h ) expresses that (, h) is overall strictly r-reasons-wise preferable to (¨, h¨) for an agent at a moment/history.

Fixing the agent, set of reasons, and moment/history pair ﬁxes the ≾r-wise ordering over

Pair relative to the relata. Thusly ﬁxed, the ≾r-wise ordering over Pair (given the agent, set of reasons, and moment/history) is immutable. However, it is allowed—but not enforced—

that every ≾r-wise ordering over Pair is dynamic, possibly varying by agent, set of reasons, or moment/history pair. The dynamics of gaining or losing reasons is modeled by an agent’s traversing accessible moments where the contents of r is relevantly distinguishable.

Defeat is likewise modeled as a dynamic phenomenon, where the ≾r-wise ordering over Pair changes for the agent as a result of changes to the contents of r over time.

Definition 2.4.15. A WWCD model is an ordered set

M = ⟨F, ℑ+, ℑ−⟩ where each element is deﬁned as follows:

∙ F = ⟨D, , , ⩽,  , Λ, ℜ, i, … , n, ≾r⟩ is a WWCD frame.

∙ ℑ+ ∶ Atom × Pair ↦ {1, 0} is a normal interpretation function assigning truth-values to atoms at world-moment/world-history pairs, for all world-moment/world-history pairs belonging to Pair and all atoms, Atom, belonging to the language WWCD.

∙ ℑ− ∶ Ψ×Pair ↦ {1, 0} is a nonnormal interpretation function assigning truth-values to well-formed formulas at mind-moment/mind-history pairs, for all mind-moment/mind- history pairs belonging to Pair and formulas belonging to the proper subset, Ψ, of the language WWCD.

A WWCD model is a WWCD frame plus two interpretation functions, one for world- moment/world-history pairs and another for mind-moment/mind-history pairs. The

normal interpretation function, ℑ+, is inherited from branching tree models: it assigns to What We Can Do 54

each WWCD atom a truth-value at every world-moment/world-history pair. By contrast,

the nonnormal interpretation function, ℑ−, is anarchical: it assigns to a subset of well- formed WWCD formulas arbitrary truth-values at mind-moment/mind-history pairs, meaning that formulas behave like atoms. Intuitively, possible mind-moments are possible

mental representations of world and ℑ− makes allowances for incomplete, inconsistent, or incoherent mental representations of world via anarchical truth assignment. Branching tree models evaluate formulas at moment/history pairs. The double index requirement for alethic evaluation is intact in WWCD, but requires speciﬁcity in lieu of the nonnormal machinery.

Definition 2.4.16. A well-formed formula ∈ WWCD is satisﬁable at a moment/history pair, (, h), in a WWCD model, M, if M, (, h) ⊨ for some (, h) ∈ Pair.

Definition 2.4.17. A well-formed formula ∈ WWCD is valid at a world-moment/world-

history pair, (w, hw), in a WWCD frame, F, denoted F, (w, hw) ⊨ , if is satisﬁed at w∕hw in every model, M, based on F.

Definition 2.4.18. A well-formed formula ∈ WWCD is valid in a WWCD frame, F,

denoted F ⊨ , if is valid at every world-moment/world-history pair w∕hw ∈ F.

Satisfiability ranges over both normal and nonnormal moments. A formula is satisfiable in a WWCD model when there is a WWCD model such that the formula is true at a moment/history pair and an interpretation. Interpretations of formulas at world- moment/world-history pairs are handled by the normal interpretation function, whereas interpretations of formulas at mind-moment/mind-history pairs are handled by the nonnormal interpretation function. Validity ranges over normal moments alone. A formula is valid a world-moment/world-history pair in a WWCD frame when the formula world- moment/world-history pair in every WWCD model. A formula is valid in a WWCD frame when the formula is valid at every world-moment/world-history pair in a WWCD frame. Summarily, in WWCD, satisfiability is nonclassical, but logical consequence is classical.

2.4.3 WWCD Semantics

In this subsection, I sketch the formal semantics for WWCD for both world-moment/world- history pairs and mind-moment/mind-history pairs. The subsubsections are thematically divided among philosophical interpretations of both the primitive and nonprimitive grammar. 2.4. The WWCD Framework 55

Normal Boolean Connectives

Oﬃcially, atoms (including ⊤ and ⊥) and material implication are elements of the WWCD primitive grammar. Nonetheless I make full use of all Booleans, where the remaining Booleans are abbreviations. Table 2.8 displays the WWCD semantics for Booleans at normal moment/history pairs.

Table 2.8: WWCD Normal Semantics: Atoms and Booleans

Operator Definition

M, (w, hw) ⊨ ℑ+(, (w, hw)) = 1 M, (w, hw) ⊨ ¬ ℑ+(, (w, hw)) = 0 M, (w, hw) ⊨ ∨ M, (w, hw) ⊨ or M, (w, hw) ⊨ M, (w, hw) ⊨ ∧ M, (w, hw) ⊨ and M, (w, hw) ⊨ M, (w, hw) ⊨ → M, (w, hw) ⊨ ¬ or M, (w, hw) ⊨ M, (w, hw) ⊨ ↔ M, (w, hw) ⊨ → and M, (w, hw) ⊨ →

Oﬃcially, none of the Booleans behave in unexpected ways at normal moment/history pairs. The atomic formula is true at a world-moment/world-history pair, (w, hw), if, and only if, the normal interpretation function assigns 1 to at (w, hw). The formula ( → ) is true at (w, hw) if, and only if, either is false at (w, hw) or is true at (w, hw). And so on. One more convenient abbreviation. Let ! be the discharge operator, where ■! or ◆! respectively denote discharged necessity and discharged possibility, for any necessity and possibility modalities ■ and ◆. When so attached to a modal formula, the discharger denotes that the modal has been discharged at the moment/history pair of evaluation. Table 2.9 displays the WWCD semantics for discharger at normal moment/history pairs. In eﬀect, the discharger ensures that the propositional object of a modal formula is true at the moment/history pair of evaluation.

Table 2.9: WWCD Normal Semantics: Discharger

Operator Definition

M, (w, hw) ⊨ ■! M, (w, hw) ⊨ ■ and (w, hw) ∈ and M, (w, hw) ⊨ M, (w, hw) ⊨ ◆! M, (w, hw) ⊨ ◆ and (w, hw) ∈ and M, (w, hw) ⊨

All modalities quantify over some portion of the domain, indicated above by the parameterization subscript attached to the symbolic modal variables. The discharge operator indicates not only that both the relevant modal formula and its propositional object are true at the moment/history pair of evaluation, but the pair of evaluation is a member of the relevant set of pairs over which the modality is deﬁned. What We Can Do 56

Normal Tense Modalities

Being an extension of branching tree structures, WWCD subsumes the previously deﬁned tense modalities. Philosophically, tense modalities operate upon both agent-independent and agent-dependent facts. Table 2.10 displays the WWCD semantics for Booleans at normal moment/history pairs.

Table 2.10: WWCD Normal Semantics: Tense Modalities

Operator Definition ¨ ¨ ¨ ¨ M, (w, hw) ⊨ □ M, (w , hw) ⊨ for all (w , hw) ∈ Pair ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ M, (w, hw) ⊨ ⊡ M, (w , hw) ⊨ for all (w , hw) ∈ Pair such that (w , hw) ≈ (w , hw) ¨ ¨ ¨ M, (w, hw) ⊨ ℙ M, (w , hw) ⊨ for some w ∈ hw such that w < w ¨ ¨ ¨ M, (w, hw) ⊨ F M, (w , hw) ⊨ for some w ∈ hw such that w < w ¨ ¨ M, (w, hw) ⊨ S M, (w, hw) ⊨ for all hw ∈ Historiesw

As far as the tense modalities are concerned, the only distinction between branching tree structures and WWCD is purely notational. The intuitive interpretations for modalities and the formal semantics is otherwise the same.

Normal Abilitive Modalities

Abilitive modalities are so-called because they are deﬁned in terms of what is true across contextually salient abilitively accessible normal moment/history pairs. Table 2.11 displays the WWCD semantics for abilitive modalities at normal moment/history pairs.

Table 2.11: WWCD Normal Semantics: Abilitive Modalities

Operator Definition ¨ ¨ ¨ ¨  ¨ ¨ M, (w, hw) ⊨ ▣ M, (w , hw) ⊨ for some (w , hw) ∈ such that (w, h)ℜ(w , h ) ¨ ¨ ¨ ¨  ¨ ¨ M, (w, hw) ⊨ ▣ M, (w , hw) ⊨ for all (w , hw) ∈ such that (w, h)ℜ(w , h )

▣ is the modality of abilitive possibility. I shall use ‘abili-consistency’ for consistency with an agent’s total suite of powers. Philosophically, ▣ means that is abili-consistent

for the agent. The formula ▣ is true at (w, hw) if, and only if, is true at some contextually ¨ ¨ salient normal moment/history pair, (w , hw), abilitively accessible to the agent from (w, hw).

Intuitively, everything true at (w, hw) is abili-consistent for the agent at (w, hw).

Whereas ▣ expresses that abili-consistent for the agent, it is worth having a notion of abili-inconsistency, where ‘abili-consistency’ is inconsistency with an agent’s totals suite

of powers. The dual of ▣ is ▣ and it serves this purpose well. ▣ is the modality of abilitive necessity. Philosophically, ▣ means that is compulsory for the agent; or, that 2.4. The WWCD Framework 57

¬ is abili-inconsistent for the agent. The formula ▣ is true at (w, hw) if, and only if, ¨ ¨ is true at every contextually salient normal moment/history pair, (w , hw), abilitively

accessible to the agent from (w, hw). Intuitively, the laws of nature and the truths of logic are abili-compulsory for an agent. By implication, the laws of nature and the truths of logic are abili-consistent. Abili-consistency and ability are conceptually distinct. Whereas the laws of nature and the truths of logic are abili-consistent, they are not within an agent’s power, which is to say that the agent has no genuine abilities over these matters. In concordance with the canonical praxeo-abilitive form, genuine abilities take well-formed praxeological formulas as their objects. Let ■x is a symbolic variable ranging over all of the praxeological modalities x x such that ■ stands for some well-formed praxeological formula. Philosophically, ▣ ■ expresses that ■x is abili-consistent, which is to say that is within the agent’s power. In this way, ▣■x expresses that ■x is abili-compulsory, which is to say that the agent is compelled to manifest some relevant power over .

Normal Praxeological Modalities

Praxeological modalities are the modals for the successful manifestations of subsuites of powers. Admittedly, the label is not ideal, as it includes modalities that are not usually circumscribed under a common sense notion of achievement or agency. Under the present classiﬁcation, some praxeological modals are performative, whereas others are not.

Definition 2.4.19. The truth set of a formula ∈ WWCD is set of all moment/history pairs in a WWCD model, M, at which is satisﬁed. The truth set of in WWCD is denoted M ‖‖ and deﬁned as follows:

M ‖‖ = {(, h) ∈ Pair ∶ M, (, h) ⊨ } where M is a WWCD model.

Definition 2.4.20. The false set of a formula ∈ WWCD is the set of all moment/history pairs in a WWCD model, M, at which is unsatisﬁed. The false set of in WWCD is M denoted −‖‖ and deﬁned as follows:

M M −‖‖ = P air − ‖‖ = {(, h) ∈ Pair ∶ M, (, h) ⊨ } where M is a WWCD model.

Definition 2.4.21. The contextual truth set of a formula ∈ WWCD is the truth set of What We Can Do 58

restricted to some parameterization ⊆ Pair. The contextual truth set of in WWCD is M denoted ‖‖ and deﬁned as follows:

M ‖‖ = {(, h) ∈ ∶ M, (, h) ⊨ }

M M where M is a WWCD model, is a contextual parameter, and ‖‖ ⊆ ‖‖ .

Definition 2.4.22. The contextual false set of a formula ∈ WWCD is the false set of

restricted to some parameterization ⊆ Pair. The contextual false set of in WWCD is M denoted −‖‖ and deﬁned as follows:

M M −‖‖ = − ‖‖ = {(, h) ∈ ∶ M, (, h) ⊨ ¬}

M M where M is a WWCD model, is a contextual parameter, and −‖‖ ⊆ −‖‖ .

To recapitulate, the truth set of a formula is the set of all moment/history at which it is true and the contextual truth set of a formula is the subset of its truth set satisfying some parameterization of moment/history pairs. Mutatis mutandis for the false set and contextual false set of a formula. In WWCD, every neighborhood function associates every normal moment/history pair with a set of neighborhoods. Praxeological modals are deﬁned over the neighborhoods associated with the moment/history at which the relevant formulas are the propositional objects of the relevant successfully manifested powers. More speciﬁcally, a praxeological modal is true at a world-moment/world-history pair when the contextual truth set of the propositional object of the modal is among the relevant neighborhoods associated with the moment/history. Table 2.12 displays the WWCD semantics for praxeological modalities at normal moment/history pairs.

Table 2.12: WWCD Normal Semantics: Monadic Praxeological Modalities

Operator Definition M M, (w, hw) ⊨ [] ‖‖ ∈ about(w, hw) M M, (w, hw) ⊨ [ ] ‖‖ ∈ assent(w, hw) M M, (w, hw) ⊨ [] ‖‖ ∈ cause(w, hw) M M, (w, hw) ⊨ [ ] ‖‖ ∈ intend(w, hw)

[] is the modality of the agent’s being a certain way or having a certain quality.

Philosophically, [] means that the agent is such that ; or, it is a stable fact about the

agent that . The formula [] is true at (w, hw) if, and only if, the contextual truth set

of is a neighborhood belonging to about(w, hw). In neighborhood semantics, necessity 2.4. The WWCD Framework 59

just is the relation of membership obtaining between the truth set of a formula and the set of neighborhoods associated with a moment/history pair. Intuitively, the truth set of is the set of moment/history pairs at which is in the relevant sense necessary; presently, it is the set of moment/history pairs at which is a stable fact about the agent and the contextual truth set of is the set of contextually salient moment/history pairs M at which is a stable fact about the agent. When ‖‖ ∈ about(w, hw), it means that the special contextually salient neighborhood of moment/history pairs at which is a stable

fact about the agent is associated with the world-moment/world-history pair (w, hw). The semantics approximates the intuition that an agent’s being a certain way is the ﬁxity of a fact across all the agent’s dispositional proﬁles.

[ ] is the modality of propositional belief. Philosophically, [ ] means that the agent

believes that ; or, that is a feature of the agent’s conception of world. The formula [ ]

is true at (w, hw) if, and only if, the contextual truth set of is a neighborhood belonging

to assent(w, hw). In other words, [ ] is true at (w, hw) when the set of contextually salient moment/history pairs at which is a part the agent’s representation of world is associated with (w, hw). The semantics approximates the intuition that believing is the ﬁxity of a fact across all the psychologically live options for ways the world could be.

[] is the modality of the agent’s being a cause of something. Philosophically, [] means that the agent does such that ; or, it is a fact caused by the agent that . The

formula [] is true at (w, hw) if, and only if, the contextual truth set of is a neigh-

borhood belonging to cause(w, hw). In other words, [] is true at (w, hw) when the set of contextually salient moment/history pairs at which the agent is causally responsible

for is associated with (w, hw). The semantics approximates the intuition that an agent’s causal responsibility the ﬁxity of a fact across all relevant states of world given the agent’s dispositional proﬁle.

[ ] is the modality of propositional intention. Philosophically, [ ] means that the

agent intends that . The formula [ ] is true at (w, hw) if, and only if, the contextual

truth set of is a neighborhood belonging to intend(w, hw). In other words, [ ] is true

at (w, hw) when the set of contextually salient moment/history pairs at which the agent is

intends that is associated with (w, hw). The semantics approximates the intuition that intending is the holding fixed a fact across all desirable ways the world could be; or, it is the representation of self effecting world as it is wished to be. It is possible to define dyadic praxeological modalities representing the satisfaction of a basing relation. Dyadic praxeological modalities are included for sake of exhaustiveness, but might be invoked in contexts where the basis plays an explanatory role for the modal.

Let ■x be a symbolic variable ranging over all of the praxeological modalities [], [ ], What We Can Do 60

[], and [ ] such that ■ can equally understood to mean any of [], [ ], [], or

[ ]. When I expand the stock of praxeological modalities, ■x will also range over the new modalities. Table 2.13 displays the schematic deﬁnition for a dyadic praxeological modality and Table 2.14 displays the instantiated deﬁnitions for dyadic praxeological modalities at normal moment/history pairs.

Table 2.13: WWCD Normal Semantics: Schematic Dyadic Praxeological Modalities

Operator Definition x ∙ Performance: M, (w, hw) ⊨ ■ x M, (w, hw) ⊨ ■(∕ ) ∙ Basis: M, (w, hw) ⊨ [] x ∙ Basis Safety: M, (w, hw) ⊨ ▣([] → ■)

Table 2.14: WWCD Normal Semantics: Dyadic Praxeological Modalities

Operator Definition

∙ Being: M, (w, hw) ⊨ [] M, (w, hw) ⊨ [](∕ ) ∙ Basis: M, (w, hw) ⊨ [] ∙ Basis Safety: M, (w, hw) ⊨ ▣([] → []) ∙ Believing: M, (w, hw) ⊨ [ ] M, (w, hw) ⊨ [ ](∕ ) ∙ Basis: M, (w, hw) ⊨ [] ∙ Basis Safety: M, (w, hw) ⊨ ▣([] → [ ]) ∙ Doing: M, (w, hw) ⊨ [] M, (w, hw) ⊨ [](∕ ) ∙ Basis: M, (w, hw) ⊨ [] ∙ Basis Safety: M, (w, hw) ⊨ ▣([] → []) ∙ Intending: M, (w, hw) ⊨ [ ] M, (w, hw) ⊨ [ ](∕ ) ∙ Basis: M, (w, hw) ⊨ [] ∙ Basis Safety: M, (w, hw) ⊨ ▣([] → [ ])

Broadly, a dyadic praxeological modal is true at (w, hw) if, and only if, the monadic praxeological modal is true at (w, hw), the basis is true at (w, hw), and the praxeological modal is true across all contextually salient abilitively accessible moment/history pairs at which the basis is true. Suppose, for example, an agent has blue eyes because the agent has a certain genetic makeup. This claim is true if, and only if, the agent has blue eyes, the agent has the genetic makeup for blue eyes, and, in all the contextually salient moment/history pairs where the agent has the genetic makeup, the agent has blue eyes. Dyadic praxeological modalities are consistent with overdetermination. It might be the case that an agent has a plurality of bases, each independently suﬃcient for the production of the relevant performance. This is permitted under the present deﬁnition because the following condition is not imposed: 2.4. The WWCD Framework 61

x Basis Sensitivity: M, (w, hw) ⊨ ▣(¬[] → ¬■)

Plainly, Basis Sensitivity says that the absence of the relevant basis suﬃces for the falsity of the relevant praxeological modal. The condition essentializes the basis of performance for the production of performance. Overdetermination violates the condition, as each independent basis is suﬃcient but not necessary for the production of performance. Excluding the condition permits cases of overdetermination.

The Theory of Alternality

Alternality is the praxeological analogue of negation. It is the notion of being, believing, doing, or intending otherwise. When an agent is, believes, does, or intends otherwise than (being, believing, doing, or intending such that) , it is false that they are, believe, do, or intend that ; and, moreover, when an agent is, believes, does, or intends that , it is false that they are, believe, do, or intend otherwise. The notion of alternality plays a crucial role in WWCD and its extensions. Let ■x be a praxeological variable and let the overbar denote alternality such that ■x is

the praxeological alternate of ■x . In this way, [] expresses that the agent is otherwise than . And so on for all other praxeological modals. Table 2.15 displays the formal semantics for schematic alternality.

Table 2.15: WWCD Normal Semantics: Schematic Alternality

Operator Definition x x x x M, (w, hw) ⊨ ■ M, (w, hw) ⊨ ■¬ or M, (w, hw) ⊨ ■¬■ x x x x M, (w, hw) ⊨ ■(∕ ) M, (w, hw) ⊨ ■(¬∕ ) or M, (w, hw) ⊨ ■(¬■∕ )

Intuitively, alternates render each other false. The schematic deﬁnition of alternality is disjunctive, corresponding to two possible ways a praxeological modal might be rendered false, but not every element of the deﬁnition is inconsistent with every praxeological modal. In particular, the left-side disjunct is not inconsistent with belief or intention: at least in principle, it is possible for an agent to have contradictory beliefs or intentions. The only genuine alternates to belief or intention is not thusly believing or intending. I’ll correct for this overgeneralization momentarily. Consider being and doing. Being or doing something implies the falsity of every alternate and vice versa. This suggests two ways to falsity either praxeological modal, each roughly corresponding to two types of defeaters: rebutting and undercutting.20

20 Compare with John Pollock and Joseph Cruz (1999), especially discussion in chapter seven. What We Can Do 62

On the one hand, there is the left-side disjunct of the schematic deﬁnition of alternality. If the agent is or does that ¬, then it is impossible for the agent to simultaneously be or do that . Put another way, if an agent is such that , then the agent isn’t such that ¬; if the agent brings it about that ¬, then the agent doesn’t bring it about that . This is the praxeological analogue of rebutting defeat; it is a kind of ﬁrst-order praxeological defeat.

On the other hand, there is the right-side disjunct of the schematic deﬁnition of alternality. If the agent is or does that ¬■x , meaning that agent is or does such that agent is not or does not that , then it is impossible for the agent to be or do that . Put another way, if an agent is such that the agent isn’t such that , then the agent isn’t such that ; if the agent refrains from bringing it about that , then they don’t bring it about that . This is the praxeological analogue of undercutting defeat; it is a kind of second-order praxeological defeat.

Dyadic alternality is much the same as monadic alternality. The alternate to being or doing that on the basis that is being or doing otherwise than on the basis that , for some basis . In the service of metaphysical neutrality, I leave it open whether it is possible for the bases, and , to be such that = .

Alternality notation is useful for quickly generalizing over praxeological modalities. I oﬀer the following reﬁnements to adequately treat belief and intention:

⎧ x M, (w, hw) ⊨ ¬■ for [ ], [ ] x ⎪ M, (w, hw) ⊨ ■ = ⎨ x x x ⎪M, (w, hw) ⊨ ■¬ or M, (w, hw) ⊨ ■¬■ for [], [] ⎩

Homologous remarks apply to dyadic alternality for belief and intention:

⎧ x M, (w, hw) ⊨ ¬■(∕ ) for [ ], [ ] x ⎪ M, (w, hw) ⊨ ■(∕ ) = ⎨ x x ⎪M, (w, hw) ⊨ ■(¬∕ ) or M, (w, hw) ⊨ ■(¬∕ ) for [], [] ⎩

Alternality notation will henceforth be regularly employed. 2.4. The WWCD Framework 63

Normal Reasons Modalities

Reasons modalities are so-called because they are defined in terms of what is performed across the maximally reasons-wise preferable contextually salient abilitively accessible normal moment/history pairs. Reasons modalities are weird creatures, and so require a few points of clarification. Reasons modalities represent reasons’ recommendation to an agent the performance of some praxeological modal. Reasons do not brutely recommend propositions, but rather that propositions be taken as the objects of certain performances. It is for this reason that reasons modalities operate all and only upon what I shall performative formulas, where a performative formula is atomic (of the form: ■x , for any well-formed formula ) or recursively built up from atomic performances using the usual Boolean and modal operations. Intuitively, performative formulas are a subset of WWCD formulas that express some number of ideas about what it is an agent is, believes, does, intends, or the like. Reasons modalities all share what I shall call an exception condition, which is the requirement that there is some relevant circumstances under which the agent performs an alternate. The relevant circumstances is a superset of the presently contextually salient set of moment/history pairs, meaning that the relevant circumstances at which the alternate is realized might—but might not—require some important differences absent in the present context. The overarching idea is that reasons are enabled to recommend performances to an agent only if the relevant subsuite of powers is nondeviantly responsive to reasons. The paradigmatic test for nondeviant reasons-responsiveness is the agent’s performance of an alternate given appropriately distinguishable inputs, such as when the context appropriately shifts or the reasons in play are appropriately different. The exception condition encodes the paradigmatic test for nondeviant reasons-responsiveness. Finally, reasons modalities appeal to abilitively accessible moment/history pairs. As- sumption 2.4.1 states that the accessibility relation, ℜ, is finite for each agent. The assumption is imposed to avoid a paradox concerning reasons-wise obligations I do not yet know how to solve. Before highlighting the paradox, I will offer two formulations of the WWCD reasons modalities, which are extensionally equivalent with the assumption but not without it. By ‘extensional equivalence’ I mean that the two formulations agree about the reasons-wise statuses of the relevant performances. The first formulation of the reasons modalities appeals to the optimality set normal

moment/history pair, (w, hw), which is the set of all r-reasons-wise best contextually salient

abilitively accessible moment/history pairs. The optimality set for an agent at (w, hw) given r the set of reasons r in context is denoted Best (w, hw). What We Can Do 64

Definition 2.4.23. A r-reasons-wise optimality set of a normal moment/history pair,

(w, hw), for an agent and set of reasons, r, is the subset of all contextually salient mo-

ment/history pairs abilitively accessible from (w, hw) containing all and only the pairs that are at least as r-reasons-wise preferable as any other. The r-reasons-wise optimality set of r (w, hw) is denoted Best (w, hw) and deﬁned as follows:

r ¨ ¨ ¨ ¨ ¨¨ ¨¨ ¨ ¨ Best (w, hw) = {(w , hw) ∈ ∶ (w, hw)ℜ(w , hw) and (w , hw) ≾r (w , hw), ¨¨ ¨¨ ¨¨ ¨¨ for all (w , hw) ∈ such that (w, hw)ℜ(w , hw)}

r where M is a WWCD model, is a contextual parameter, and Best (w, hw) ⊆ ⊆ Pair.

The first formulation quantifies over an optimality set. Table 2.16 displays the first formulation of WWCD semantics for reasons modalities at normal moment/history pairs.

Table 2.16: WWCD Normal Semantics: Reasons Modalities (First Formulation)

Operator Definition ¨ ¨ x ¨ ¨ r ∙ Positivity: M, (w , hw) ⊨ ■ for some (w , h ) ∈ Best (w, hw) M, (w, h ) ⊨ ■x ¨¨ ¨¨ x ¨¨ ¨¨ ¨ w  ∙ Exception: M, (w , hw) ⊨ ■ for some (w , h ) ∈ such ¨ ¨¨ ¨¨ that ⊇ and (w, h)ℜ(w , h ) ¨ ¨ x ¨ ¨ r ∙ Positivity: M, (w , hw) ⊨ ■ for some (w , h ) ∈ Best (w, hw) ∙ Uniqueness: M, (w¨¨, h¨¨) ⊨ ■x for no (w¨¨, h¨¨) ∈ Bestr(w, h ) x w w w M, (w, hw) ⊨ ■ ¨¨¨ ¨¨¨ x ¨¨¨ ¨¨¨ ¨ ∙ Exception: M, (w , hw ) ⊨ ■ for some (w , h ) ∈ such ¨ ¨¨¨ ¨¨¨ that ⊇ and (w, h)ℜ(w , h )

 is the modality of reasons-wise permissibility. Philosophically, ■x means that some reasons recommend to the agent that ■x ; or, it is reasons-wise permissible for the agent to ■x . More speciﬁcally, for external reasons, ■x means that there is some reason for the agent to ■x ; or, for internal reasons, ■x means that the agent has some reason x x x to ■. The formula ■ is true at (w, hw) if, and only if, ■ is true at some reasons-wise optimiﬁc moment/history pair and ■x is true at some excepting moment/history pair. Observe that the excepting moment/history pair at which ■x is true might not be a

member of over which the positivity condition is deﬁned, meaning that the excepting moment/history pair is not guaranteed to be contextually salient. Whereas ■x expresses that ■x is reasons-wise permissible for the agent, it is worth having a stronger notion for reasons-wise obligation. The dual of ■x is ■x and it serves this purpose well.  is the modality of reasons-wise obligation. Philosophically, ■x means that most reasons recommend to the agent that ■x ; or, it is reasons-wise 2.4. The WWCD Framework 65

obligatory for the agent to ■x . More specifically, for external reasons, ■x means that there is most reason for the agent to ■x ; or, for internal reasons, ■x means that the x x x agent has most reason to ■. The formula ■ is true at (w, hw) if, and only if, ■ is true at some reasons-wise optimific moment/history pair and ■x is true at some excepting moment/history pair, but no such excepting pair is optimific. Simplifying, ■x is true x at (w, hw) if, and only if, ■ is uniquely reasons-wise permissible at (w, hw). On the first formulation, the crucial difference between the some reasons and most reasons modalities comes down to a matter of quantification over the optimality set. Reasons-wise permissibility requires that there is some optimific moment/history pair where the relevant performance occurs, but leaves open what occurs in any remaining optimific moment/history pairs. It is equally allowable by the definition that the excepting moment/history pair is a member or a nonmember of the optimific set. When the excepting moment/history pair is a member of the optimific set, the performance is reasons-wise optional. Contrastingly, reasons-wise obligation requires that the relevant performance occurs at every optimific moment/history pair and therefore ensures that the excepting moment/history pair is not a member of the optimific set. The second formulation of the reasons modalities does not appeal to optimality sets. Instead the thrust of the positivity condition is captured by the commission and favorability conditions. Table 2.17 displays the second formulation of WWCD semantics for reasons modalities at normal moment/history pairs.

Table 2.17: WWCD Normal Semantics: Reasons Modalities (Second Formulation)

Operator Definition ¨ ¨ x ¨ ¨ ∙ Commission: M, (w , hw) ⊨ ■ for some (w , h ) ∈ such that (w, h)ℜ(w¨, h¨) ∙ Exception: M, (w¨¨, h¨¨) ⊨ ■x for some (w¨¨, h¨¨) ∈ ¨ such x w M, (w, hw) ⊨ ■ ¨ ¨¨ ¨¨ that ⊇ and (w, h)ℜ(w , h ) ¨¨¨ ¨¨¨ x ¨¨¨ ¨¨¨ ∙ Favorability: M, (w , hw ) ⊨ ■ for no (w , h ) ∈ such ¨¨¨ ¨¨¨ ¨ ¨ ¨¨¨ ¨¨¨ that (w, h)ℜ(w , h ) and (w , hw) ≺r (w , h ) ¨ ¨ x ¨ ¨ ∙ Commission: M, (w , hw) ⊨ ■ for some (w , h ) ∈ such that (w, h)ℜ(w¨, h¨) and ∙ Exception: M, (w¨¨, h¨¨) ⊨ ■x for some (w¨¨, h¨¨) ∈ ¨ such x w M, (w, hw) ⊨ ■ ¨ ¨¨ ¨¨ that ⊇ and (w, h)ℜ(w , h ) ¨¨¨ ¨¨¨ x ¨¨¨ ¨¨¨ ∙ Favorability: M, (w , hw ) ⊨ ■ for no (w , h ) ∈ such ¨¨¨ ¨¨¨ ¨ ¨ ¨¨¨ ¨¨¨ that (w, h)ℜ(w , h ) and (w , hw) ≾r (w , h )

x x On the second formulation, ■ is true at (w, hw) if, and only if, ■ is true at some commissive moment/history pair, ■x is true at some excepting moment/history pair, and What We Can Do 66

no excepting pair is strictly r-reasons-wise preferable to the commissive pair. Analogously, x x ■ is true at (w, hw) if, and only if, ■ is true at some commissive moment/history pair, ■x is true at some excepting moment/history pair, and no excepting pair is at least as r- reasons-wise preferable to the commissive pair. Summarily, the crucial difference between the some reasons and most reasons modalities for the second formulation comes down to the strictness of the reasons-wise preferability relation when comparing commissive and excepting moment/history pairs. Reasons-wise permissibility requires only nonstrict preferability, whereas reasons-wise obligation requires strict preferability. On the assumption that each agent ever has access to a finite number of moment/history pairs, both formulations of the reasons-wise modalities are extensionally equivalent. More precisely, the assumption of finite accessibility makes the first formulation’s positivity condition extensionally equivalent to the second formulation’s commission and favoring conditions. The argument is straightforward. The set of accessible moment/history pairs is always nonempty. The optimality set is the set of reasons-wise best accessible moments. When accessibility is finite for an agent, the optimality set is guaranteed to be nonempty. The first formulation’s positivity condition is a commissive moment’s membership in the optimality set. A commissive moment/history pair is a member of an optimality set when no moment is strictly preferable to it, and a fortiori when no excepting moment is strictly preferable to it. So, the first formulation’s positivity condition satisfies the second formulation’s commissive and favorability conditions, but, sadly, the converse implication fails. A moment/history pair satisfies the second formulation’s commissive and favorability conditions when it is a commissive pair such that no excepting pair is strictly preferable, but does not satisfy the first formulation’s positivity condition when there are other commissive pairs that are strictly preferable. However, despite the fact that the two formulations are not logically equivalent, they agree about the reasons-wise status of the performance committed at the commissive pair because in either case no strictly preferable excepting moment/history pair exists. On the first formulation, this is guaranteed by the definition of the optimality set; on the second formulation, this is guaranteed by the favorability condition. The two formulations are extensionally distinguishable when the assumption of finite accessibility is suspended. Suppose there is an agent that access to an infinite number of moment/history pairs. It does not matter whether the pairs are distributed over a finite or infinite number of times. Consider two versions of the core puzzle, the one appealing to infinite times and the other to a single instance of time:

EverBetter Wine Paradox. There is an immortal agent in possession of a bottle of EverBetter Wine. The wine continuously and linearly improves with 2.4. The WWCD Framework 67

age such that reasons always strictly prefer that the agent drinks the wine at a later time to an earlier time. What is the minimum amount of time that reasons require the agent to wait before drinking the bottle of EverBetter Wine?21 EverFuller Wallet Paradox. There is a ﬁnite agent in possession of an Ever- Fuller Wallet. The wallet is such that for any n, the agent can once and only once donate exactly n number of dollars to a charity. (Assume that reasons-wise preferability is continuously linear with number of dollars donated such that reasons always strictly prefer that the agent donates n + 1 dollars to n dollars, for any n.) What is the minimum amount of money that reasons require the agent to donate to charity from the EverFuller Wallet?22

What do the two formulations of reasons modalities say is reasons-wise obligatory for the agent? I briefly consider each in turn. On the first formulation, the agent has no reasons-wise minimal obligations: there is no minimum amount of time that the agent is reasons-wise obliged to wait to drink the EverBetter Wine and there is no minimum amount of dollars that the agent is reasons-wise obliged to donate from the EverFuller Wallet. In fact, the agent has no reasons-wise obligations whatever to ever drink the wine or to donate any money to charity. The first formulation defines permissions and obligations by existentially quantifying over members of the optimality set. However, in both cases, the optimality set is empty: ¨ ¨ ¨ ¨ for every (w, hw) ∈ , there exists a (w , hw) ∈ such that (w, hw) ≺r (w , hw), in which case there is no special equivalence class of strictly preferable moment/history pairs. Existentially quantifying over an empty optimality set entails the falsity of all relevant reasons-wise statuses. On the second formulation, the agent has infinite reasons-wise minimal obligations: it is reasons-wise obligatory for the agent to wait at least until time t, for any t, to drink the EverBetter Wine and it is reasons-wise obligatory for the agent to donate to charity at least n dollars, for any number n, from the EverFuller Wallet. Happily, the agent likewise has reasons-wise obligations to drink the wine at some time and to donate dollars of some amount. The second formulation defines permissions and obligations by universally quantifying over commissive moment/history pairs. However, in both cases, universal quantification over infinitely large sets yields problems: for every relevant commissive ¨ ¨ (w , hw) ∈ where the agent wait some amount of time or donates some amount of money, ¨ ¨ ¨ ¨ every (w , hw) ∈ such that (w, hw) ≺r (w , hw) are moments at which the amount is likewise

21 See John Pollock (1983) for the original formulation of the EverBetter Wine paradox. 22 Thanks to Tim Williamson for the EverFuller Wallet paradox. What We Can Do 68

committed waited or donated. But since this true for any amount of time waited or money donated, the minimum requirements are infinitely large. Universally quantifying over infinitely many strictly preferable moment/history pairs entails the truth of all relevant reasons-wise statuses. The two formulations force us into the impossible choice between accounts when faced with an infinite number of strictly preferable alternates. If we choose the first formulation, we are devoured by Scylla, who says that no reasons-wise statuses of any kind are incumbent upon us in such circumstances. If we choose the second formulation, we are devoured by Charybdis, who says that every reasons-wise statuses kind are incumbent upon us in such circumstances. Faced with the choice, I would not know which way to go. The imposition of Assumption 2.4.1 obviates the paradox by refusing the possibility of infinite accessibles. It is not a solution or even a principled stand. I let the assumption do its work, but if I am required to choose, then I shall follow the footsteps of Ulysses and take my chances with Scylla. As a proponent of Kant’s Law, I endorse the idea that an agent’s having too little ability robs them of any relevant obligations. As a matter of theoretical symmetry, perhaps having too much ability likewise robs agents of any relevant obligations. Or perhaps having too many options results in analysis paralysis, a kind of temporary loss of executive ability. I wish now to switch tacks to invent formalism that recognizes that reasons can be disappointed. There is, on the one hand, what reasons recommend to an agent and, on the other hand, what the agent effects, which may not accord with reasons’ recommendation. The agent can also disappoint reasons when compliance is a pure accident or occurs without appropriate regard for reasons. My point is that there is a distinction between what reasons recommend and the discharge of reasons’ recommendation, which is to say that reasons-wise modals can be true without being discharged, just as an agent can have unfilled obligations. Recall that ! is the discharge operator. When attached to a reasons modality, it denotes that the modal has been discharged. Intuitively, this can be interpreted to mean that reasons play the appropriate role in the occurrence of the praxeological modal. What exactly counts as the appropriate role will, I suspect, partially be determined by the nature and content of the reasons in play. Formally, a reasons modal is relevantly discharged just in case the agent does what reasons favor at the relevant world-moment/world-history of evaluation. Plainly, discharging something means making it appropriately happen. Table 2.18 displays the WWCD semantics for discharged reasons modalities at normal moment/history pairs.

x ! is discharged some reasons. The formula !■ is true at (w, hw) if, and only if, 2.4. The WWCD Framework 69

Table 2.18: WWCD Normal Semantics: Discharged Reasons Modalities

Operator Definition x r ∙ Positivity: M, (w, hw) ⊨ ■ and (w, h) ∈ Best (w, hw) M, (w, h ) ⊨ !■x ¨¨ ¨¨ x ¨¨ ¨¨ ¨ w  ∙ Exception: M, (w , hw) ⊨ ■ for some (w , h ) ∈ such ¨ ¨¨ ¨¨ that ⊇ and (w, h)ℜ(w , h ) x r ∙ Positivity: M, (w, hw) ⊨ ■ and (w, h) ∈ Best (w, hw) ∙ Uniqueness: M, (w¨, h¨ ) ⊨ ■x for no (w¨, h¨ ) ∈ Bestr(w, h ) x w w w M, (w, hw) ⊨ !■ ¨¨ ¨¨ x ¨¨ ¨¨ ¨ ∙ Exception: M, (w , hw) ⊨ ■ for some (w , h ) ∈ such ¨ ¨¨ ¨¨ that ⊇ and (w, h)ℜ(w , h )

x ■ is true at (w, hw) and (w, hw) is a member of the reasons-wise optimality set and there x exists an excepting moment/history pair. In other words, !■ is true at (w, hw) if, and x x only if, ■ is true at (w, hw) because the ■ is true at (w, hw) and (w, hw) is a member of the reasons-wise optimality set. Strictly speaking, this will but tend to mean that that x reasons play the appropriate role in the production of ■. x ! is discharged most reasons. The formula !■ is true at (w, hw) if, and only x if, ■ is true at (w, hw) and (w, hw) is a member of the reasons-wise optimality set and there exists an excepting moment/history pair but no excepting moment/history pairs are members of the optimality set. Strictly speaking, again, this will tend to mean that that x reasons play the appropriate role in the production of ■. Reasons-wise modals tend to attach to things where the reasons play the appropriate role in their occurrence. Only a tendency is guaranteed because it is possible for something to occur in reasons-wise optimific moment/history pair despite its lack of accord with reasons. Maybe it isn’t something that reasons favor or disfavor. Maybe its disfavor is washed out or swamped by a sufficient number of other things that reasons smile upon. To be clear, WWCD implies the counterintuitive consequence that a performance can be reasons-wise permissible or obligatory despite the fact that it is not itself individually favored by reasons. The counterintuitive consequence can be defended on philosophical grounds. Though I offer an extended defense in Chapter5, it is worth outlining the thrust of the idea. The overall reasons-wise value of a moment/history pair is a function of its reasons-wise value atoms. When an agent has more reason for one option than another option, then, ceteris paribus, the moment/history pairs at which the one option is realized are reasons-wise better than the moment/history pairs at which the other option is realized. Depending on the variety of reasons, a multitude of such evaluations must take place for a plurality of different options. Yet, the ‘most reason’ and ‘some reason’ devices speak with a single voice. What We Can Do 70

When there is, or an agent has, most reason for a number of different performances, then it is univocally true of all that each stands in the appropriate relation to the relevant most reasons. So, too, with some reasons. My point is that the natural choice for preserving the pretheoretic behavior of reasons-wise locutions is to define the modalities in the way that WWCD does: by appeal to reasons-wise optimific world-moment/world-history pairs. This entails the counterintuitive consequence. Denying the consequence means that the reasons-wise modalities do not speak with a single voice.

The Theory of Intentional Action and Knowledge

WWCD makes possible an integrative theory of intentional action and knowledge. Both praxeological modalities are deﬁnable from already existing machinery, and so are in this sense derived. Table 2.19 displays the WWCD semantics for derived monadic praxeological modalities at normal moment/history pairs.

Table 2.19: WWCD Normal Semantics: Derived Monadic Praxeological Modalities

Operator Definition

∙ Intention: M, (w, hw) ⊨ [ ] M, (w, hw) ⊨ [ ] ∙ Action: M, (w, hw) ⊨ [] ∙ Nomic Connection: M, (w, hw) ⊨ ▣([ ] → []) ∙ Justified Belief: M, (w, hw) ⊨  ![ ] M, (w, hw) ⊨ [ ] ∙ True Belief: M, (w, hw) ⊨ [ ]! ∙ Epistemic Connection: M, (w, hw) ⊨ ▣( ![ ] → [ ]!)

[ ] is the modality of intentional action. Philosophically, [ ] means that the agent

intentionally brings it about that . The formula [ ] is true at (w, hw) if, and only if, [ ]

is true at (w, hw), [] is true at (w, hw), and every contextually salient abilitively accessible

moment/history pair at which [ ] is true is such that [] is also true. Simplifying,

[ ] is true at (w, hw) if, and only if, there is a nomically safe connection at (w, hw) between what the agent intends at (w, hw) and what the agent is causally responsible for at (w, hw). The semantics approximates the intuition that intentional action is causal responsibility because intentionality.

[ ] is the modality of propositional knowledge. Philosophically, [ ] means that

the agent knows that . The formula [ ] is true at (w, hw) if, and only if,  ![ ] is

true at (w, hw),  ! is true at (w, hw), and every contextually salient abilitively accessible moment/history pair at which  ![ ] is true is such that is also true. Simplifying,

[ ] is true at (w, hw) if, and only if, there is an epistemologically safe connection at (w, hw)

between what the agent justiﬁedly believes at (w, hw) and what the agent accurately be- 2.4. The WWCD Framework 71

lieves at (w, hw). The semantics approximates the intuition that propositional knowledge is true belief because justification. Officially, the analysis of knowledge invokes a discharged justification operator,  !, not presently defined in WWCD. The notation is operationalized in Chapter4. Presently, the formula  ![ ] means that the agent’s belief that is epistemically justified (given some distinctly epistemic evaluative criteria). Until operationalized, the justification modality should be swapped out for one of the reasons modalities, either  or , at the reader’s option. The substitution is viable because epistemically justified beliefs are, roughly, held in virtue of what overall epistemic reasons recommend. Formally, the substitution makes the analysis of knowledge mathematically tractable because reasons modalities are defined in WWCD. Happily, the substitution is permissible because, as I will later show, the justification modality is interdefinable with the reasons modalities. The nomic connection and epistemic connection conditions are variants of the basis safety condition for dyadic praxeological modalities. The broad aim of all these basis safety conditions, variant or nonvariant, is to explain the success of the consequent in terms of the antecedent. When safely based, a performance is successful because—but not necessarily only because—its basis. In this way, the nomic connection condition requires that intentionality explains causal responsibility and the epistemic connection condition requires that justified belief explains true belief. Just as the dyadic praxeological modalities are consistent with overdetermination, the intentional action and propositional knowledge modalities are consistent with overdetermination. In other words, it is allowed that an agent’s causal responsibility for the fact that is overdetermined by a plurality of intentions and it is allowed that an agent’s true belief that is overdetermined by a plurality of justified beliefs. Assuming some basic logical proficiency, for example, both an agent’s true belief that and causal responsibility for the fact that might be overdetermined in some cases where the agent both intends and justifiedly believes both and the biconditional ( ↔ ). Instances of an agent intentionally acting for reasons or knowing on the basis of reasons invoke dyadic variants of the intentional action and propositional knowledge modalities. Luckily, it is possible to define dyadic variants representing the satisfaction of some basis. Table 2.20 displays the instantiated definitions for derived dyadic praxeological modalities at normal moment/history pairs. The dyadic variants of the intentional action and propositional knowledge modalities merely instantiates the WWCD schema for dyadic praxeological modalities. As such, the dyadic variant of a praxeological modal is true at (w, hw) if, and only if, the monadic variant is true at (w, hw), the basis is true at (w, hw), and the basis of performance is safe at (w, hw). What We Can Do 72

Table 2.20: WWCD Normal Semantics: Derived Dyadic Praxeological Modalities

Operator Definition

∙ Intentional Action: M, (w, hw) ⊨ [ ] M, (w, hw) ⊨ [ ](∕ ) ∙ Basis: M, (w, hw) ⊨ [] ∙ Basis Safety: M, (w, hw) ⊨ ▣([] → [ ]) ∙ Propositional Knowledge: M, (w, hw) ⊨ [ ] M, (w, hw) ⊨ [ ](∕ ) ∙ Basis: M, (w, hw) ⊨ [] ∙ Basis Safety: M, (w, hw) ⊨ ▣([] → [ ])

Nonnormal Semantics

Truth assignment at world-moment/world-history pairs is patterned in the usual way in branching tree structures. Truth assignment at mind-moment/mind-history pairs is patterned after Rantala structures, which assigns truth-values to formulas anarchically at counterpossibles.23 Table 2.21 displays the formal semantics for some subset of WWCD formulas at nonnormal moment/history pairs.

Table 2.21: WWCD Nonnormal Semantics

Operator Definition

M, (m, hm) ⊨ ℑ−(, (m, hm)) = 1

Truth assignment at nonnormal moment/history pairs is quite simple: well-formed formulas behave like atomic formulas. More explicitly, a well-formed formula, , is true at

a mind-moment/mind-history pair, (m, hm), if, and only if, the nonnormal interpretation

function, ℑ−, assigns truth-value 1 to at (m, hm); otherwise, is false at (m, hm). In this way, for example, it is possible that both and ¬ are true at (m, hm) and, further, that the

conjunction ( ∧ ¬) is false at (m, hm).

2.4.4 WWCD Syntax In this subsection, I sketch some of the axiom schemata, inference rules, and theorems for

WWCD extending ℒBT not already covered by the discussion of branching tree structures. Strictly speaking, WWCD is a normal modal logic because it admits rules RN▣ and axiom schemata K▣ in addition to the analogues of rule RN and axiom K for tense modalities. The subsubsections are thematically divided among rules, axioms, and theorems. In an eﬀort to eliminate the unnecessary duplication of tables, I continue with the symbolic shorthand. Let ■ be a symbolic variable ranging over all of the WWCD modalities

23 Compare with Rantala (1982), Wansing (1990), and Berto (2013). 2.4. The WWCD Framework 73

□, ⊡, ℙ, F , S, [], [ ], [], [ ], [ ], or [ ] such that ■ can equally understood to mean any of □, ⊡, ℙ, F , S, [], [ ], [], [ ], [ ], or [ ]. Observe that the only modalities that ■ does not range over are the reasons modalities. Furthermore, let ■x be a symbolic variable ranging over all of the WWCD praxeological modalities [],

[ ], [], [ ], [ ], or [ ] such that ■x can equally understood to mean any of [],

[ ], [], [ ], [ ], or [ ].

Proof Rules

WWCD contains all the ℒBT proof rules and more besides. Table 2.22 displays some of the standard WWCD proof rules.

Table 2.22: WWCD Inference Rules

Rule Name Rule Schema RN▣ If ⊢ , then ⊢ ▣

RN ▣ If ⊢ ¬, then ⊢ ¬ ▣ RN[] If ⊢ ¬, then ⊢ ¬[] RN[] If ⊢ ¬, then ⊢ ¬[] RN[ ] If ⊢ ¬, then ⊢ ¬[ ] RN[ ] If ⊢ ¬, then ⊢ ¬[ ] RM▣ If ⊢ → , then ⊢ ▣ → ▣ RM[] If ⊢ → , then ⊢ [] → [] RM[] If ⊢ → , then ⊢ [] → [] RR▣ If ⊢ ( ∧ ) → , then ⊢ ▣( ∧ ) → ▣ RR[] If ⊢ ( ∧ ) → , then ⊢ []( ∧ ) → [] RR[] If ⊢ ( ∧ ) → , then ⊢ []( ∧ ) → [] RE▣ If ⊢ ↔ , then ⊢ ▣ ↔ ▣ RE[] If ⊢ ↔ , then ⊢ [] ↔ [] RE[] If ⊢ ↔ , then ⊢ [] ↔ [] Closure▣ ▣, ▣( → ) ⊢ ▣ Closure[] [], []( → ) ⊢ [] Closure[] [], []( → ) ⊢ []

Summarily, by inspecting the valid versions of rules RN, RM, RR, and RE, the table suggests that the belief, intention, intentional action, and knowledge modalities are all nonclassical, whereas the compulsion, being, and doing modalities are all classical. The table additionally suggests that the being and doing modalities are nonnormal, whereas the compulsion modality is normal. The rule Closure■x is valid for the compulsion, being, and doing modalities, but is invalid for the belief, intention, intentional action, and knowledge modalities. More explicitly, it is false that the agent believes, intends, intentionally brings about, or knows What We Can Do 74

every logical consequence of what the agent already believes, intends, intentionally does, or knows. Philosophically, this means that agents are neither logically omnipotent nor logically omniscient in WWCD. Closure■x fails for intentional action and knowledge because agent might fail to intend or believe some of the logical consequences of what they intentionally do or know. The agent might fail to so believe or intend owing to cognitive imperfection. Agents with stronger cognitive or conative powers can be modeled in WWCD by imposing constraints upon the behavior of the nonnormal interpretation function. I want to pay special attention the the epistemic variant of Closure■x . Plainly, the

inference rule Closure[ ] may be stated as follows: if the agent knows that , and the agent knows that entails , then the agent knows that . Epistemologists roundly deny this principle.24 Paradigmatic counterexamples invoke cases in which the agent fails to believe that . Since belief is a requirement of knowledge, the failure to relevantly believe suﬃces for the failure to relevantly know. Happily, WWCD agrees with epistemology’s substantive diagnosis. With few exceptions, it is generally thought that knowledge is closed under known 25 entailment. The lesson learned from the failure of Closure[ ] is that knowledge closure principles need to be sensitive to the agent’s limited cognitive life. John Hawthorne (2004) nicely states two of perhaps the most famous improved knowledge closure principles:

∙ Single Premise Closure (SPC): If knows that , competently deduces from , and thereby comes to believe that , while retaining the knowledge that throughout, then knows that (2004: 34).

∙ Multi-Premise Closure (MPC): If knows that 1, … , n, competently deduces

from 1, … , n, and thereby comes to believe that , while retaining the knowledge that

1, … , n throughout, then knows that (2004: 33).

The main thing to note is that both are limited to what the agent believes on the basis of competent deduction. The only interesting diﬀerence between Hawthorne’s two principles is how many premises may be cited in the competent deduction. SPC permits the closure of knowledge over competent deduction from exactly one premise. MPC permits the closure of knowledge over competent deduction from any number of premises. Whereas the former is uncontroversial, the latter is contentious.26 In WWCD, a version of the former

24 See John Hawthorne (2004) for citations and discussion. 25 Fred Dretske (1970) and Robert Nozick (1981) are the locus classicus of knowledge closure denialism. 26 Henry Kyburg (1961) offers an early version of the now-standard worry that MPC fails because, roughly, epistemic risks can accumulate over many premises such that a deductively valid inference is insufficiently probable. See Richard Foley (1992) for a recent statement of the objection. 2.4. The WWCD Framework 75 is a valid inference rule (no matter the conception of epistemic justification), but the latter may be valid or invalid depending on the preferred conception of epistemic justification. Fully rendered, the WWCD knowledge closure principles analogous to Hawthorne’s originals are as follows:

Single Premise Knowledge Closure (SPKC)

[ ]( ∧ □( → )), [ ]( ∕[ ]( ∧ □( → ))), ▣( ![ ] → ) ⊢ [ ] «¯¬ «¯¬ «¯¬ «¯¬ know ( and entails ) believe because it is deduced from epistemic connection know

Multi-Premise Knowledge Closure (MPKC)

[ ], [ ]□( → ), [ ]( ∕[ ] ∧ [ ]□( → )), ▣( ![ ] → ) ⊢ [ ] «¯¬ «¯¬ «¯¬ «¯¬ «¯¬ know know entails believe because it is deduced from epistemic connection know

As I hope is clear, SPKC and MPKC are the WWCD analogues, respectively, of SPC and MPC. There are three important differences between the Hawthorne and WWCD closure principles. First, Hawthorne’s originals include a knowledge retention clause lacked by WWCD’s analogues. Hawthorne intends his principles to apply synchronically or diachronically, whereas the WWCD rules are strictly synchronic. Second, Hawthorne requires that the deductively-based belief is competent, but the WWCD analogues don’t. Hawthorne does not explain what a competent deduction is, but I suspect that worries about incompe- tent deductions are covered by the third difference. Third, the WWCD knowledge closure principles include an epistemic connection clause lacked by the Hawthorne originals. The last difference is potentially very important and I’ll return to discuss it in later chapters. The analysis of knowledge should determine which knowledge closure principles are valid or invalid. As I see it, knowledge is modalized justified true belief; or, true belief whose justification tracks truth. In WWCD, both the justified belief and epistemic connection conditions impose modal requirements upon knowledge. The belief that is epistemically justified if, and only if, roughly, the agent believes that for most/some epistemic reason. The belief that is epistemically connected if, and only if, roughly, the agent justifiedly believes that only if the agent accurately believes that in all the contextually salient abilitively accessible moment/history pairs; or, simplifying, justified belief tracks truth across the relevant accessible moment/history pairs. SPKC is a valid WWCD inference rule no matter whether epistemic justification is a reasons-wise obliging or reasons-wise permitting notion. MPKC is valid if epistemic What We Can Do 76

justification is tantamount to believing for most reason, but invalid if justification is tantamount to believing for merely some reason. This is reflected by the reasons to believe closure principles:

Single Premise Some Reason to Believe Closure (SPSRBC)

![ ]( ∧ □( → )), [ ]( ∕[ ]( ∧ □( → ))) ⊢ ![ ] «¯¬ «¯¬ «¯¬ justiﬁedly believe ( and entails ) believe because it is deduced from justiﬁedly believe

Single Premise Most Reason to Believe Closure (SPMRBC)

![ ]( ∧ □( → )), [ ]( ∕[ ]( ∧ □( → ))) ⊢ ![ ] «¯¬ «¯¬ «¯¬ justiﬁedly believe ( and entails ) believe because it is deduced from justiﬁedly believe

Multi-Premise Most Reason to Believe Closure (MPMRBC)

justifiedly believe entails ©®ª ![ ], ![ ]□( → ), [ ]( ∕[ ] ∧ [ ]□( → )) ⊢ ![ ] «¯¬ «¯¬ «¯¬ justifiedly believe believe because it is deduced from justifiedly believe

All three reasons to believe closure principles are valid WWCD inference rules. Running under the assumption that epistemic justification is belief held for epistemic reasons, SPSRBC and SPMRBC agree that justified belief is closed over deduction from a single premise. There is no multi-premise variant for epistemic justification conceived as belief held for some epistemic reason, but MPMRBC says that justified belief is closed over deduction from multiple premises. Because knowledge requires epistemic justification, the failure of multi-premise closure for the discharged some reason modality explains why MPKC is false for epistemic justification conceived as belief held for some epistemic reason. By the same token, the validity of MPMRBC is corroborates MPKC for epistemic justification conceived as belief held for most epistemic reason. The reasons to believe closure principles instantiate reasons-wise WWCD inference meta-rules. They may be stated as follows: 2.4. The WWCD Framework 77

Single Premise Some Reason Closure (SPSRC)

■x because of/based upon ■x ©®ª !■x ( ∧ ( → )), ■x ( ∕■x ( ∧ ( → ))) ⊢ !■x «¯¬ «¯¬ some reason to ■x ( and implies ) some reason to ■x

Single Premise Most Reason Closure (SPMRC)

■x because of/based upon ■x ©®ª !■x ( ∧ ( → )), ■x ( ∕■x ( ∧ ( → ))) ⊢ !■x «¯¬ «¯¬ most reason to ■x ( and implies ) most reason to ■x

Multi-Premise Most Reason Closure (MPMRC)

■x because of/based upon ■x ©®ª !■x ( ∧ ( → )), ■x ( ∕■x ( ∧ ( → ))) ⊢ !■x «¯¬ «¯¬ most reason to ■x ( and implies ) most reason to ■x

As made evident by inspection, SPSRBC is a variant instantiator of SPSRC, SPMRBC is a variant instantiator of SPMRC, and MPMRBC is a variant instantiator of MPMRC.

Axiom Schemata

WWCD contains all the ℒBT axiom schemata and more besides. Table 2.23 displays some of the standard WWCD axiom schemata. WWCD has—and lacks—several noteworthy axiom schemata. I’ll mention but a few, but the essentials of the discussion apply equally well elsewhere. The first noteworthy point is that the Dual■x axiom schema so fundamental to so many modal logics fails for all praxeological modalities. More specifically, the implication (¬■x ¬ → ◆x ) fails. This is obvious insofar as no duals for any of the praxeological modals are defined in WWCD. But the philosophical motivation runs deeper than mathematical convenience. If it is false that, say, the agent is such that ¬, it doesn’t thereby follow that the it is consistent with the agent’s powers to be such that . It might be the case that neither nor ¬ expresses anything at all about the agent. Pick any proposition that cannot be appropriately paraphrased to make an agent the subject. Mutatis mutandis for nonintentional action. If the agent isn’t causally responsible for the fact that ¬, it cannot What We Can Do 78

Table 2.23: WWCD Axiom Schemata

Axiom Name Axiom Schema

E▣ ▣ ↔ ¬ ▣ ¬ N▣ ▣⊤

N ▣ ¬ ▣ ⊥ N[] ¬[]⊥ N[] ¬[]⊥ N[ ] ¬[ ]⊥ N[ ] ¬[ ]⊥ M▣ ▣( ∧ ) → (▣ ∧ ▣ ) M[] []( ∧ ) → ([] ∧ [] ) M[] []( ∧ ) → ([] ∧ [] ) C▣ (▣ ∧ ▣ ) → ▣( ∧ ) C[] ([] ∧ [] ) → []( ∧ ) C[] ([] ∧ [] ) → []( ∧ ) R▣ ▣( ∧ ) ↔ (▣ ∧ ▣ ) R[] []( ∧ ) ↔ ([] ∧ [] ) R[] []( ∧ ) ↔ ([] ∧ [] ) K▣ ▣( → ) → (▣ → ▣ )

D▣ ▣ → ▣ T▣ ▣ → T[] [] → T[] [] → T[ ] [ ] → T[ ] [ ] → thereby be inferred that it is consistent with the agent’s causal powers that . It might be the case that, say, ¬ is true but happens to express a fact with respect to which it is impossible for the agent to exert any causal inﬂuence. Pick any proposition whose truth is a matter of pure chance. I trust that the reader can extrapolate the rationale and apply it to the remaining praxeological modalities. The second noteworthy point is that the N■x axiom schema fails for all praxeological modalities. More explicitly, it is false that, for every tautology, the agent is, believes, does, intends, intentionally bring about, and knows the tautology. I take this to indicate that WWCD models imperfect agents that are neither logically omnipotent nor logically omniscient. In fact, even the variant of N■x that excluding contradictions fails for belief and intention operators! It is possible in WWCD for an agent to believe or intend contradictions. I think this a desirable consequence of the anarchical nature of nonnormal moment/history pairs, but can be avoided, if so wished, by imposing constraints on mind-moments. It is, however, impossible in WWCD for an agent to intentionally bring about or know 2.4. The WWCD Framework 79

contradictions. The third, and final, noteworthy point is that the K■x axiom schema fails for the belief, intention, intentional action, and knowledge modalities. It fails for intentional action and knowledge, respectively, because the agent might fail to intend or believe the logical consequences of what they intentionally do or know. It fails for belief and intention because, again, nonnormal moment/history pairs are anarchical, but this agrees with intuition. A cognitively finite agent will inevitably fail to cognize all the logical consequences of what they cognize. Sometimes the agent will run out of mental space and sometimes the consequences will be too complex for the agent to process. If the agent is anything like a typical human being, the agent will also sometimes suffer bouts of idiocy and simply fail to take notice of the obvious.

Table 2.24: WWCD Reasons-Wise Axiom Meta-Schemata

Axiom Name Axiom Meta-Schema N ¬⊥ M■x (■x ∨ ■x ) → ■x ( ∨ ) M■x ■x ( ∧ ) → (■x ∧ ■x ) C■x ■x ( ∨ ) → (■x ∨ ■x ) C■x (■x ∧ ■x ) → ■x ( ∧ ) R■x (■x ∨ ■x ) ↔ ■x ( ∨ ) R■x ■x ( ∧ ) ↔ (■x ∧ ■x ) K■x ■x ( → ) → (■x → ■x ) D■x ■x → ■x T!■x !■x → ■x

There are variants of many of the axiom schemata for the reasons modalities. These variants are displayed by Table 2.24 for both some reason and most reason modalities. It is absolutely crucial to observe that the reasons modalities do not outstrip the praxeological modalities. When ■x is instantiated as a speciﬁc praxeological modality, some of the aforementioned reasons-wise axiom schemata may fail, depending on whether—and which—of the analogous axiom schemata fail for the instantiated praxeological modality. In other words, whatever axiom schemata fail for the instantiated praxeological modalities must likewise fail for the reasons modalities because the latter supervene upon the former.

Interaction Theorems

Interaction theorems describe how diﬀerent modalities in a polymodal logic interact with one another. They can be seen as a kind of mapping of the hierarchy of modal strength within a logic. As to be expected, WWCD has a number of interaction theorems. What We Can Do 80

I have elected to depict the mapping in the form of a lattice, where arrows between well-formed formulas depict direction of entailment. Bear in mind that entailments are transitive, obviating the need to depict every conceivable interaction between the relevant modalities. Figure 2.3 displays the interaction lattice for nonpraxeological modalities. Figure 2.4 displays the interaction lattice of praxeological modalities. There are two separate necessity lattices because there are no interactions between nonpraxeological and praxeological modalities.

Figure 2.3: Lattice of Nonpraxeological Interactions

□

⊡ ℙ F S

▣ ▣

⊡

◇

Figure 2.4: Lattice of Praxeological Interactions

[ ] [ ]

[ ] [ ] [] []

The lattice of nonpraxeological interactions may be summarized as follows. Alethic necessity implies all other nonpraxeological modalities. Contextually salient necessity implies abili-compulsoriness and contextually salient possibility. Abili-compulsoriness implies abili-consistency, which in turns implies contextually salient possibility, which in turn implies alethic possibility. The lattice of praxeological interactions may likewise be 2.4. The WWCD Framework 81

summarized as follows. Propositional knowledge implies propositional belief. Intentional action implies intention and causal responsibility. I want to brieﬂy turn attention a set of WWCD meta-theorems. Ishtiyaque Haji (2012, 2016) argues for a version of the following:

∙ Haji’s Law (HL): If has most/some reason to that , then is able to that and is able to otherwise than .27

The blank space should literally be ﬁlled in with a performance. HL is so-named in recognition of Haji’s pioneering work. The principle states that if an agent has has most/some reason to perform a performance, the agent is able to perform that performance and able to perform otherwise. As Haji says, HL is a reasons-wise variation of a famous deontic principle:

∙ Kant’s Law (KL): If it is obligatory for to that , then is able to that .28

27 Compare with the following passage from Ishtiyaque Haji (2012):

Indeed, the moral ‘ought’ implies ‘can’ principle appears just to be a more restricted verion of the following general principle that if you have most reason to do something, you can do it: Reasons-Wise ‘Ought’ Implies ‘Can’ (Reason Ought/Can): If has most reason to do something, A, and, thus, if reasons-wise ought to do A, then can do A (2012: 24).

Haji later goes on to argue for an alternate possibility requirement for reasons-wise and deontic modals. Essentially the same points are repeated and expanded upon in Haji (2016). 28 Like many other philosophers, G. E. Moore (1922) attributes the deontic principle to Immanuel Kant:

The philosopher Kant laid down a well-known proposition to eﬀect that ‘ought’ implies ‘can’: that is to say that it cannot be true that you ‘ought’ to do a thing, unless it is true that you could do it, if you chose (1922: 317).

The accuracy of the historical attribution does not matter for my purposes. Readers might be interested to know that Robert Stern (2004) explores the attributive accuracy and in the process cites a number of supporting passages:

Now this ‘ought’ expresses a possible action, the ground of which is nothing other than a mere concept, whereas the ground of a merely natural action must always be an appearance. Now of course the action must be possible under natural conditions if the ought is directed to it; but these natural conditions do not concern the determination of the power of choice itself, but only its eﬀect and result in appearance (Kant 1781: A548/B576).

Impulses of nature, accordingly, involve obstacles within the human being’s mind to his fulﬁllment of duty and (sometimes powerful) forces opposing it, which he must judge that he is capable of resisting and conquering by reason not at some time in the future but at once (the moment he thinks of duty): he must judge that he can do what the law tells him unconditionally that he ought to do (Kant 1785: 380). What We Can Do 82

KL states that if an agent has an obligation to perform a performance, the agent is able to perform that performance. HL is a genuine strengthening of KL. With respect to the antecedent, it expands the range of applicable deontic modals from mere obligations to include permissions and substitutes the deontic modals for reasons modals. With respect to the consequent, it adds to the commissive ability a corresponding excepting ability. Whereas KL imposes ability requirements for obligations, HL imposes dual ability requirements for reasons modals. Assuming the intersubstitutability of deontic modals and reasons modals, HL implies KL. Reactions to Haji’s arguments vary. I want to make clear that WWCD is sympathetic to the Hajian project, but does not explicitly endorse it. The following variants of KL are WWCD meta-theorems:

x x KL/MR. ■ → ▣ ■ Kant’s Law/Most Reason

x x KL/SR. ■ → ▣ ■ Kant’s Law/Some Reason

Jointly call these the Kantian reasons meta-theorems. They say that reasons modalities imply corresponding commissive ability. The proof showing that the Kantian reasons meta- theorems are contained in WWCD is straightforward. The positivity condition of the first formulation and jointly the commission and favorability conditions of the second formulation entail the Kantian reasons meta-theorems. Roughly, reasons modalities are defined by appeal the agent’s performances across the reasons-wise optimific moment/history pairs, where a moment/history pair is optimific only if it is contextually salient and abilitively accessible. Since all members of the optimality set are accessible, and abilities are defined by appeal to what an agent does in accessible moment/history pairs, it follows that an agent has the ability to performance whatever they have most/some reason to perform. So, too, are the following WWCD meta-theorems:

x x ∗ x HL/MR. ■ → ( ▣ ■ ∧ ▣ ■) Haji’s Law/Most Reason

x x ∗ x HL/SR. ■ → ( ▣ ■ ∧ ▣ ■) Haji’s Law/Some Reason

Jointly call these the Hajian meta-theorems. They say that reasons modalities imply corresponding commissive ability and some kind of excepting ability. Strictly speaking, the kind of ability to do otherwise may not be exercisable in the salient context, which

For if the moral law commands that we ought to be better human beings now, it inescapably follows that we must be capable of being better human beings (Kant 1793: 6:50). 2.5. Adequacy Desiderata Satisﬁed 83

I’ve indicated above with a superscripted asterisk noting the diﬀerence in ability between x ∗ x ▣ ■ and ▣ ■. The proof showing that the Hajian meta-theorems are contained in WWCD is no less straightforward. The commissive ability implication has already been demonstrated. The excepting ability implication is the consequence of the excepting condition. Roughly, both formulations of the reasons modalities require that there is an excepting moment/history pair, where the excepting pair is abilitively accessible and a member of the superset of contextually salient moment/history pairs. While it is possible that the excepting pair is contextually salient, it is not guaranteed, meaning that the excepting ability implied by reasons modalities is logically weaker than its commissive counterpart. To get a sense of the diﬀerence, consider the following claims:

x x ∗ x ( ▣ ■ ∧ ¬ ▣ ■ ∧ ▣ ■)

x ∗ x (▣■ ∧ ▣ ■)

Both of the above formulas are two different ways of expressing some case in which an agent is both locally compelled to perform some performance and able—for a less localized notion of ability—to do otherwise. I take it that John Locke’s famous case of a man who is unknowingly locked in a room but decides of his own accord to not leave instantiates such a combination of modalities. So, too, might paradigmatic Frankfurt cases be examples of local compulsion plus nonlocal ability to do otherwise. My point is that the Hajian meta-theorems are weaker than HL because they are consistent with such cases, but HL is intended to be inconsistent with them. It is possible to strengthen the Hajian meta-theorems to more perfectly match the intended understanding of HL by tweaking the excepting condition of reasons modalities. Very simply, the tweak would require that the excepting moment/history is as contextually salient as the commissive moment/history pair, which is achieved by locating the excepting pair in the very same context set containing the commissive pair used to define either the first formulation’s positivity condition or the second formulation’s commission condition. I have declined such a revision because it is philosophically contentious and because it outstrips my professed motivation for the exception condition.

2.5 Adequacy Desiderata Satisﬁed

In this section, I show that WWCD satisﬁes the adequacy desiderata. What We Can Do 84

2.5.1 Satisfying Mele’s Constraint

Recall Mele’s Constraint:

∙ Mele’s Constraint: An adequate logic of ability must be able to characterize and distinguish the twelve possible interpretations for each applicable praxeo-abilitive molecular compound.

In effect, the constraint requires that an adequate praxeo-abilitive logic respects the three distinctions between: first, capabilities, general abilities, and specific abilities; second, simple abilities and competent abilities; and, third, nonperformative abilities and performative abilities. The substance of the distinctions is borne out by an analysis that appreciates the elements of the canonical praxeo-abilitive compound form.

Abilitive Index ©®ª Agent can at time t that at time t¨. «¯¬ Praxeological Index The abilitive index ascribes an abilitive ‘can’ to an agent and takes the praxeological index as its object. The praxeological index ascribes some praxeological modal (e.g., ‘be’, ‘believe’, ‘do’, ‘know’) to the agent and takes a well-formed formula as its object. Broadly, the form describes an abilitively possible way for an agent to be. WWCD satisﬁes Mele’s Constraint because it appreciably distinguishes between the elements of the canonical praxeo-abilitive compound form and permits contextual quantiﬁcation over the domain of possible moments. The subsections are thematically divided among the abilitive and praxeological indices and the last shows how they interact.

Variations on the Abilitive Index

The distinction between capabilities, general abilities, and specific abilities is achieved by attending to the abilitive index. Roughly, an agent can be, do, intend, intentionally do, or know something if, and only if, the agent is, does, intends, intentionally does, or knows that thing in some relevant abilitively accessible world-moment/world-history pair. Capabilities quantify over all abilitively accessible world-pairs in the domain; or, perhaps, all abilitively accessible world-pairs occurring at the same time or later than the moment/history pair of evaluation. General abilities quantify over all abilitively accessible world-pairs that are temporally co-occurring with the moment/history pair of evaluation. Specific abilities quantify over all abilitively accessible world-pairs that are nearby to, and temporally co-occurring with, the moment/history pair of evaluation. 2.5. Adequacy Desiderata Satisfied 85

The distinction between capabilities, general abilities, and speciﬁc abilities is ultimately

understood as a diﬀerence in the paramaterization of the domain. Let (w, hw) be the relevant normal moment/history pair of evaluation. The relevant parameterizations deﬁning the

membership conditions for are as follows:

∙ Capability Parameterization: Assuming that capabilities are deﬁned from all accessible normal moment/history pairs, Λ receives a null parameterization: Λ sorts all

world-pairs from Pair into , excluding none because is empty. Assuming that capabilities are deﬁned from present or future accessible normal moment/history pairs, ¨ ¨ Λ is inclusively temporally parameterized: Λ sorts all and only the world-pairs, (w , hw), ¨ ¨ from Pair into such that (w, hw) ⩽ (w , hw). ∙ General Ability Parameterization: Λ is exclusively temporally parameterized: Λ sorts (w¨, h¨ ) Pair (w, h ) ≈ (w¨, h¨ ) all and only the world-pairs, w , from  into such that w  w . ∙ Specific Ability Parameterization: Λ is similarly-wise parameterized: Λ sorts ll and ¨ ¨ ¨ ¨ only the world-pairs, (w , hw), from Pair into such that (w, hw) and (w , hw) are past- (w, h ) ≈ (w¨, h¨ ) wise indiscernible and w  w .

To be clear, the above parameterizations deﬁne the membership conditions of as a way of determining whether the abilitive index denotes a capability, general ability, or speciﬁc ability. An unparameterized domain is the same as a null parameterization and therefore denotes capability.

Variations on the Praxeological Index

The distinctions between, on the hand, simple and competent abilities and, on the other hand, nonperformative and performative abilities, is achieved by attending to the praxeological index. An ability is simple or competent by virtue of taking a simple or competent praxeological modal as its object. An ability is nonperformative or performative by virtue of taking a nonperformative or performative praxeological modal as its object. Begin with the distinction between simple and competent praxeological modals. Roughly, an agent simply is, does, intends, intentional does, or knows something if, and only if, the agent is, does, intends, or knows that thing in one relevant abilitively accessible world-moment/world-history pair; or, in all abilitively accessible world-moments that are content-wise indiscernible from the normal moment/history pair of evaluation. Simple praxeological modals quantify over a single world-pair; or, all content-wise indiscernible world-pairs. Roughly, an agent competently is, does, intends, intentionally does, or knows something if, and only if, the agent is, does, intends, intentionally does, What We Can Do 86

or knows across all of the relevantly abilitively accessible world-moment/world-history pairs. Competence can be evaluated on a spectrum. Modest competence quantifies over all abilitively accessible world-pairs that are nearby to, and temporally co-occurring with, the moment/history pair of evaluation. Most competence quantifies over all abilitively accessible world-pairs that are temporally co-occurring with the moment/history pair of evaluation. Put a different way, praxeological modals of modest competence obey Specific Ability Parameterization and praxeological modals of most competence obey General Ability Parameterization. Common sense competence lies somewhere between the two extremes, quantifying over a sufficiently large set of moment/history pairs that are varyingly dissimilar from both each other and the moment/history pairs of evaluation in the relevant respects. The distinction between simple and competent praxeological modalities is ultimately

understood as a diﬀerence in the paramaterization of the domain. Let (w, hw) be the relevant normal moment/history pair of evaluation. The relevant parameterizations

deﬁning the membership conditions for are as follows:

∙ Simple Parameterization: Assuming that simple praxeological modals are deﬁned from a single normal moment/history pair, Λ receives an identity parameterization:

Λ sorts exactly one world-pair from Pair into , excluding all except (w∕hw) itself. Assuming that simple praxeological are deﬁned from content-wise indiscernibility, Λ is inclusively exclusively content-wise parameterized: Λ sorts all and only the normal ¨ ¨ ¨ ¨ moment/history pairs, (w ∕hw), from Pair into such that (w∕hw) and (w ∕hw) agree on truth assignments for all well-formed formulas.

∙ Competent Parameterization: Λ is inclusively dissimilarly parameterized: Λ sorts all ¨ ¨ ¨ ¨ and only the world-pairs, (w ∕hw), from Pair into such that (w∕hw) and (w ∕hw) are w ≈ w¨ relevantly dissimilar and  .

To be clear, again, the above parameterizations deﬁne the membership conditions of as a way of determining whether the praxeological index denotes a simple or competent praxeological modal. Turn now to the distinction between nonperformative and performative praxeological modals. Roughly, an agent’s being, believing, doing, intending, intentionally doing, or knowing something is performative if, and only if, the agent is, believes, does, intends, intentionally does, or knows that thing for reasons; otherwise, the praxeological modal is nonperformative. This corresponds to the intuition that performances are based upon, caused by, or otherwise relevantly sensitive to, the agent’s reasons. The satisfaction of the 2.5. Adequacy Desiderata Satisﬁed 87

basing relation is denoted by appeal to dyadic operators. Performances are denoted by dyadic operators conditioned upon reasons. The distinction between nonperformative and performative praxeological modalities is ultimately understood by appeal to what, if anything, the modal is conditioned upon. Recall that ■x is a symbolic variable ranging over all praxeological modalities. The relevant criteria for performativity are as follows:

∙ Nonperformative Critereon: A praxeological modal is nonperformative if, and only if, it fails to satisfy Performative Criterion.

∙ Performative Critereon: A praxeological modal is performative if, and only if, ■x (∕ ) r x r x at (w, hw), where stands for  ■,  ■, or some other well-formed formula denoting the presence of the relevant reasons upon which the performance is based.

As twice before, ﬁlling the praxeological index with a reasons-based praxeological modal results in a performative praxeological modal; nonperformative otherwise. To be clear, the above criteria deﬁne the performativity conditions of any praxeological modal.

Generating the Characteristic Praxeo-Abilitive Compounds

The abilitive and praxeological variants can be mixed and matched to form a sundry myriad of diﬀerent praxeo-abilitive compounds. Putting all the elements altogether, the recipe for generating any of the twelve possible praxeo-abilitive compounds is as follows:

1. Simple Nonperformative Capability:

∙ The abilitive index satisﬁes the Capability Parameterization. ∙ The praxeological index satisﬁes both the Simple Parameterization and the Non- performative Critereon.

2. Simple Nonperformative General Ability:

∙ The abilitive index satisﬁes the General Ability Parameterization. ∙ The praxeological index satisﬁes both the Simple Parameterization and the Non- performative Critereon.

3. Simple Nonperformative Specific Ability:

∙ The abilitive index satisﬁes the Specific Ability Parameterization. ∙ The praxeological index satisﬁes both the Simple Parameterization and the Non- performative Critereon. What We Can Do 88

4. Competent Nonperformative Capability:

∙ The abilitive index satisﬁes the Capability Parameterization. ∙ The praxeological index satisﬁes both the Competent Parameterization and the Nonperformative Critereon.

5. Competent Nonperformative General Ability:

∙ The abilitive index satisﬁes the General Ability Parameterization. ∙ The praxeological index satisﬁes both the Competent Parameterization and the Nonperformative Critereon.

6. Competent Nonperformative Specific Ability:

∙ The abilitive index satisﬁes the Specific Ability Parameterization. ∙ The praxeological index satisﬁes both the Competent Parameterization and the Nonperformative Critereon.

7. Simple Performative Capability:

∙ The abilitive index satisﬁes the Capability Parameterization. ∙ The praxeological index satisﬁes both the Simple Parameterization and the Per- formative Critereon.

8. Simple Performative General Ability:

∙ The abilitive index satisﬁes the General Ability Parameterization. ∙ The praxeological index satisﬁes both the Simple Parameterization and the Per- formative Critereon.

9. Simple Performative Specific Ability:

∙ The abilitive index satisﬁes the Specific Ability Parameterization. ∙ The praxeological index satisﬁes both the Simple Parameterization and the Per- formative Critereon.

10. Competent Performative Capability:

∙ The abilitive index satisfies the Capability Parameterization. ∙ The praxeological index satisfies both the Competent Parameterization and the Performative Critereon. 2.5. Adequacy Desiderata Satisfied 89

11. Competent Performative General Ability:

∙ The abilitive index satisﬁes the General Ability Parameterization. ∙ The praxeological index satisﬁes both the Competent Parameterization and the Performative Critereon.

12. Competent Performative Specific Ability:

∙ The abilitive index satisﬁes the Specific Ability Parameterization. ∙ The praxeological index satisﬁes both the Competent Parameterization and the Performative Critereon.

Recall that Table 2.1 depicts and numbers the twelve possible positions each praxeo- abilitive compound and assigns each a number. The above enumerated list corresponds to the table’s numbered positions. The WWCD recipe preserves the logical relations between the possible praxeo-abilitive positions depicted by Figure 2.1 in an obvious way.

2.5.2 Satisfying Kenny’s Constraint

Recall Kenny’s Constraint:

Recall that ⧆ abbreviates the multimodal praxeo-abilitive ‘can do’ compound, where

the formula ⧆ means that the agent is able to intentionally bring it about that . The constraint requires the failure of all the following theorems:

Table 2.25: Unacceptable Kenny Axiom Schemata

Axiom Name Axiom Schema

4 ⧆ ⧆ ⧆ → ⧆

T ⧆ → ⧆

C ⧆ ⧆ ( ∨ ) → ( ⧆ ∨ ⧆ )

In eﬀect, the constraint requires that an adequate praxeo-abilitive logic respects that agents have certain limitations, both cognitive and conative.

The ⧆ operator abbreviates a multimodal praxeo-abilitive compound. The WWCD variant of the unacceptable Kenny axiom schemata is generated by the uniform substitution

of ⧆ for ▣ [ ]. It may be depicted as follows: What We Can Do 90

Table 2.26: WWCD Variants of Unacceptable Kenny Axiom Schemata (for Intentional Action)

Axiom Name Axiom Schema

4 ▣ [ ] ▣ [ ] ▣ [ ] → ▣ [ ]

T ▣ [ ] → ▣ [ ]

C ▣ [ ] ▣ [ ]( ∨ ) → ( ▣ [ ] ∨ ▣ [ ] )

Kenny’s Constraint requires of WWCD that none are meta-theorems. Indeed, a perfectly generalized WWCD variant of the unacceptable Kenny axiom schemata can be generated x by uniformly substituting for ▣ ■. The generalized variant may be depicted as follows:

Table 2.27: WWCD Variants of Unacceptable Kenny Axiom Schemata (Generalized)

Axiom Name Axiom Schema x x x x 4 ▣ ■ ▣ ■ ▣ ■ → ▣ ■ x x T ▣ ■ → ▣ ■ x x x x C ▣ ■ ▣ ■( ∨ ) → ( ▣ ■ ∨ ▣ ■ )

x x x An inspection of the proof theory should reveal that none of 4 ▣ ■,T ▣ ■, or C ▣ ■ are WWCD meta-theorems. I’ll brieﬂy sketch the proofs for each and leave it to the reader to ﬁll in any remaining details.

x Proposition 2.5.1. 4 ▣ ■ is not a meta-theorem of WWCD.

x Proof. Let x be the neighborhood function from which ■ is deﬁned. No assumptions are made about its properties, but the proof nonetheless avoids violations of the properties

had by about or cause. Let all of the following conditions hold:

¨ ¨ ¨¨ ¨¨ ¨¨¨ ¨¨¨ ∙ Domain: Pair = {(w, hw), (w , hw), (w , hw), (w , hw )}

¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨¨ ¨¨ ∙ Accessibility Relations: (w, hw)ℜ(w, hw), (w, hw)ℜ(w , hw), (w , hw)ℜ(w , hw), (w , hw)ℜ(w , hw), ¨¨ ¨¨ ¨¨ ¨¨ ¨¨ ¨¨ ¨¨¨ ¨¨¨ ¨¨¨ ¨¨¨ ¨¨¨ ¨¨¨ (w , hw)ℜ(w , hw), (w , hw)ℜ(w , hw ), (w , hw )ℜ(w , hw )

¨ ¨ ¨ ¨ ¨¨ ¨¨ ¨¨ ¨¨ ∙ Neighborhood Relations: x(w, hw) = {(w, hw)}, x(w , hw) = {(w , hw), (w , hw)}, x(w , hw) = ¨¨ ¨¨ ¨¨¨ ¨¨¨ {(w , hw), (w , hw )} M M ¨¨ ¨¨ ¨¨¨ ¨¨¨ x ¨ ¨ ¨¨ ¨¨ ∙ Truth Sets: ‖‖ = {(w , hw), (w , hw )}, ‖ ▣ ■‖ = {(w , hw), (w , hw)}

x x The formula ▣ ■ ▣ ■ is true at (w, hw) if, and only if, there is a relevantly accessible ¨ ¨ x x x x ¨ ¨ moment/history pair, (w , hw), at which ■ ▣ ■ is true. In turn, ■ ▣ ■ is true at (w , hw) if, M M x ¨ ¨ x ¨ ¨ ¨¨ ¨¨ and only if, ‖ ▣ ■‖ ∈ x(w , hw). The set ‖ ▣ ■‖ = {(w , hw), (w , hw)}, and inspection M x ¨ ¨ x x shows that ‖ ▣ ■‖ ∈ x(w , hw). It follows that ▣ ■ ▣ ■ is true at (w, hw). 2.5. Adequacy Desiderata Satisﬁed 91

x The formula ▣ ■ is true at (w, hw) if, and only if, there is a relevantly accessible x ¨ ¨ moment/history pair at which ■ is true. The only candidates are (w, hw) and (w , hw). x M M ¨ ¨ So, ▣ ■ is true at (w, hw) if, and only if, either ‖‖ ∈ x(w, hw) or ‖‖ ∈ x(w , hw). x Inspection shows that neither obtains. It follows that ▣ ■ is false at (w, hw). x Consequently, 4 ▣ ■ is not a WWCD meta-theorem.

x Proposition 2.5.2. T ▣ ■ is not a meta-theorem of WWCD.

x Proof. Let x be the neighborhood function from which ■ is deﬁned. No assumptions are made about its properties, but the proof nonetheless avoids violations of the properties

had by about or cause. Let all of the following conditions hold:

¨ ¨ ∙ Domain: Pair = {(w, hw), (w , hw)}

¨ ¨ ¨ ¨ ¨ ¨ ∙ Accessibility Relations: (w, hw)ℜ(w, hw), (w, hw)ℜ(w , hw), (w , hw)ℜ(w , hw)

¨ ¨ ¨ ¨ ∙ Neighborhood Relations: x(w, hw) = {(w, hw)}, x(w , hw) = {(w , hw)}

M ¨ ¨ ∙ Truth Sets: ‖‖ = {(w, hw), (w , hw)}

Suppose that is true at (w, hw). x ▣ ■ is true at (w, hw) if, and only if, there is a relevantly accessible moment/history x ¨ ¨ x pair at which ■ is true. The only candidates are (w, hw) and (w , hw). So, ▣ ■ is true M M ¨ ¨ at (w, hw) if, and only if, either ‖‖ ∈ x(w, hw) or ‖‖ ∈ x(w , hw). Inspection shows x that neither obtains. It follows that ▣ ■ is false at (w, hw). x Consequently, T ▣ ■ is not a WWCD meta-theorem.

x Proposition 2.5.3. C ▣ ■ is not a meta-theorem of WWCD.

x Proof. Let x be the neighborhood function from which ■ is deﬁned. No assumptions are made about its properties, but the proof nonetheless avoids violations of the properties

had by about or cause. Let all of the following conditions hold:

¨ ¨ ∙ Domain: Pair = {(w, hw), (m, hm), (m , hm)}

∙ Accessibility Relations: (w, hw)ℜ(w, hw)

∙ Neighborhood Relations: x(w, hw) = {(w, hw), (m, hm)}

M M M ¨ ¨ ∙ Truth Sets: ‖ ∨ ‖ = {(w, hw), (m, hm)}, ‖‖ = ‖ ‖ = {(w, hw), (m , hm)}

x The formula ▣ ■( ∨ ) is true at (w, hw) if, and only if, there is a relevantly accessible

moment/history pair at which is true. In this case, the relevantly accessible pair is (w, hw) What We Can Do 92

x M itself. The formula ■( ∨ ) is true at (w, hw) if, and only if, ‖ ∨ ‖ ∈ x(w, hw) and x inspection shows that this obtains. It follows that ▣ ■( ∨ ) is true at (w, hw). x x The formula ▣ ■∨ ▣ ■ is true at (w, hw) if, and only if, there is a relevantly accessible moment/history pair at which either ■x or ■x is true. In this case, again, the relevantly x M accessible pair is (w, hw) itself. The formula ■ is true at (w, hw) if, and only if, ‖‖ ∈ x M x(w, hw) and ■ is true at (w, hw) if, and only if, ‖ ‖ ∈ x(w, hw). However, the sets M M ¨ ¨ ‖‖ = ‖ ‖ = {(w, hw), (m , hm)}, and inspection shows neither obtains. It follows that x x ▣ ■ ∨ ▣ ■ is false at (w, hw). x Consequently, C ▣ ■ is not a WWCD meta-theorem.

2.6 Conclusion

I have sketched a polymodal counterpossible branching tree framework for ability, action, belief, intention, knowledge, and reasons called What We Can Do (WWCD). The framework, and its complexity, is in part motivated by appeal to two adequacy desiderata. First, there are a number of theoretically crucial distinctions applicable to abilitive and praxeological modalities. The failure to respect the distinctions means that the formal theory is fundamentally impotent in the sense that it lacks sufficient expressive power to grapple with concepts at the heart of so many debates. Second, agent and their abilities are limited in various ways. A formal theory of ability shouldn’t unduly or implausibly idealize agents or their powers, cognitive or conative. Whereas much of the existing competition fails to meet all the adequacy desiderata, WWCD does not. WWCD is an elegant foundation for deontic theory. In the next chapter, I define a deontic extension. However the framework raises more questions and more issues than I have space to acknowledge. While the majority will continue to go unacknowledged, I think that there are worries about the WWCD analysis of knowledge that deserve attention. I devote space to the topic in the final chapter. CHAPTER 3

DOING THE BEST WE CAN

Abstract

I develop a general theory of deontic modals called Doing the Best We Can (DBWC) extending WWCD to account for obligation, permission, and kin. The philosophical upshot is that a robust deontic theory can be built out of a theory of performativity and an axiology.

3.1 Introduction

gents are intelligent creatures able to perform certain things. An agent can be certain A ways. An agent have have certain beliefs or intentions. An agent can bring certain things about. An agent can achieve knowledge. Aﬀective states, cognitive states, and conative states are performances insofar as they are products of powers responsive to reasons had by the agent. Deontic appraisals are the normative appraisal of possible performances for an agent. A performance type might be obligatory, permissible, impermissible, omissible, optional, or it might lack deontic status altogether for an agent. Deontic modals target praxeological modals. Deontic theory is a natural outgrowth of the theory of ability. To fully appreciate the range of possible deontic appraisals, we must return to the source. In this chapter, I lay out a formal theory—a modal logic—of obligation and kin. All are conceptualized through the lens of an agent’s suite of powers, both cognitive and conative. Broadly, deontic modals are deﬁned from value-wise rankings over the things the agent can do. I proceed in the tradition of the Massachusetts school, a family of teleological theories that analyze deontic modalities from the more fundamental notions of ability and value

93 Doing the Best We Can 94

using a broadly Chisholmian methodology.1 The Massachusettsian framework seizes upon a familiar insight beautifully elucated by Fred Feldman (1986):

There is a magniﬁcent old idea according to which the concept of obligation can be understood by appeal to the concepts of possibility and goodness. Roughly, the idea is that something is obligatory if and only if it is the best of the possibilities. This idea appears in very simple guise in the popular maxim that “you ought to do the best you can” (1986: 3).

That said, ‘ought’ should be replaced with ‘must’: one must do the best one can. My aim is to refine and precisify the Massachusettsian framework to give a general formal theory of untyped deontic modalities. As I see it, deontic modalities are typed by the currency of goodness that marks their trade. Epistemic, moral, prudential, et cetera, obligations (permissions, prohibitions, et cetera) are all deontic modals operationalized by some epistemic, moral, prudential, et cetera, axiology, respectively. A general theory of untyped deontic modalities is achieved by abstracting away from substantive axiology and using placeholder notions of value instead. In short, I attempt to capture the truth- conditions of what it is for a person to have an obligation (permission, prohibition, et cetera) of any type using counterpossible branching tree structures. The result is a sophisticated framework called Doing the Best We Can (DBWC).2 The intended purpose of this chapter is to sketch a general framework of praxeo- deontic modals. My hope for later chapters is to directly apply the framework to the analysis of deontic justification in general and epistemic justification in particular. The chapter is structured as follows. In Section 3.2, I highlight the normative phenomena of interest and sketch some preliminary conceptual distinctions. In particular, the abilitive distinctions drawn from the last chapter have a central role to play in filling out the ability requirements for various deontic modals. In Section 3.3, I motivate three adequacy desiderata for any praxeo-deontic logic worth its salt. In Section 3.4, I expound the philosophical foundations, formal semantics, and axiomatization for the DBWC framework. A number of philosophically substantive theses are vindicated by the framework. There are a number of interest theorems that interrelate deontic modals, ability modals, and reasons-wise modals. In Section 3.5, I argue that DBWC satisfies the adequacy desiderata. Finally, in Section 3.6, I conclude by summarizing the findings of the chapter.

1 See Chapter2 footnote2 for citations. 2 The framework is named in homage to F. Feldman (1986). 3.2. The Structure of Praxeo-Deontives 95

3.2 The Structure of Praxeo-Deontives

In this section, I elucidate the praxeo-deontic multimodal compounds of interest and discuss a number of crucial qualiﬁcations. Ultimately, the objects of interest ﬁt a praxeo-deontic multimodal compound form structurally similar to the praxeo-abilitive compound form. Some possible variations on the canonical praxeo-deontic form are as follows:

Agent can at time t that at time t¨.

Agent could at time t that at time t¨.

Agent may at time t that at time t¨.

Agent must at time t that at time t¨.

Agent ought at time t that at time t¨.

Agent shall at time t that at time t¨.

Agent should at time t that at time t¨.

Agent at time t that at time t¨.

The compounds is built up out of two components, namely the relevant deontic auxiliary and the relevant praxeological auxiliary. The former takes the latter as its propositional object and the latter takes a proposition as its propositional object. This structure can be made visually more perspicuous:

Deontic Index ©®ª Agent at time t that at time t¨. «¯¬ Praxeological Index

The deontic index of a praxeo-deontic compound functions to ascribe some deontic sense of ‘can’, ‘must’, ‘ought’, ‘shall’, ‘should’, or the like to the agent. The praxeological index is the compliment of the deontic index and functions to describe the nature of the performance Doing the Best We Can 96 at stake. As a compound conceptual unit, a praxeo-deontic multimodal form attributes some deontic status to a performance for an agent.

3.2.1 Primary Deontic Statuses

Modal logic is the logic of necessity, possibility, and contingency. Figure 3.1 depicts the classical conception of the logical relations between the alethic modalities.

Figure 3.1: Alethic Square of Opposition

Necessity (□) Impossibility (□¬)

Possibility (◇) Non-Necessity (◇¬)

Contingency (◇ ∧ ◇¬) (iﬀ both true)

Accordingly, necessity and impossibility are contraries. Possibility and non-necessity are subcontraries. Possibility is the subaltern of necessity and non-necessity is the subaltern of impossibility. Contingency is non-necessary possibility. Philosophical logics reinterpret the modal operators. Deontic logic is the deontic reinterpretation of the modal operators. In canonical deontic theory, there are ﬁve primary deontic statuses. Enumerated schematically, they are as follows:

∙ It is obligatory (at time t) for to that (at time t¨). ∙ It is permissible (at time t) for to that (at time t¨). ∙ It is prohibited (at time t) for to that (at time t¨). ∙ It is omissible (at time t) for to that (at time t¨). ∙ It is optional (at time t) for to that (at time t¨).

Each of the ﬁve primary deontic statuses exhibits the praxeo-deontic moluecular structure. Keeping this structure in mind, and letting ■x range over the praxeological modalities 3.2. The Structure of Praxeo-Deontives 97

(viz., [], [ ], [], [ ], [ ], and [ ]), Figure 3.2 depicts the classical conception of the logical relations between the deontic modalities.

Figure 3.2: Deontic Square of Opposition

Obligation ( ■x ) Impermissibility ( ■x )

Permissibility ( ■x ) Omissibility ( ■x )

Optionality ( ■x ) (iﬀ both true)

According to the classical conception of deontic logic, obligation and prohibition are contraries. Permissibility and omissibility are subcontraries. Permissibility is the subaltern of obligation and omissibility is the subaltern of impermissibility. Optionality is nonobligatory permissibility. While I fundamentally agree with the classical conception of the schematic relations between the deontic modalities, it merits an important qualiﬁcation. Strictly speaking, the classical conception is false. More speciﬁcally, all of the following implications fail:

¬ ■x →  ■x

¬ ■x →  ■x

¬ ■x →  ■x

¬ ■x →  ■x

Summarily, the failure to attribute one deontic status to a possible performance is not alone suﬃcient to attribute some other deontic status. After all, a possible performance might lack any deontic status whatsoever. The paradigmatic example of nondeonticality is any thing far beyond the agent’s relevant control. So, the deontic square of opposition Doing the Best We Can 98

must be understood with the background qualiﬁcation that the relevant performance in fact has some deontic status. Assuming that the performance has deontic status, then the square holds and e.g. a performance’s not being obligatory implies that it is omissible.

3.2.2 Normative Language: Axiological and Deontic

Despite its apparent polysemy, normative discourse is dominated by ‘ought’ language. Though it has been subject to countless permutations of accounts or descriptions, there is a substantive distinction between the evaluative and deliberative senses of ‘ought’. To the best of my knowledge, Alexius Meinong (1917) is the ﬁrst to draw the distinction.3 The evaluative ‘oughts’ (and cognates) go by many names with a host interrelated descriptions. Lloyd Humberstone calls them “situational ‘oughts’” (1971: 8). Michael Zimmerman calls them the “ideal, nonbinding sense of ‘ought’” (1996: 2). Mark Schroeder calls them the “evaluative sense [of ‘ought’]” (2011: 1). Derk Pereboom calls them the “‘ought’ of axiological evaluation” (2014: 139). The evaluative ‘ought’ is most commonly known as the ‘ought-to-be’. Paradigmatic evaluative ‘oughts’ exhibit the following form:

impersonal ©®ª It ought to be the case that . «¯¬ nonperformative

Evaluative ‘oughts’ are axiological appraisals in virtue of denoting the desirability or ideality of the occurrence of some state of affairs. Axiological appraisals evaluate the value or disvalue borne by states of affairs. Everything that ought to be is a valuable state of affair; or, a feature of an ideal world. Deliberative ‘oughts’ (and cognates) also go by many names with a host interrelated descriptions. Humberstone calls them “agent-implicating ‘oughts’” (1971: 8). Zimmerman calls them the “binding sense of ‘ought’” (1996: 2). Schroeder calls them the “deliberative sense of ‘ought’” (2011: 2). Pereboom call them the “‘ought’ of specific action demand” (2014: 139). The deliberative ‘ought’ is most commonly known as the ‘ought-to-do’. Paradigmatic deliberative ‘oughts’ exhibit the following form:

personal ©®ª Agent ought to do such that . «¯¬ performative

3 See J. L. A. García (1986) for discussion. 3.2. The Structure of Praxeo-Deontives 99

Deliberative ‘oughts’ are deontic appraisals in virtue of denoting the impingement of some binding demand for a speciﬁc agent to perform some performance. Deontic appraisals evaluate the permissibility or impermissibility borne by permformances, possible or actual. Everything that an agent ought to do is a recommendation/requirement imposed upon the agent to make actual a performance. The distinction between evaluative and deliberative senses of ‘ought’ is not exhaustive.4 Nor is it intended to be. Rather the distinction is invoked to illustrate an important point that extends to any modal auxiliary exhibiting the kind of polysemy that ranges across logically independent classes of normative appraisals. My point is that the evaluative and deliberative senses of ‘ought’ (and any other relevant modal auxiliary) are categorically diﬀerent things. The former is axiological, the latter deontic. The former belongs squarely within the bounds of value theory, the latter squarely within the bounds of deontic theory. The former is a categorically mistaken object of study for deontic theory proper, the latter a categorically correct object of study for deontic theory proper. The last point deserves special emphasis. If a deontic theory, substantive or formal, interprets its obligation operators along the lines of the evaluative ‘ought’, then the theory is a failure from the very start. It simply doesn’t capture the class of normative phenomena that it aims to capture. In point of fact, deontic theory musn’t interpret its obligation operators as an ‘ought’ of any kind.

3.2.3 Deontic Language: ‘Must’ and ‘Ought’

The normative theorizing of ethics, epistemology, and rational choice theory have in common the aim of investigating and elucidating the nature of obligation in its varying guises, diﬀering only in qualiﬁcation as to whether it is moral, epistemic, or prudential, respectively. Obligation is deontic necessity. As such, substantive deontic theory and deontic logic share the aim of explicating the nature of deontic necessity. With very few exceptions, theorists of many stripes have taken ‘ought’ to express deontic necessity.5 The precedent is mistaken. An often ignored and unappreciated inconvenience of the deontic ‘ought’ is that it poorly designates the obligatory and invites paradox. The cultish fetishization of ‘ought’ is something that must be abandoned. My hyperbolic utterance ‘[t]he cultish fetishization of ‘ought’ is something that must

4 See, for example, Judith Jarvis Thomson (1986), Richard Feldman (1988), Christen Krogh and Henning Herrestad (1996), and Michael Zimmerman (1996) for discussion. 5 Exceptions include Joel Feinberg (1961), Roderick Chisholm (1963b), Roger Wertheimer (1972), Alan White (1975), Angelika Kratzer (1977), Andrew Jones and Ingmar Pörn (1986), Paul McNamara (1996c), and Judith Lichtenberg (2010). Doing the Best We Can 100

be abandoned’ is an unequivocally strong statement. Rhetoric aside, it means that the abandonment of ‘ought’ fetishism is obligatory—it is imperative, required, a matter of necessity. By the way, it is also the case that the cultish fetishization of ‘ought’ ought to be abandoned. It is clear that this statement is comparatively weaker. It means that the abandonment of ‘ought’ fetishism is advisable or preferable, but fails to denote obligation. I am not the ﬁrst to notice that the deontic ‘must’ denotes obligation but deontic ‘ought’ doesn’t. Roderick Chisholm makes an observation along these lines in passing:

If I seek advice [. . . ] and ask, “Shall I do this?” I may well be told, “You ought to, but you don’t have to”—it is advisable, but not obligatory (1982: 102).

Andrew Jones and Ingmar Pörn devote a paper to the topic:

‘Must’ is logically stronger than ‘ought’, i.e., ‘must’ entails but is not entailed by ‘ought’. We ﬁnd evidence for this in such statements as

Not only ought you to see him, but you must see him. It’s not just that you ought to see him, you’ve got to see him.

and

You don’t have to see him, but you ought to.

and in the fact that it is logically odd to say, e.g.,

You must see him, but you ought not to.

You must not see him, but you ought not to (1986: 89).

Paul McNamara further motivates the distinction with a nice example:

Imagine that we are driving to work together and there are two routes we often take, respectively involving two exits on a certain highway. I, but not you, know that a certain bridge on the route involving the second exit is closed for repairs this week. As a result, the route involving the ﬁrst exit is the only acceptable route today. At the last minute, as we come to Exit 1, I remember and say: “You ought to turn here.” What I have said is true of course, but it is also inappropriate. For by saying, “You ought to turn here,” I leave open the 3.2. The Structure of Praxeo-Deontives 101

possibility that the second route (the one you were intending to take) is still an acceptable alternative. I have thus misleadingly suggested that the first exit is merely preferable and hence optional. In contrast, had I said, “You must turn here,” there would have been no such suggestion of optionality. To say, “You must turn here,” is not to assert that turning here is the preferable alternative (though it implies this), but that it is the only acceptable alternative—period! Thus, by saying what I did, and not what I could have said, I have misled. And we can easily imagine that when you find out about the bridge, you will be a bit irked: “Paul, if you knew Exit 2 was out of the question today, why didn’t you say, ‘You must turn here’ at Exit 1? Had you, I would have veered off and we wouldn’t be wasting our time now doubling back, destined to be late!" . . . And what it is to be late for work, anyway? Is it to arrive later than you ought? Surely this is too weak. To be late for work is to arrive later than you must, not merely later than you ought (1996c: 156).

McNamara goes on to make the diﬀerence between ‘must’ and ‘ought’ salient by contrasting two groupings of allied deontic locutions. The ﬁrst grouping smacks of deontic necessity:

∙ must bring it about that .

∙ has to bring it about that .

∙ is obligated to bring it about that .

∙ is required to bring it about that .

∙ It is incumbent upon to bring it about that .

∙ It is imperative that brings it about that .

Whereas the second grouping smacks of deontic maximality:

∙ ought to bring it about that .

∙ should bring it about that .

∙ It is advisable that brings it about that .

∙ It is best that brings it about that .

∙ It is ideal that brings it about that .

∙ It is preferable that brings it about that . Doing the Best We Can 102

As McNamara observes, these rough groupings feel natural enough and indicate that ‘must’ implies ‘ought’ but that ‘ought’ does not imply ‘must’. The totality of these remarks make it highly plausible—but do not conclusively settle— that ‘must’ expresses deontic necessity whereas ‘ought’ expresses deontic maximality. The obligatory and the maximal come apart. So, ‘must’ and ‘ought’ do too.

3.2.4 A Structural Taxonomy

Deontic theory is the theory of deontic appraisals and deontic appraisals are the class of normative assessments that evaluate the (in)appropriateness, (in)aptness, (im)propriety, (im)permissibility, et cetera, of possible performances for an agent. Deontic modals are the formal representation of the deontic appraisals. All deontic appraisals—and all deontic modals—are both personal and performative. They are personal in the sense that they denote the deontic status of possible performances for an agent. Performances do not have or lack deontic status simpliciter. Rather the deontic status of a performance is indexed to an agent upon whom the performance is relevantly incumbent. Obligations oblige the agent to make the relevant performance actual. Permissions permit the agent to make the relevant performance actual. And so on. Deontic appraisals—and modals—are performative. They are performantive in the obvious sense that they denote the deontic status of possible performances for an agent. As I see it, performativity is essentially the output of powers reactive, responsive, or otherwise functionally sensitive to reasons-as-inputs. In a word, performances are products of reasons had by an agent. The restriction that deontic modals operate solely upon well- formed praxeological formulas represents the performativity of deontic appraisals. Many affective, cognitive, and conative states are products of reasons-responsive powers. Reactive attitudes can be appropriate or inappropriate, roughly, to the extent that the agent’s affective state is the product of good reasons to be in that state. If, for instance, an agent is angry that for the reason that , then the agent’s reactive attitude is appropriate, roughly, insofar as that is a good reason to be angry that . Appropriateness is a deontic modal, either obligation or permission depending. Parallel remarks go for cognitive and conative states. My point is that deontic appraisals do not belong to the conative alone. There are deontic modals for affective states, cognitive states, and conative states. Further subdivisions in the taxonomy of deontic modals is possible. Some are free, others unfree. Plausibly, most affective and cognitive states are not within the purview of an agent’s voluntary control, but some conative states are voluntary. The deontic modals for affective and cognitive states are not freedom-implicating, whereas some deontic modals for conative state are freedom-implicating. 3.3. Adequacy Desiderata for Praxeo-Deontic Logics 103

My interest in the topic is general and abstract. Only cognitive and conative deontic modals are explicitly considered; aﬀective deontic modals are ignored entirely. Issues concerning metaphysical freedom are also left to one side. The framework is freedom- agnostic. The abilities invoked to explain deontic modalities are not oﬃcially tied to either free will or its absence.

3.3 Adequacy Desiderata for Praxeo-Deontic Logics

In this section, I postulate and motivate three important desiderata for any adequate praxeo-deontic logic. The joint satisfaction of the desiderata is a necessary, but not suﬃcient, condition for theoretical adequacy. To be clear, my goal is neither to evaluate the merits of competing deontic logics nor is it to situate DBWC among them.

3.3.1 Meinong’s Constraint

The evaluative sense of a modal auxiliary is axiological, the deliberative sense deontic. The former is a categorically mistaken object of study for deontic theory proper, the latter a categorically correct object of study for deontic theory proper. This suggests the ﬁrst adequacy desideratum for an adequate logic of obligation:

∙ Meinong’s Constraint: An adequate logic of obligation must heed the distinction between the evaluative and deliberative senses of modal auxiliaries.

This desideratum is dubbed Meinong’s Constraint in recognition of the contributions of Alexius Meinong (1917) who, as far as I know, is the earliest 20th century thinker to systematically draw the evaluative/deliberative distinction. All things being equal, then, a deontic logic is inadequate to the extent that it fails to satisfy Meinong’s Constraint.

3.3.2 Marcus’s Constraint

What is the relationship, if any, between a modal auxiliary’s evaluative and deliberative senses? As with everything in philosophy, there is a substantive debate about the answer to this question.

∙ Meinong/Chisholm Thesis: The deliberative sense of a modal auxiliary is deﬁned from its evaluative sense taking a praxeological construction as its propositional object (e.g., ought to do such that if, and only if, it ought to be that brings it about that ).6

6 The thesis is named after Alexius Meinong (1917) and Roderick Chisholm (1963b, 1964, 1974). Chisholm also cites Nicoli Hartmann (1932) as an advocate of the thesis. Doing the Best We Can 104

∙ Uniformism: The Meinong/Chisholm Thesis is true.7

∙ Anti-Uniformism: The Meinong/Chisholm Thesis is false.8

The Meinong/Chisholm Thesis reduces all deontic appraisals to a set of simple axiological appraisals. Accordingly, obligation is a matter of what is true at ideal world-moments. In slogan form: one must do the best thing possible. To be clear, the concept of possibility invoked by the slogan is not abilitive. Uniformism is the endorsement of the thesis and Anti-Uniformism the rejection. Meinong’s Constraint requires that an adequate praxeo-deontic logic distinguishes between the evaluative and deliberative senses of a modal auxiliary. A theory best accom- plishes this by deﬁning operators that approximate the two senses, which suggests that it is impossible for an adequate deontic logic to remain neutral on the issue. But if a side must be taken, which and why? The Meinong/Chisholm Thesis is false. So, Anti-Uniformism is correct, Uniformism incorrect. At its heart, the problem is that axiological appraisals lack the prescriptivity constitutive of deontic appraisals. In a beautifully insightful early passage, Ruth Barcan Marcus (1966) puts the problem as follows:

The problem of interpreting multiple occurrence of the deontic operators is significant because it reveals that at least two uses of ‘ought’ are confounded in the arguments which are supposed to give intuitive grounds for theses such as (2). Consider the reading of the parenthetic clause of (2): “What ought to be the case is the case.” The latter is descriptive of a state of affairs, and contrary to Leibniz, we take it as false. But true or false, it does not describe an action which can be prescribed or enjoined. When we assert that it ought to be the kind of world where a person’s actions always flow from his obligations, this expresses our belief about a state of affairs which, if obtain, would make for a better world. Such beliefs may provide reasons for justifying a prescription, but they are themselves not prescriptions (1966: 87).

7 The list of Uniformism advocates includes, among others, Alan Ross Anderson (1956), Stig Kanger (1957, 1972), Stig Kanger and Helle Kanger (1966), Angelika Kratzer (1977, 1981), Bernard Willams (1982), G. E. M. Anscombe (1987), Christen Krogh and Henning Herrestad (1996), Paul McNamara (2004), and Stephen Finlay and Justin Snedegar (2013). 8 The list of Uniformism opponents includes, among others, G. H. von Wright (1951a, 1981), C. D. Broad (1952), Ruth Barcan Marcus (1966), I. Lloyd Humberstone (1971), Hector-Neri Castañeda (1981), Peter Geach (1982), Gilbert Harman (1973, 1977, 1986), Fred Feldman (1986), J. L. A. García (1986), John Horty (1996, 2001), Michael Zimmerman (1996, 2006b), John Broome (1999), Ishtiyaque Haji (2002, 2012, 2016), Ralph Wedgwood (2006, 2007), Jacob Ross (2010), and Mark Schroeder (2011). 3.3. Adequacy Desiderata for Praxeo-Deontic Logics 105

The problem of manifests itself in a number of different ways. Most arguments for Uniformism assume that the deontic ‘ought’ denotes deontic necessity. It doesn’t, but grant for the sake of argument that it does. Suppose that it ought to be the case that the agent brings it about that . Roughly, this means that there is a possible world-moment/world-history pair at which agent brings it about that better than any other at which the agent fails to do just that. According to Uniformism, this is everything, both necessary and sufficient, for the agent’s having an obligation to bring it about that . While I think that all deontic appraisals are reducible to a special class of axiological appraisals, I think that Meinong/Chisholm Thesis is demonstrably false in both directions. Allow me to explain. Agents who don’t in fact exist cannot have obligations, but it is possible for agents to exist in ideal world-moment/world-history pairs that don’t exist in fact. Pick any favorite heroic fictional character and the world would in fact be a better place if that person existed. Indeed the world would be among the best if it were filled with people who clothed the naked, inspired the hopeless, fed the hungry, pacified the hateful, sheltered the homeless, soothed the afflicted, et cetera, in such a way that all worldly evils were the hazy memory of a bad dream. It ought to be that the Superman persuades all those with malicious intent to set aside their malcontent and devote themselves to humanity. In ideality, Superman brings about world peace. But Superman doesn’t in fact have any obligations of any kind because he doesn’t in fact exist. The big picture lesson is that ideality need look nothing like reality. The totality of biological, ecological, economic, geographic, political, social, technological, et cetera, arrangements might be very different in an ideal world. The resultant behaviors of individual agents in ideality might indeed be impossible in actuality. For example, those who are oppressed in reality would be afforded very different lives were the world a better place. Those who are not, for instance, afforded the opportunity to choose between meals, or homes, or educations would make exactly those sorts of choices in better worlds. If the things that agents do in ideality cannot be readily translated into reality, it cannot be said that agents have any obligations corresponding to what they do in ideality. If, in an ideal world, a homeless person isn’t homeless but rather wealthy enough to shelter others in their happy home, and does just that in ideality, how can it be that the homeless person has an obligation to shelter the needy in the happy home that doesn’t exist? A defender of Uniformism might propose to narrow the relevant class of world-pairs. Instead of the best of all possible world-pairs, it is insisted that ideality is somehow defined in terms of the best of relevantly similar world-pairs. Details aside, the aim of the restriction is to guarantee that ideality is never too far away from reality. Doing the Best We Can 106

The gambit’s prospects depend upon on how well the relevance criteria for candidate world-moment/world-history pairs is specified, but I think the prospects rather dim. I worry that the solution will be both too inclusive and too exclusive. On the one hand, too inclusive in the sense that ideality will still be too ideal to obviate the original set of difficulties. It must be guaranteed that all the agents exist in their actually prevailing circumstances lest it be possible that nonexisting agents perform nonexisting options in nonexisting circumstances. On the other hand, too exclusive because, contrary to Leibniz, the actuality looks nothing like ideality. Modeling ideality after reality is to aspire in the wrong direction. More to the point, some obligations are never incurred in ideality. Paradigmatic examples include reparative obligations, the obligations incurred as a result of wrongdoing, such as the requirement of apology in the aftermath of offense. Ideally, agents never seek reconciliation because the preconditions never arise. My point is that solving the inclusivity problem runs afoul of the exclusivity problem and vice versa. In sum, the Meinong/Chisholm Thesis makes systematically mistaken predictions about deontic appraisals. Even granting the false assumption that the deontic ‘ought’ denotes deontic necessity, ‘ought-to-be’ is neither necessary nor sufficient for obligation. It is not sufficient because agents might do things in ideality that are impossible in reality. It is not necessary because some obligations (such as paradigmatic reparative obligations) would not be incurred at all in ideality. At bottom, the Meinong/Chisholm Thesis is false because it invokes the wrong concept of possibility. On my view, obligation is a matter of what an agent does in their best abilitively possible world-moment/world-history pairs. I interpret this as a kind of Anti-Uniformism because it is possible—and actual—that the best of an agent’s abilitively accessible world-pairs are strictly worse than the best possible world-moment/world-history pairs simpliciter. These reflections suggest another adequacy desideratum, which can be seen as a special consequence of Meingong’s Constraint. The desideratum may be stated as follows:

∙ Marcus’s Constraint: The Meinong/Chisholm Thesis must be false in an adequate logic of obligation.

This desideratum is dubbed Marcus’s Constraint for obvious reasons. All things being equal, then, a praxeo-deontic logic is inadequate to the extent that it fails to satisfy Marcus’s Constraint.

3.3.3 Urmson’s Constraint

Traditional deontic theories tend to recognize only the primary deontic statuses of the obligatory, permissible, prohibited, omissible, and the optional. Among these, obligation, 3.3. Adequacy Desiderata for Praxeo-Deontic Logics 107

right, and wrong seem to attract nearly all of the attention. As J. O. Urmson famously complains, and many others since, this a serious defect of traditional theorizing:

To my mind this threefold classification [of obligation, right, and wrong], or any classification that is merely a iation on or elaboration of it, is totally inadequate to the facts of morality; any moral theory that leaves room only for such a classification will in consequence also be inadequate (1958: 198–199).

The problem is that there are rich normative categories that enjoy genuine pretheoretic life that are left to the wayside by this threefold classiﬁcation. Begin with the notion of supererogation. It is easily identiﬁed by appeal to examples:

Example 3.1. An extremely poor homemaker takes notice of a dishevelled foreigner taking refuge in a local barn. The weary foreigner is on a long ancestral pilgrimage, but a recent run-in with bandits made it so that the foreigner could no longer aﬀord food or shelter. Taking pity upon the foreigner, the homemaker oﬀers the pilgrim a hot meal and a warm bed, thereby foregoing a meal and a bed that evening. When they bid each other farewell the next morning, the homemaker gives the foreigner the little coin that the homemaker has managed to scrounge and save to speed the foreigner along the way. Example 3.2. A group of military recruits practices the throwing of live hand grenades. A grenade slips from the hand of one of the recruits, making its way into a nearby group of soldiers. One of the soldiers dives atop the live grenade to shield the others from the blast and is subsequently killed (Urmson 1958: 202–203).

In Example 3.1, it is supererogatory for the homemaker to aid the pilgrim. In Example 3.2, it is supererogatory for the soldier to perform the ultimate act of self-sacriﬁce. These are dictates of common sense. While it is perhaps possible to contrive similar cases in which the relevant acts are obligatory, they are intended to be threadbare ordinary circumstances. In agreement with Paul McNamara (1996a, 1996b, 1996c, 2011a, 2011b) and Terry Hor- gan and Mark Timmons (2010), reﬂection upon such cases suggests that supererogatives have three constitutive features:

∙ Axiological: The supererogatory thing is better than at least some of its permissible alternatives. ∙ Deontic: The supererogatory thing is optional. ∙ Hypological: In doing what is supererogatory, the agent deserves credit/praise; in refraining from doing what is supererogatory, the agent does not deserve criticism/blame. Doing the Best We Can 108

To illustrate, consider Example 3.1. With respect to the axiological condition, helping the pilgrim is clearly morally better than not. With respect to the deontic condition, helping is optional. It isn’t obligatory because it is assumed that the homemaker is poor enough forego any such obligation. It isn’t wrong because it is assumed that the homemaker isn’t poor enough to require failing to help the pilgrim. With respect to the hypological condition, the homemaker is praiseworthy because the homemaker helps the pilgrim for morally decent reasons. The homemaker is sensitive to the blight of the pilgrim and, despite knowing full well the personal costs, is moved to help. The homemaker would not deserve blame were they to refrain from helping, because their doing so would not be the result of callousness or malice, but legitimate self-directed concern stemming from the daily struggle with crushing poverty. After all, having the ability to render assistance unto others is not infrequently a moral privilege afforded to persons by their socioeconomic status. This is a privilege that the homemaker should be understood to lack. Analogous remarks are extractable from Example 3.2. The upshot is that supererogatives are constituted by the three normative features outlined above. Supererogation is a compound normative concept. It is constituted by three different normative dimensions: axiological, deontic, and hypological. Insofar as pure deontic theory aims to elucidate the nature of our deontic concepts, it isn’t obliged to capture the notion of supererogation per se. It is, however, required to lay the foundations for its accommodation. It can legitimately ignore the satisfaction of the hypological condition and define operators that attend to the joint satisfaction of the axiological and deontic conditions. The resultant operator captures the notion of something’s being beyond the call of duty. I appeal to but one example to highlight the difference between the compound status of supererogation and the subsidiary deontic status of being beyond the call:

Example 3.3. There pharisee who, as a matter of policy, does just the minimum for others required by morality’s demands, enters into a business deal with a laborer, and agrees to trade for service 14 pounds of wheat that the laborer needs. However, the pharisee mistakenly recalls the promise to give the laborer 15 pounds of wheat, and does so (McNamara 2011a: 209).

Example 3.3 is a case in which the agent goes beyond the call but does not supererogate.9 The pharisee does not supererogate because the pharisee deserves no praise. The pharisee is moved to act neither by morally decent reasons nor morally indecent reasons. Were the pharisee to realize their mistake, they would seek to reclaim the pound of wheat overpaid. There are versions of this case where the pharisee deserves blame for giving 15 points

9 See also Horgan and Timmons for discussion of “nonmeritorious supererogation” (2010: 33). 3.3. Adequacy Desiderata for Praxeo-Deontic Logics 109

of wheat to the laborer instead of the 14 pounds agreed upon. The upshot is that going beyond the call and supererogation come apart. They are distinguished by the presence or absence of a hypological condition. Turn now to suberogation, the unhappy mirror of supererogation. It is admittedly a less intuitive normative category, but has nonetheless been noticed and defended by a number of individuals.10 In agreement with Paul McNamara op. cit., suberogatives are the mirror image of supererogatives in the sense that they are analogously constituted by three normative features:

∙ Axiological: The suberogatory thing is worse than at least some of its permissible alternatives.

∙ Deontic: The suberogatory thing is optional.

∙ Hypological: In doing what is suberogatory, the agent deserves criticism/blame; in refraining from doing what is supererogatory, the agent does not deserve credit/praise.

With these features in mind, here are what I take to be two examples of suberogation:

Example 3.4. Albert, who is a very generous person, has in the past done many favours for Bill. . . . Albert’s sister has suddenly taken ill, and he needs to get her to a doctor’s appointment. If he takes time out to return his books to the library, he will be unable to do so. So, he asks Bill to return the books for him, as a favour. Until Bill agrees to return the books, he has no obligation to do so. If Bill refuses to take the books back, saying, “I realize that this will help you out a lot, and it requires almost no eﬀort on my part, but I just don’t feel like it,” Albert might well be taken aback. He might even feel angry with Bill, because Bill owes him a favour. But Bill is not doing anything wrong. Still, some negative judgement about Bill seems appropriate. The type of negative judgement called for in this case [. . . ] is captured in the concept of the suberogatory (Driver 1992: 289).

Example 3.5. Scholastica is a scholar working on a book project on a tight deadline, but the project comes to an impasse. Unless Scholastica somehow accesses copies of some relevant obscure literature, she will surely fail to meet the pending deadline. There are only permissible three ways for her to gets her hands on the books. The best option is to purchase them from a local book vendor that deals in obscure books.

10 In addition to the discussion provided by McNamara and Horgan and Timmons, see, for example, Roderick Chisholm (1963b, 1964, 1974), Roderick Chisholm and Ernest Sosa (1966), Gregory Mellema (1991, 2005), Julia Driver (1992), Eleonore Stump (1992), Michael Zimmerman (1996, 1997, 2002), Ishtiyque Haji (1998, 2002, 2012, 2013, 2014, 2016), and Justin Capes (2012). Doing the Best We Can 110

The second best option is to borrow the books from her cantankerous colleague Dominic—provided that he gives her permission. Her worst option option is to drive to a library very far out of the way and borrow the books. Despite the fact that Dominic refuses to lend his books out, Scholastica asks permission to borrow the relevant books anyway and, surprisingly, he permits it—albeit in a very idiosyncratic way. Scholastica reasonably mistakes this for polite refusal. Believing that she doesn’t have permission to borrow the books, Scholastica decides to clandestinely take Dominic’s books and subsequently hide this fact from him.

Because the suberogatory is a comparatively less intuitive normative category than the suberogatory, it is worth briefly discussing each of these examples. Example 3.4 is a candidate case of suberogation. Driver appeals to it because she is of the view that paradigmatic instances of failure to return an “owed favor” is suberogatory. Of course, the notion of an owed favor is somewhat paradoxical. Favors, like gifts, are things that cannot be literally owed. A favor is a nonobligatory service in the same way that a gift is a nonobligatory good. If it is obligatory to render the service or good unto another party, then it is something to which they have some correlative claim, but favors and gifts conceptually preclude any such accountability. While it is perfectly sensible to say that Bill owes Albert a favor, it is does not literally mean that he is obligated to return Albert’s books for him. It is in principle permissible for him to refuse. With respect to the deontic condition, then, refusing to return Albert’s books is optional for Bill. With respect to the axiological condition, it is clearly worse for Bill to refuse to return Albert’s books than to return them. With respect to the hypological condition, common sense dictates that Bill deserves criticism for refusing Albert. Perhaps this is because Bill is moved by selfish reasons, or perhaps because Bill is insufficiently moved by decent reasons. If it insisted that Bill’s blameworthiness indicates wrongdoing, then I think we must eliminate owed favors (and owed gifts) from our conceptual scheme. The phenomenon is saved by accommodating the suberogatory. Example 3.5 is also a candidate case of suberogation. As far as the axiological condition goes, it is stipulated that at least one option is better than borrowing Dominic’s books. Perhaps time is a relevant factor such that the easier to get the books, and the longer Scholastica is allowed to keep them, the better. Maybe she knows that Dominic will demand them back before her need dissipates. Given such considerations, simply buying them best saves Scholastica from headache. With respect to the deontic condition, it is optional to borrow Dominic’s books. It is permissible in virtue of Dominic’s consent, but his consent doesn’t make it obligatory for Scholastic to borrow his books. With respect to the hypological condition, Scholastica deserves criticism for borrowing Dominic’s books 3.3. Adequacy Desiderata for Praxeo-Deontic Logics 111

but would not merit credit for doing something else instead. Scholastic is blameworthy because she is moved by selfish or indecent reasons to act. She reasonably takes herself to lack any permission but helps herself to Dominic’s books anyway—by her own lights, she does wrong. Suberogation is a compound normative concept. It is constituted by three different normative dimensions: axiological, deontic, and hypological. Like its happy counterpart, pure deontic theory cannot strictly speaking capture it, but it should lay the foundations for doing so. In particular, deontic theory can define an operator that attends to the joint satisfaction of the axiological and deontic conditions. The resultant operator captures the notion of something’s being permissibly suboptimal or deontically satisfactory. As before, I appeal to but one example to highlight the difference between the compound status of suberogation and the subsidiary deontic status of being permissibly suboptimal:

Example 3.6. Suppose that I am obligated to be the first to convey some slightly delicate information, and that I can do so via email, phone, or in person. Add that these exhaust the ways to satisfy my obligation. Since it is obligatory for me to be the first to convey the information to you, the obligation is personal and agential: I am not only responsible for your getting the information, but for delivering it myself. Now it is easy to imagine that although any of the three ways of discharging my obligation is permissible, nonetheless, the more personal the manner of delivery the better morally speaking. Assume also that the three alternatives are mutually exclusive for some reason. We might then describe the options this way. My doing the minimum implies my e-mailing you—this is the way to discharge my obligation in the minimally acceptable way. On the other hand, if I convey the information in person, I will be doing the maximum (what morality recommends). Finally, we can easily imagine that it is a matter of moral indifference that I carry my pen with me when I deliver the message (McNamara 2011b: 154).

Example 3.6 illustrates many interesting subsidiary deontic modalities, including permissible suboptimality. Both emailing and phoning are permissibly suboptimal for McNamara. Presumably, McNamara does not suberogate when doing either because he is not motivated by particularly indecent reasons. Perhaps he is busy balancing other aspects of his life but genuinely cares about discharging the obligation, so he opts for the middle ground and conveys the information by phone. Of course, there are ways that McNamara might be motivated so that he suberogates. The upshot is that permissibly suboptimizing and suberogation come apart. They are distinguished by the presence or absence of a hypological condition. Doing the Best We Can 112

Finally, there is a difference between optionality, insignificance, and nondeonticality.11 Optionality is a primary deontic status. Something is optional for an agent when it is both permissible and omissible. Insignificance is indifference in the extreme. Something is insignificant for an agent when it is optional in all abilitively possible world-moment/world- history pairs. Everything that is either supererogatory or suberogatory is optional, but no such thing is deontically insignificant. I take it that the main reason why something lacks deontic significance is that it is normatively uninteresting. In Example 3.6, whether Mc- Namara carries his pen with him is insignificant presumably because it has no normative bearing. Nondeonticality is the absence of any deontic status. Something is nondeontic when it is not obligatory, permissible, impermissible, or omissible. Canonical nondeontic facts are those with respect to which the agent lacks any relevant powers or capabilities. Putting it all together, these reflections suggest the following adequacy desideratum:

∙ Urmson’s Constraint: An adequate logic of obligation must accommodate the subsidiary deontic statuses.

This desideratum is dubbed Urmson’s Constraint in recognition of the influence of Urmson’s work, which is largely responsible for the recent decades of rekindled interest in the wider corpus of normative concepts. All things being equal, then, a deontic logic is inadequate to the extent that it fails to satisfy Urmson’s Constraint. I want to offer an auxiliary motivation for the adequacy desideratum. Following Paul McNamara (1996a, 1996b, 1996c, 2010), and others, I have said that, read in the deontic mood, ‘must’ denotes necessity and ‘ought’ denotes maximality. I appealed to linguistic evidence for this claim. I now want to consider some puzzles of expressive inadequacy discussed by McNamara. McNamara’s first puzzle is generated by considering natural language sentences that describe situations where that the obligatory and the advisable come apart:

∙ Damian can stay home, but he ought go check on Regan.

∙ Bill may do whatever he likes, but he should return the books for Albert.

∙ It is advisable, but certainly not required, that Dana store her valuables in the safe while she’s away.

∙ Of course Dominic is permitted to refuse to help Scholastica, but he shouldn’t.

11 I admit that ‘nondeonticality’ is an exceedingly ugly, obtuse word. Unfortunately, I can think of none better. Haji (2016) uses ‘amoral’ but I ﬁnd it unduly ethical. Apart from its monstrous ambiguity, ‘arational’ is hypologically-laden and therefore completely unsuitable for pure deontic nomenclature. 3.3. Adequacy Desiderata for Praxeo-Deontic Logics 113

∙ Lily doesn’t have to go to the meeting, but she really ought to go.

∙ It is best for Scholastica if she simply buys the research materials she needs, but Dominic also has them and she can get permission to use them.

All these sentences, and many others like them, are perfectly intelligible when the modal auxiliaries are read in the deontic mood. They describe situations relevantly like Example 3.6, where the most McNamara can do is have a tête-à-tête with his colleague. Each of these expressions suggest that it is both optional and most advisable for the agent to do the relevant thing. Optionality implies not obligatory. So, it isn’t possible to felicitously represent such sentences in any theory where the deontic ‘ought’ denotes the obligatory. The problem deepens in two interesting ways. First, if the deontic ‘ought’ denoted obligation, any such utterance would be predictably infelicitous when read in the deontic mood. Second, the most straightforward attempts to represent sentences like those oﬀered above in standard deontic logic results in contradiction. Consistency may be preserved by jettisoning the inference pattern stating that obligation implies permissibility. This desperate maneuver violates the working assumption that the interrelations of deontic modals are typiﬁed by the square of opposition. McNamara’s second puzzle is likewise generated by considering natural language sentences, except these sentences describe situations where there is a lower bound on deontic acceptability:

∙ The least Damian can do is call to see how Regan is holding up.

∙ Bill may do whatever he likes, but he must at least tell Albert whether he’ll return the books for him.

∙ At minimum, Dana should lock the door to her house while she’s away.

∙ Dominic doesn’t have to help Scholastica, but the least he can do is refuse her politely.

∙ Lily doesn’t have to go to the meeting, but she can’t do anything less than work at her desk. She cannot, for instance, call it a day and go home.

∙ It isn’t an option for Scholastica to forget about the research materials, and either purchasing them or borrowing them from the library is better for her than borrowing the materials from Dominic.

All these sentences, and many others like them, are, again, perfectly intelligible when the modal auxiliaries are read in the deontic mood. They describe situations relevantly like Example 3.6, where the least McNamara can do is email his colleague. Each of these Doing the Best We Can 114

expressions suggest that it is both optional and least advisable for the agent to do the relevant thing. Optionality implies not impermissible. So, it isn’t possible to felicitously represent such sentences in any theory where the deontic ‘ought’ denotes the obligatory because it ascribes impermissibility to what is pretheoretically described as the least permissible option. The second problem deepens in ways analogous to the ﬁrst. The lesson of both is that traditional deontic theory and standard deontic logic are expressively inadequate. The solution to both problems is the deontic ranking of permissible alternatives. If the theory is developed to treat ‘ought’ as the deontic modal of permissible maximality, then those same resources will can be used for the analogous deontic modal of permissible minimality. Urmson’s Constraint requires that subsidiary deontic modalities are accommodated. It simply falls out of the constraint that an adequate deontic logic has the resources to make sense of the kinds of natural language sentences I’ve appealed to without explaining them away. Deontic theories that fail Urmson’s Constraint lack the theoretical resources to systematically resolve the problems of expressive inadequacy.

3.4 The DBWC Framework

DBWC is a modal logic of obligation and permission founded upon WWCD. In this section, I specify DBWC’s frames, models, semantics, and syntax. I deﬁne an array of modal operators designed to approximate a spectrum of intuitive concepts pertaining to obligation, permission, prohibition, and kin.

3.4.1 DBWC Assumptions, Frames, and Models

DBWC is a language extending WWCD. In addition to all the elements of WWCD, all of the following are well-formed DBWC formulas:

Φ ∶= … | ■x

DBWC adds a primitive deontic operator for permissibility to WWCD’s eleven primitive modal operators. Deontic modalities are subject to the same restrictions as reasons modalities, which is to say that they operate solely upon atomic performances (of the form: ■x , for any praxeological modality) or formulas recursively built up from atomic performances using the admissible Boolean or modal operations. 3.4. The DBWC Framework 115

The Massachusettsian framework theorizes about deontic modals by appeal to the notions of ability and value. DBWC belongs squarely to this tradition, adding to WWCD, the general theory of performativity, a single element representing value.

Definition 3.4.1. A DBWC frame is an ordered set

∗ F = ⟨D, , , ⩽,  , Λ, ℜ, i, … , n, ≾r, ≾v, ≾v⟩ extending a WWCD frame (see Definition 2.4.8), where the new elements are deﬁned as follows:

∙ ≾v is a partial normative ordering relation over Pair such that each of Pair and Pair

are nonstrictly totally ordered. The irreﬂexive dual of ≾v is ≺v. Both are normative ordering relations representing the overall normative value of a moment/history pair.

Every ≾v-value-wise ordering over P air is indexed to an agent, a set of normative values, v, speciﬁed by an axiology, and a moment/history pair.

∗ ∙ ≾v is a partial normative ordering relation over performative formulas. The irreﬂexive ∗ ∗ dual of ≾v is ≺v. Both are normative ordering relations representing the overal normative ∗ value of a performance. Every ≾v-value-wise ordering over performative formulas is indexed to an agent, a set of normative values, v, speciﬁed by an axiology, and a moment/history pair.

The relation, ≾v, is a partial normative ordering over the domain, which is, again, partitioned into the subdomain of world-moments, , and the subdomain of mind- moments, . It sorts moment/history pairs into v-value-wise equivalence classes, where each member of an equivalence class is equally overall v-wise-valuable. More speciﬁcally,

≾v imposes two distinct nonstrict normative suborderings over the domain, one for the world subdomain and one for the mind subdomain. While all world-moments are ≾v- value-wise comparable and all mind-moments are ≾v-value-wise comparable, the two

normative suborderings are not intercomparable. Every ≾v-value-wise ordering over P air is indexed to an agent, a set of normative values, v, and a moment/history pair. ∗ Whereas ≾v normatively orders moment/history pairs, the relation ≾v does the same for collections of performative formulas. It sorts sets of performative formulas into v- value-wise equivalence classes, where each member of an equivalence class is equally overall v-wise-valuable. DBWC invokes a placeholder concept of value that, following others in the Mas- sachusetts school, I shall simply label ‘deontic value’.12 As I use it, ‘deontic value’ is

12 Compare with McNamara (1996b) and Haji (2002, 2012, 2016). Doing the Best We Can 116

a term denoting whatever evaluative quantity in virtue of which performances are assessed for the presence of right-making features. Whereas an axiology is a theory of value, I shall use ‘deontic axiology’ for a theory of deontic value.13 I assume that all axiologies, deontic or otherwise, satisfy a certain schema:

∙ Property P , … , P ¨ Axiology: All and only states of aﬀairs exhibiting properties P , … , P ¨ realize any v-wise-value. More precisely:

∙ Value Clause: The state of aﬀairs of is v-wise-valuable to degree n if, and only if, has properties P , … , P ¨. ∙ Disvalue Clause: The state of aﬀairs of is v-wise-disvaluable to degree m if, and only if, lacks properties P , … , P ¨. ∙ Neutrality Clause: Nothing else is either v-wise-valuable or v-wise-disvaluable.

At minimum, an axiology identifies all the things the realize either value or disvalue and specify how they relate to the valuation of world-moment/world-history pair as a whole.14 The axiology schema assigns value of quantity n to states of affairs exhibiting properties P , … , P ¨ and disvalue of quantity m to states of affairs failing to exhibit properties P , … , P ¨. It is possible that n is greater than, equal to, or less than m. Deontic value and disvalue can benefit from, or be penalized by, various situational modifiers or multipliers, but I omit any such inclusions for sake of simplicity. The deontic value of a world-moment/world-history pair is a function of the deontic values of the relevant formulas representing the relevant states of affairs occurring there, but I say nothing about the nature of this function. It might be merely additive or it might be something else entirely.15 DBWC does not assume a theory of deontic value. The good-making properties P , … , P ¨ can in principle be anything. Deontologists should interpret ‘deontic value’ roughly as degree of concordance with, or degree of stringency of, the agent’s operative duties. On this conception, a world-moment/world-history pair has deontic value to the extent that the agent lives up to their operative duties at that world-pair. Divine command

13 This is an abuse of language. Strictly speaking, an axiology denotes all and only theories of value (qua axiological judgments). A deontic axiology that evaluates performances on the basis of elements other than value or disvalue (e.g., deontology or virtue theory) is not, strictly speaking, an axiology at all because the attenuated notion of deontic value is not axiological in character. Nevertheless I shall avail myself to the language because, on the one hand, it is easy to remember and, on the other hand, it suggests that a kind of second order teleologism is unavoidable. 14 See Gilbert Harman (1967) and F. Feldman (1986, 2000, 2004) for discussion, especially concerning basic intrinsic value states and how they should be used to resolve various axiological paradoxes. 15 For related discussion, see F. Feldman (1997, 2000) and Bradford Skow (2011). 3.4. The DBWC Framework 117

theorists and natural law theorists should interpret ‘deontic value’ roughly as degree of degree of concordance with the relevant correct laws. On this conception, a world- moment/world-history pair has deontic value to the extent that the agent complies with the relevant correct laws at that world-pair. Social constructivists should interpret ‘deontic value’ roughly as degree of degree of concordance with the relevant cultural standards. On this conception, a world-moment/world-history pair has deontic value to the extent that the agent practices the relevant cultural standards at that world-pair. Teleologists should interpret ‘deontic value’ roughly as intrinsic goodness. On this conception, a world-moment/world-history pair has deontic value to the extent that some totality of instrinic goodness is realized at that world-pair. Reasons firsters should interpret ‘deontic value’ roughly as the overall reasons-wise weight for reasons of the relevant kind. On this conception, a world-moment/world-history pair has deontic value to the extent that certain performances are favored by the agent’s reasons at that world-pair. Virtue theorists should interpret ‘deontic value’ roughly as degree to which the agent exemplifies of the virtues operative the circumstances. On this conception, a world-moment/world-history pair has deontic value to the extent that the agent exemplifies the operative virtues at that world-pair. And so on for any deontic axiology. To be perfectly clear, ‘deontic value’ is, again, merely a placeholder term compatible with any deontic theory that is at least in principle capable of ordinally ranking an agent’s options at a world-moment/world-history pair—which, I take it, is a minimal adequacy desideratum for any deontic axiology. As far as the official DBWC goes, nothing essential hinges upon the reader’s preferred deontic axiology. Formally, the concept of deontic value is represented by the index v, which is the agent- and moment/history pair-relativized evaluative quantity in question. DBWC allows the deontic ranking of well-formed formulas and moment/history pairs to vary by agent, moment/history pair, or set of deontic values (e.g., epistemic, moral, or prudential; pro tanto or ultima facie; et cetera). In this sense, the set v is perfectly analogous to the set

r, just as the ≾v-wise ordering over Pair is perfectly analogous to the ≾r-wise ordering over Pair. It cannot be emphasized enough that DBWC is officially neutral on the issue of the nature of deontic value, including the meta-ethical debates over whether deontic value is, on the one hand, agent-neutral or agent-relative and, on the other hand, moment- neutral or moment-relative. If deontic value is agent-neutral, then v is the same for every agent at a given moment/history pair; if agent-relative, then v can differ between agents at a moment/history pair. If deontic value is moment-neutral, then v is the same for every moment/history pair for a given agent ; if moment-relative, then v can differ between moment/history pairs for . Finally, if deontic value is defeasible, the dynamics of Doing the Best We Can 118

gaining or losing deontic value is modeled diachronically as the agent traversing abilitively accessible world-pairs where the contents of v vary.

Definition 3.4.2. A DBWC model is an ordered set

M = ⟨F, ℑ+, ℑ−⟩ extending a DBWC frame, where each element is deﬁned as follows:

∙ F = ⟨D, , , ⩽,  , Λ, ℜ, i, … , n, ≾r, ≾v⟩ is a DBWC frame.

A DBWC model is a DBWC frame plus two interpretation functions, one for world- moment/world-history pairs and another for mind-moment/mind-history pairs. Both are inherited from WWCD, each serving the same role as it did before and for the same reasons. The DBWC definitions of satisfiability and validity are likewise inherited from WWCD, meaning that satisfiability is nonclassical but validity classical.

3.4.2 DBWC Semantics In this subsection, I sketch the formal semantics for WWCD at world-moment/world- history pairs. The formal semantics at mind-moment/mind-history pairs is unchanged from WWCD. The subsubsections are thematically divided among philosophical interpretations of both the primitive and nonprimitive grammar.

Normal Primitive Deontic Modalities

DBWC has one primitive deontic modality, namely permissibility. It is deﬁned in terms of what is performed across the maximally deontically valuable contextually salient abilitively accessible moment/history pairs. In other words, deontic modalities are deﬁned by appeal to a deontic value optimality set. Deontic modalities are as weird as reasons modalities in the same three ways. First, they operate all and only upon performative formulas. This is because deontic modalities 3.4. The DBWC Framework 119

represent the deontic status of a performance for an agent at a moment/history pair. Second, deontic modalities all share an exception condition as a quality control measure on performativity. Deontic status apply only to nondefective performances, and so apply only to performances that satisfy the exception condition. Third, deontic modalities appeal to abilitively accessible moment/history pairs, which is assumed to be finite for each agent. In the previous chapter, I offered two formulations of the formal semantics for reasons modalities. Unsurprisingly, there are analogues of each formulations for deontic modalities. All the main points and paradoxes offered in light of the two formulations of reasons modalities apply equally well to the analogues for deontic modalities. I won’t repeat the discussion, so I offer only one—my presently preferred—formulation. This formulation

appeals to the deontic optimality set normal moment/history pair, (w, hw), which is the set of all v-value-wise best contextually salient abilitively accessible moment/history pairs.

The optimality set for an agent at (w, hw) given the set of deontic values v in context is v denoted Best (w, hw).

Definition 3.4.3. A v-value-wise optimality set of a normal moment/history pair, (w, hw), for an agent and set of values, v, is the subset of all contextually salient moment/history

pairs abilitively accessible from (w, hw) containing all and only the pairs that are at least

as v-wise-valuable as any other. The v-value-wise optimality set of (w, hw) is denoted v Best (w, hw) and deﬁned as follows:

v ¨ ¨ ¨ ¨ ¨¨ ¨¨ ¨ ¨ Best (w, hw) = {(w , hw) ∈ ∶ (w, hw)ℜ(w , hw) and (w , hw) ≾v (w , hw), ¨¨ ¨¨ ¨¨ ¨¨ for all (w , hw) ∈ such that (w, hw)ℜ(w , hw)}

v where M is a DBWC model, is a contextual parameter, and Best (w, hw) ⊆ ⊆ Pair.

Deontic modalities quantify over the optimality set. Table 3.1 displays the DBWC semantics for the primitive deontic modality at normal moment/history pairs.

Table 3.1: DBWC Normal Semantics: Primitive Deontic Modality

Operator Definition ¨ ¨ x ¨ ¨ v ∙ Positivity: M, (w , hw) ⊨ ■ for some (w , h ) ∈ Best (w, hw) M, (w, h ) ⊨ ■x ¨¨ ¨¨ x ¨¨ ¨¨ ¨ w  ∙ Exception: M, (w , hw) ⊨ ■ for some (w , h ) ∈ such ¨ ¨¨ ¨¨ that ⊇ and (w, h)ℜ(w , h )

 is the modality of v-value-wise permissibility. Philosophically, ■x means that it is permissible for the agent to ■x . More speciﬁcally, ■x means that some of the overall Doing the Best We Can 120

normative considerations in virtue of which value is realized recommend agent to ■x . x x The formula ■ is true at (w, hw) if, and only if, ■ is true at some deontically optimiﬁc moment/history pair and ■x is true at some excepting moment/history pair. Just as with the reasons modalities, observe that the excepting moment/history pair at which ■x is

true might not be a member of over which the positivity condition is deﬁned, meaning that the excepting moment/history pair is not guaranteed to be contextually salient. Obligations and permissions, like reasons, can be disappointed. On the one hand, an agent can fail to live up to the letter of a permission by failing to do the right thing altogether. On the other hand, an agent can fail to live up to the spirit of a permission by accidentally conforming with the right thing or without appropriate sensitivity to its rightness. My point is that deontic modalities, like reasons modalities, can be true without being discharged, just as an agent can have reasons while ignoring them. The mere having of permissions and the discharge of permissions is an important diﬀerence that DBWC approximates. Recall that ! is the discharge operator. When attached to a deontic modality, it denotes that the modal has been discharged. Intuitively, this can be interpreted to mean that the agent lives up to the spirit of the deontic modal. Not only is the agent’s performance in conformity with the agent’s obligations, but the agent’s performance complies with them in such a way as to permissibly discharge them. Formally, a deontic modal is relevantly discharged just in case the agent does what is required at the moment/history pair of evaluation. Table 2.18 displays the DBWC semantics for the discharged permissibility at normal moment/history pairs.

Table 3.2: DBWC Normal Semantics: Discharged Primitive Deontic Modality

Operator Definition x v ∙ Positivity: M, (w, hw) ⊨ ■ and (w, h) ∈ Best (w, hw) M, (w, h ) ⊨ !■x ¨ ¨ x ¨ ¨ ¨ w  ∙ Exception: M, (w , hw) ⊨ ■ for some (w , h ) ∈ such that ¨ ¨ ¨ ⊇ and (w, h)ℜ(w , h )

x x ! is discharged permission. The formula !■ is true at (w, hw) if, and only if, ■

is true at (w, hw) and (w, hw) is a member of the optimality set and there exists an excepting x x moment/history pair. Simplifying, !■ is true at (w, hw) if, and only if, ■ is true at x (w, hw) because the ■ is true at (w, hw) and (w, hw) is a member of the deontic optimality set. Strictly speaking, this will but tend to mean that that sensitivity to the considerations in virtue of which the performance is permissible will tend to play the appropriate role in the production of the performance. 3.4. The DBWC Framework 121

In general, deontic modals tend to attach performances where the relevant considerations of deontic value play the appropriate role in their occurrence. Only a tendency is guaranteed because it is possible for an agent to perform a performance in deontically optimific moment/history pair despite its lack of accord with the sources of deontic value. Maybe it isn’t something that realizes deontic value or disvalue. Maybe its deontic disvalue is washed out or swamped by a sufficient number of other things that realize deontic value. DBWC implies that a performance can have positive deontic status despite the fact that it itself does not realize deontic value, just as WWCD implies that a performance can be reasons-wise permissible or obligatory despite the fact that it is not itself individually favored by reasons. In effect, DBWC allows for the dual possibilities that something is right without being good or that something is good without being right. From the standpoint of the distinction between axiological appraisals and deontic appraisals, and from the standpoint of intuition, this is a desirable consequence.

Normal Primary Deontic Modalities

There are ﬁve primary deontic modalities: obligation, permissibility, prohibition, omissibility, and optionality. Only permissibility is primitive. Table 3.3 displays the DBWC semantics for the remaining primary deontic modalities at normal moment/history pairs.

Table 3.3: DBWC Normal Semantics: Primary Deontic Modalities

Operator Definition ¨ ¨ x ¨ ¨ v ∙ Positivity: M, (w , hw) ⊨ ■ for some (w , h ) ∈ Best (w, hw) ∙ Uniqueness: M, (w¨¨, h¨¨) ⊨ ■x for no (w¨¨, h¨¨) ∈ Bestv(w, h ) x w w w M, (w, hw) ⊨ ■ ¨¨¨ ¨¨¨ x ¨¨¨ ¨¨¨ ¨ ∙ Exception: M, (w , hw ) ⊨ ■ for some (w , h ) ∈ such ¨ ¨¨¨ ¨¨¨ that ⊇ and (w, h)ℜ(w , h ) ¨ ¨ x ¨ ¨ r ∙ Positivity: M, (w , hw) ⊨ ■ for some (w , h ) ∈ Best (w, hw) ¨¨ ¨¨ x ¨¨ ¨¨ r x ∙ Uniqueness: M, (w , h ) ⊨ ■ for no (w , h ) ∈ Best (w, hw) M, (w, hw) ⊨ ■ w w  ¨¨¨ ¨¨¨ x ¨¨¨ ¨¨¨ ¨ ∙ Exception: M, (w , hw ) ⊨ ■ for some (w , h ) ∈ such ¨ ¨¨¨ ¨¨¨ that ⊇ and (w, h)ℜ(w , h ) ¨ ¨ x ¨ ¨ v ∙ Positivity: M, (w , hw) ⊨ ■ for some (w , h ) ∈ Best (w, hw) x ¨¨ ¨¨ x ¨¨ ¨¨ ¨ M, (w, hw) ⊨ ■ ∙ Exception: M, (w , hw) ⊨ ■ for some (w , h ) ∈ such ¨ ¨¨ ¨¨ that ⊇ and (w, h)ℜ(w , h ) ¨ ¨ x ¨ ¨ v ∙ Positivity: M, (w , h ) ⊨ ■ for some (w , h ) ∈ Best (w, hw) x w M, (w, hw) ⊨ ■  ¨¨ ¨¨ x ¨¨ ¨¨ v ∙ Positivity: M, (w , hw) ⊨ ■ for some (w , h ) ∈ Best (w, hw)

 is the modality of v-value-wise obligation. Philosophically, ■x means that it is obligatory for the agent to ■x . More speciﬁcally, ■x means that most of the overall normative considerations in virtue of which value is realized recommend agent to ■x . Doing the Best We Can 122

x x Obligation is unique permissibility. The formula ■ is true at (w, hw) if, and only if, ■ is true at some deontically optimific moment/history pair and ■x is true at some excepting moment/history pair, but no such excepting pair is optimific. Simplifying, ■x is true x at (w, hw) if, and only if, ■ is true at every deontically optimific moment/history pair and there’s an excepting pair.  is the modality of v-value-wise prohibition. Philosophically, ■x means that it is impermissible for the agent to ■x . Prohibition is obligation to perform an alternate. The x x formula ■ is true at (w, hw) if, and only if, ■ is true at some deontically optimific moment/history pair and ■x is true at some excepting moment/history pair, but no such x x excepting pair is optimific. Simplifying, ■ is true at (w, hw) if, and only if, ■ is true at every deontically optimific moment/history pair and there’s an excepting pair.  is the modality of v-value-wise omissibility. Philosophically, ■x means that it is omissible for the agent to ■x . Omissibility is permission to perform an alternate. The x x formula ■ is true at (w, hw) if, and only if, ■ is true at every deontically optimific moment/history pair and ■x is true at some excepting moment/history pair.  is the modality of v-value-wise optionality. Philosophically, ■x means that it is omissible for the agent to ■x . Optionality is simultaneous permissibility and omissibility. x x The formula ■ is true at (w, hw) if, and only if, ■ is true at some deontically optimific moment/history pair and ■x is true at some deontically optimific moment/history pair. Turn now to the discharged variants. Table 3.3 displays the DBWC semantics for the remaining discharged primary deontic modalities at normal moment/history pairs.

x x ! is discharged obligation. The formula !■ is true at (w, hw) if, and only if, ■

is true at (w, hw) and (w, hw) is a member of the deontic optimality set and there exists an excepting moment/history pair but no excepting moment/history pairs are members of the optimality set. Strictly speaking, again, this will tend to mean that considerations in virtue of which the performance is permissible will play the appropriate role in the production of the performance.

x ! is discharged prohibition. The formula !■ is true at (w, hw) if, and only if, x ■ is true at (w, hw) and (w, hw) is a member of the deontic optimality set and there exists an excepting moment/history pair but no excepting moment/history pairs are members of the optimality set.

x x ! is discharged omissible. The formula !■ is true at (w, hw) if, and only if, ■

is true at (w, hw) and (w, hw) is a member of the deontic optimality set and there exists an excepting moment/history pair.

x ! is discharged prohibition. The formula !■ is true at (w, hw) if, and only if, x x either ■ or ■ is true at (w, hw) and (w, hw) is a member of the deontic optimality set and 3.4. The DBWC Framework 123

Table 3.4: DBWC Normal Semantics: Discharged Primary Deontic Modalities

Operator Definition x v ∙ Positivity: M, (w, hw) ⊨ ■ and (w, h) ∈ Best (w, hw) ∙ Uniqueness: M, (w¨, h¨ ) ⊨ ■x for no (w¨, h¨ ) ∈ Bestv(w, h ) x w w w M, (w, hw) ⊨ !■ ¨¨ ¨¨ x ¨¨ ¨¨ ¨ ∙ Exception: M, (w , hw) ⊨ ■ for some (w , h ) ∈ such ¨ ¨¨ ¨¨ that ⊇ and (w, h)ℜ(w , h ) x v ∙ Positivity: M, (w, hw) ⊨ ■ and (w, h) ∈ Best (w, hw) ∙ Uniqueness: M, (w¨, h¨ ) ⊨ ■x for no (w¨, h¨ ) ∈ Bestv(w, h ) M, (w, h ) ⊨ !■x w w w w  ¨¨ ¨¨ x ¨¨ ¨¨ ¨ ∙ Exception: M, (w , hw) ⊨ ■ for some (w , h ) ∈ such ¨ ¨¨ ¨¨ that ⊇ and (w, h)ℜ(w , h ) x v ∙ Positivity: M, (w, hw) ⊨ ■ and (w, h) ∈ Best (w, hw) x ¨ ¨ x ¨ ¨ ¨ M, (w, hw) ⊨ !■ ∙ Exception: M, (w , hw) ⊨ ■ for some (w , h ) ∈ such that ¨ ¨ ¨ ⊇ and (w, h)ℜ(w , h ) x x ∙ Actuality: M, (w, hw) ⊨ ■ or M, (w, hw) ⊨ ■ and v (w, hw) ∈ Best (w, hw) x M, (w, hw) ⊨ !■ ¨ ¨ x ¨ ¨ v ∙ Positivity: M, (w , hw) ⊨ ■ for some (w , h ) ∈ Best (w, hw) ¨¨ ¨¨ x ¨¨ ¨¨ v ∙ Positivity: M, (w , hw) ⊨ ■ for some (w , h ) ∈ Best (w, hw)

¨ ¨ ¨ ¨ the alternate is true at (w , hw) and (w , hw) is a member of the deontic optimality set.

Normal Subsidiary Deontic Modalities

Subsidiary deontic modalities are so-called because they are the deﬁned by appeal to deontic value rankings over the performances to which the primary deontic modalities already apply. Table 3.5 displays the formal semantics for subsidiary deontic modalities.

Table 3.5: DBWC Normal Semantics: Subsidiary Deontic Modalities

Operator Definition ∙ Positivity: M, (w, h ) ⊨ ■x M, (w, h ) ⊨ ■x w  w  x ∗ x ∙ Pro-Ranking: ■ ≾v ■, for every M, (w, hw) ⊨  ∙ Positivity: M, (w, h ) ⊨ ■x M, (w, h ) ⊨ ■x w  w  x ∗ x x ∙ Con-Ranking: ■ ≾v ■ , for every M, (w, hw) ⊨ ■ ∙ Positivity: M, (w, h ) ⊨ ■x M, (w, h ) ⊨ ■x w  w  x ∗ x x ∙ Pro-Ranking: ■ ≺v ■, for some M, (w, hw) ⊨ ■ ∙ Positivity: M, (w, h ) ⊨ ■x M, (w, h ) ⊨ ■x w  w  x ∗ x x ∙ Con-Ranking: ■ ≺v ■ , for some M, (w, hw) ⊨ ■ ∙ Positivity: M, (w, h ) ⊨ ■x M, (w, h ) ⊨ ■x w  w  ¨ ¨ x ¨ ¨ ∙ Neu-Ranking: M, (w , hw) ⊨ ■ for all (w , hw) ∈ x x x M, (w, hw) ⊨ ■ M, (w, hw) ⊨ ¬■ and M, (w, hw) ⊨ ¬■

 is the modality of v-value-wise maximality. Philosophically, ■x means that it Doing the Best We Can 124

is maximal for the agent to ■x ; or, that ■x is the most the agent can permissibly perform. x x The formula ■ is true at (w, hw) if, and only if, ■ is true at (w, hw) and no relevant x alternative is strictly v-value-wise better than ■ at (w, hw).

 is the modality of v-value-wise minimality. Philosophically, ■x means that it is minimal for the agent to ■x ; or, that ■x is the least the agent can permissibly perform. x x The formula ■ is true at (w, hw) if, and only if, ■ is true at (w, hw) and no relevant x alternative is strictly v-value-wise worse than ■ at (w, hw).

 is the modality of v-value-wise optimality. It is the status of a performance’s being beyond the call. Philosophically, ■x means that it is beyond the call for the agent to x x x ■. The formula ■ is true at (w, hw) if, and only if, ■ is true at (w, hw) and at x least one relevant alternative is strictly v-value-wise worse than ■ at (w, hw).

 is the modality of v-value-wise suboptimality. It is the status of a performance’s permissibly suboptimal or merely deontically satisfactory. Philosophically, ■x means x x that it is permissibly suboptimal for the agent to ■. The formula ■ is true at (w, hw) x if, and only if, ■ is true at (w, hw) and at least one relevant alternative is strictly x v-value-wise better than ■ at (w, hw).

 is the modality of v-value-wise indiﬀerence. It is the status of a performance being normatively irrelevant, but not lacking status altogether. Philosophically,  ■x means x x that it is insigniﬁcant for the agent to ■. The formula  ■ is true at (w, hw) if, and only x if, ■ is true at (w, hw) and indeed at every contextually salient abilitively accessible moment/history pair.

 is the modality of v-value-wise nondeonticality. It is the lack of any v-value-wise deontic status whatsoever. Philosophically, ■x means that it is nondeontic for the x x x x agent to ■. The formula ■ is true at (w, hw) if, and only if, both ■ and ■

are false at (w, hw).

The discharge operator can be attached to subsidiary deontic modalities. Table 3.6 displays the formal semantics for discharged subsidiary deontic modalities.

Subsidiary deontic modalities are discharged when the deontic modal specified in the appropriateness condition is discharged. Thusly, discharged maximality and discharged minimality require discharged permissibility. Discharged going beyond the call, discharged permissible suboptimality, and discharged indifference require discharged optionality. There are no other differences between the formal semantics for subsidiary deontic modals and their discharged variants. 3.4. The DBWC Framework 125

Table 3.6: DBWC Normal Semantics: Discharged Subsidiary Deontic Modalities

Operator Definition ∙ Appropriateness: M, (w, h ) ⊨ !■x M, (w, h ) ⊨ !■x w  w  x ∗ x ∙ Pro-Ranking: ■ ≾v ■, for every M, (w, hw) ⊨  ∙ Appropriateness: M, (w, h ) ⊨ !■x M, (w, h ) ⊨ !■x w  w  x ∗ x x ∙ Con-Ranking: ■ ≾v ■ , for every M, (w, hw) ⊨ ■ ∙ Appropriateness: M, (w, h ) ⊨ !■x M, (w, h ) ⊨ !■x w  w  x ∗ x x ∙ Pro-Ranking: ■ ≺v ■, for some M, (w, hw) ⊨ ■ ∙ Appropriateness: M, (w, h ) ⊨ !■x M, (w, h ) ⊨ !■x w  w  x ∗ x x ∙ Con-Ranking: ■ ≺v ■ , for some M, (w, hw) ⊨ ■ ∙ Appropriateness: M, (w, h ) ⊨ !■x M, (w, h ) ⊨ !■x w  w  ¨ ¨ x ¨ ¨ ∙ Neu-Ranking: M, (w , hw) ⊨ ■ for all (w , hw) ∈

3.4.3 DBWC Syntax

In this subsection, I sketch some of the axiom schemata, inference rules, and theorems for DBWC extending WWCD not previously covered.

Proof Meta-Rules

DBWC contains all the WWCD proof rules and more besides. Table 3.7 displays some of the standard DBWC proof rules.

Table 3.7: DBWC Inference Meta-Rules

Rule Name Rule Schema RN If ⊢ ¬, then ⊢  FDetach■x ■x , (■x → ■x ) ⊢ ■x Prereq■x ■x , □(■x → ■x ) ⊢ ■x

RN is the DBWC principle stating that contradictions lack deontic status. By implication, if the conjunctive performance (■x ∧ … ∧ ■x ) is alethically impossible, then it lacks deontic status. In other words, RN entails that agents cannot be obliged—or anything else, for the matter—to perform an impossible combination of performances. FDetach■x is the DBWC rendering of factual detachment for permissions. It is here understood as an instance of modus ponens and so is valid for all praxeological modals. Prereq■x is the DBWC rendering of the following intuitive deontic principle:

∙ Deontic Prerequisites (DP): If it is permissible for agent to ■x , and it is a necessary prerequisite of ■x that ■x , then it is permissible for to ■x . Doing the Best We Can 126

DP—and, by extension, Prereq■x —says that the necessary prerequisites of what is permissible are likewise permissible. The principle is valid in DBWC for all praxeological modals.

Axiom Meta-Schemata

DBWC contains all the WWCD axiom schemata and more besides. Inspection reveals that the deontic axiom meta-schemata are nigh identical to the WWCD reasons axiom meta- schemata. textbfTable 3.8 displays some of the standard DBWC axiom meta-schemata.

Table 3.8: DBWC Axiom Meta-Schemata

Axiom Name Axiom Meta-Schema N ¬⊥ M■x (■x ∨ ■x ) → ■x ( ∨ ) M■x ■x ( ∧ ) → (■x ∧ ■x ) C■x ■x ( ∨ ) → (■x ∨ ■x ) C■x (■x ∧ ■x ) → ■x ( ∧ ) R■x (■x ∨ ■x ) ↔ ■x ( ∨ ) R■x ■x ( ∧ ) ↔ (■x ∧ ■x ) K■x ■x ( → ) → (■x → ■x ) D■x ■x → ■x T!■x !■x → ■x

DBWC has—and lacks—several noteworthy axiom meta-schema. The main thing to observe is that there is a kind of symmetry between the deontic and praxeological meta- schemata in the sense that the former do not outstrip the latter. If an axiom schema fails for a praxeological modal, its deontic variant will also fail. Arguably the most interesting instance of this observed symmetry is the failure of the deontic duality axiom. Recall that Dual◆x axiom fails for any praxeological modality in WWCD. More speciﬁcally, (¬■x ¬ → ◆x ) fails. DBWC inherits this feature and the corresponding deontic duality is false:

■x ↔ ¬¬■x

More speciﬁcally, (¬¬■x → ■x ) fails. In other words, permissibility is not merely the absence of obligation to the contrary. Philosophically speaking, DBWC holds that permissibility is a matter of the performance’s being at least somewhat preferable from a deontic point of view, just as obligation requires that the performance is most deontically preferable. The mere fact that an alternate lacks most deontic preferability does not imply that the the thing has a whit of deontic preferability. By analogy, the absence of 3.4. The DBWC Framework 127

counterevidence weighing against that p, for some proposition p, is not itself evidence supporting that p. Just as an agent can lack any evidence one way or the other with respect to that p, a performance can lack any deontic preferability speaking for it or against it. The nondeontic is not obligatory because it lacks any deontic preferability in any direction at all, which also explains why the nondeontic is not permissible, not impermissible, not omissible, and not optional.

Interaction Theorems

Interaction theorems describe how diﬀerent modalities in a polymodal logic interact with one another. As to be expected, DBWC has a number of interaction theorems, which are depicted with lattices. Arrows between well-formed formulas depict direction of entailment. Bear in mind that entailments are transitive, obviating the need to depict every conceivable interaction between the relevant modalities. Figure 3.3 displays the interaction lattice for deontic modalities. Figure 3.3: Lattice of Deontic Interactions

■x ■x

■x ■x ■x ■x

■x ■x

■x

■x  ■x ■x ■x

The lattice may be summarized as follows. Obligation implies both maximality and minimality, and each in turn implies permissibility. Prohibition implies both alternate maximality and alternate minimality, and each in turn implies omissibility. Beyond the call, indiﬀerence, and permissible suboptimality each imply optionality, which in turn implies both permissibility and omissibility. Nondeonticality neither implies, nor is implied by, any other deontic modality. Doing the Best We Can 128

In point of fact, the relation between nondeonticality and the other deontic modals is stronger than the lattice suggests. Nondeonticality implies the falsity of every other deontic modal and each deontic modal implies the falsity of nondeonticality. This is enshrined in the following nondeonticality meta-theorem:

ND. ■x ↔ (¬■x ∧ ¬■x ) Nondeonticality

The proof of this theorem simply cites the definition of nondeonticality. Relatedly, DBWC is rich with interdefinability meta-theorems. There is a pair of meta-theorems that describe the interdefinability of obligation and prohibition:

OB/IM. ■x ↔ ■x Obligation/Prohibition

IM/OB. ■x ↔ ■x Prohibition/Obligation

And a set of meta-theorems to the eﬀect that all primary deontic modals are deﬁnable from permissibility:

OB/PE. ■x ↔ (■x ∧ ¬■x ) Obligation/Permission

IM/PE. ■x ↔ (¬■x ∧ ■x ) Prohibition/Permission

OM/PE. ■x ↔ ■x Omission/Permission

OP/PE. ■x ↔ (■x ∧ ■x ) Option/Permission

And a set of meta-theorems to the eﬀect that all primary deontic modals are deﬁnable from omissibility:

OB/OM. ■x ↔ (¬■x ∧ ■x ) Obligation/Omission

PE/OM. ■x ↔ ■x Permission/Omission

IM/OM. ■x ↔ (■x ∧ ¬■x ) Prohibition/Omission

OP/OM. ■x ↔ (■x ∧ ■x ) Option/Omission

The totality of the interdeﬁnability meta-theorems uphold the logical relations between praxeo-deontic compounds schematized by the deontic square of opposition. 3.4. The DBWC Framework 129

A close inspection of the deontic lattice and interdeﬁnability theorems immediately suggests the following deontic exhaustion meta-theorem:

DE. ■x ∨ ■x ∨ ■x Deontic Exhaustion

The meta-theorem says that a performance is either permissible, omissible, or nondeontic for an agent. It is a trivial consequence of the interdeﬁnability meta-theorems. I want to brieﬂy turn attention to a set of substantive deontic principles:

∙ Harman’s Law (GL): If it is obligatory for to that , then has most/some reason to that .16

∙ Haji’s Law (HL): If has most/some reason to that , then is able to that and is able to otherwise than .17

∙ Moore’s Law (ML): If it is obligatory for to that , then is able to that and is able to otherwise than .18

∙ Kant’s Law (KL): If it is obligatory for to that , then is able to that .

GL says that if it is obligatory for an agent to perform some performance, whether that performance is being, believing, doing, intending, intentionally doing, knowing, or something else entirely, then the agent has most/some reason to perform that performance. HL says if an agent has most reason to perform some performance, then the agent can perform that performance and can perform otherwise. ML says if it is obligatory for an agent to

16 Compare with the following passage from Gilbert Harman (1977): The evaluative ‘ought’, which is an ‘ought to be’, carries no implications about an agent’s having reasons to act. The moral ‘ought’, which is an ‘ought to do’, does carry the implication that the person who ought to do something has a reason to do it (1977: 87). Since the HL acronym is already denotes Haji’s Law, I employ the GL acryonym for Harman’s Law.I oﬀer two heuristics to aid memory: G after ‘Gilbert’ and G is alphabetically prior to H. 17 See Chapter2 footnote 27. 18 Compare with the following passage from G. E. Moore (1912): [A]n action is only right, if it produces the best possible consequences; and by “the best possible consequences” was meant “consequences at least as good as would have followed from any action which the agent could have done instead”. It does, therefore, hold that the question whether an action is right or wrong does always depend upon a comparison of its consequences with those of all the other actions which the agent could have done instead. It assumes, therefore, that wherever a voluntary action is right or wrong (and we have throughout only been talking of voluntary actions), it is true that the agent could, in a sense, have done something else instead. This is an absolutely essential part of the theory (1912: 102–103). Doing the Best We Can 130

perform some performance, then the agent can perform that performance and can perform otherwise. KL says if it is obligatory for an agent to perform some performance, then the agent can perform that performance. GL and HL entail ML. ML entails KL. Though each is controversial, I want to observe that all are in some way vindicated by DBWC, though some not without qualiﬁcation. Allow me to explain. There is a very special set of DBWC theorems relating deontic modals to the reasons modals. If v = r, then deontic value is nothing more than reasons-wise weight, in which

case ≾v = ≾r, by which I mean to indicate that the ≾v-wise orderings over Pair is identical to

the ≾r-wise orderings over Pair. I shall denote the reasons-wise conception of the deontic operators with the appropriate subscript pairs. All of the following equivalence claims are DBWC meta-theorems:

x x OB/MR. r■ ↔ ■ Obligation/Most Reason

x x PE/SR. r■ ↔ ■ Permission/Some Reason

x x IM/MR. r■ ↔ ■ Prohibition/Most Reason

x x OM/SR. r■ ↔ ■ Omission/Some Reason

x x x OP/SR. r■ ↔ (■ ∧ ■) Optionality/Some Reason

Jointly call these the Harmanian meta-theorems because they state that all deontic modalities are interdeﬁnable with reasons modalities. Obligation is having most pro-reason. Permissibility is having some pro-reason. Prohibition is having most con-reason. Omissi- bility is having some con-reason. Optionality is having both some pro-reason and some con-reason. If it indeed turns out that v = r, then reasons-wise modals are deontic modals simpliciter, which is to say that obligation of any kind is a matter of having most of the relevant kind of pro-reason and permission of any kind is a matter of have some of the relevant kind of pro-reason and so on. I have already shown that HL is vindicated by the WWCD Hijian meta-theorems, though with the disclaimer that the relevant excepting ability is weaker than the relevant commissive ability, which is indicated with a superscripted asterisk. DBWC inherits this family of meta-theorems. The following are also all DBWC meta-theorems: 3.4. The DBWC Framework 131

x x ∗ x OB/ML. ■ → ( ▣ ■ ∧ ▣ ■) Obligation/Moore’s Law

x x ∗ x PE/ML. ■ → ( ▣ ■ ∧ ▣ ■) Permission/Moore’s Law

x ∗ x x IM/ML. ■ → ( ▣ ■ ∧ ▣ ■) Prohibition/Moore’s Law

x ∗ x x OM/ML. ■ → ( ▣ ■ ∧ ▣ ■) Omission/Moore’s Law

x x x OP/ML. ■ → ( ▣ ■ ∧ ▣ ■) Optionality/Moore’s Law

Jointly call these Moorean meta-theorems because they relate deontic modals with praxeo-abilitive modals. OB/ML says that if it is obligatory for an agent to be, believe, do, intend, intentionally do, or know something, then the agent can be, do, intend, or know that thing as well as can be, do, intend, or know otherwise. PE/ML, IM/ML, OM/ML, and OP/ML say the same except for permissibility, impermissibility, omissibility, and optionality respectively. The Moorean meta-theorems imply ML and more besides. As should be made explicit, the caveat applying to the Hajian meta-theorems likewise applies to the Moorean meta-theorems. In both cases, the relevant excepting ability is logically weaker than the relevant commissive ability, which is, again, indicated with a superscripted asterisk attached to the relevant abili-consistency modal. In fact, the Moorean meta-theorems can be perfectly generalized across any number of coexisting deontic modals:

x x x ∗ x x ∗ x G/OB/ML. (■ ∧ … ∧ ■ ) → ( ▣ ■ ∧ ▣ ■ ∧ … ∧ ▣ ■ ∧ ▣ ■ )

x x x ∗ x x ∗ x G/PE/ML. (■ ∧ … ∧ ■ ) → ( ▣ ■ ∧ ▣ ■ ∧ … ∧ ▣ ■ ∧ ▣ ■ )

x x ∗ x x ∗ x x G/IM/ML. (■ ∧ … ∧ ■) → ( ▣ ■ ∧ ▣ ■ ∧ … ∧ ▣ ■ ∧ ▣ ■ )

x x ∗ x x ∗ x x G/OM/ML. (■ ∧ … ∧ ■ ) → ( ▣ ■ ∧ ▣ ■ ∧ … ∧ ▣ ■ ∧ ▣ ■ )

x x x x x x G/OP/ML. (■ ∧ … ∧ ■ ) → ( ▣ ■ ∧ ▣ ■ ∧ … ∧ ▣ ■ ∧ ▣ ■ )

The generalized Moorean meta-theorems jointly state that the agent has the ability to live up to every deontic appraisal incumbent upon the agent. There is a parallel set of Kantian meta-theorems relating deontic modals with the relevantly ability to commit or except. The Kantian meta-theorems imply KL and more besides. As to be expected, they can also be generalized across any number of coexisting deontic modals. They are an obvious consequence of the Moorean meta-theorems and Doing the Best We Can 132

omitted for sake of space. So, too, are there a set of generalized Kantian meta-theorems that are likewise omitted for sake of space. My point is that DBWC elegantly elucidates the theoretical ties betweens obligations, reasons, and abilities. The Moorean—and therefore Kantian—meta-theorems are easily derivable from the Harmanian and Hajian meta-theorems. The Hajian meta-theorems can just as well be derivable from the Harmanian and Moorean meta-theorems. All these families of meta-theorems are independently and easily derivable from the relevant modalities’ formal semantics.

3.5 Adequacy Desiderata Satisﬁed

In this section, I show that DBWC satisﬁes the three adequacy desiderata for any praxeo- deontic logic worth its salt.

3.5.1 Satisfying Meinong’s Constraint

Recall Meinong’s Constraint:

∙ Meinong’s Constraint: An adequate logic of obligation must heed the distinction between the evaluative and deliberative senses of modal auxiliaries.

In effect, the constraint requires that an adequate praxeo-deontic logic does not conflate axiological and deontic appraisals. In particular, the evaluative ‘ought’ and obligation operators should be distinguishable. DBWC satisfies Meinong’s Constraint. The evaluative ‘ought’ and obligation are easily distinguishable within the framework. I shall briefly discuss each in turn. Table 3.3 displays the WWCD semantics for obligation and kin. Roughly, it is obligatory for the agent to be, believe, do, intend, intentionally do, or know that at a world- moment/world-history pair if, and only if, the agent is, believes, does, intends, intentionally does, or knows that in all the agent’s best abilitively accessible contextually salient world-pair and there’s an excepting world-pair. In a word, a performance is obligatory in virtue of the agent’s performing it in all the relevant optimific world-pairs. Table 3.9 displays the DBWC semantics for the evaluative ‘ought’ at normal moment/history pairs.  is the modality of evaluative ‘ought’. Philosophically,  means that it v-value-wise ought to be the case that (provided that ‘ought’ is read in the evalua-

tive mood). The formula  is true at (w, hw) if, and only if, is true at a contextually salient world-moment/world-history pair and there is no contextually salient world-pair 3.5. Adequacy Desiderata Satisﬁed 133

Table 3.9: DBWC Normal Semantics: The Evaluative ‘Ought’

Meta-Operator Definition ¨ ¨ ¨ ¨ ∙ Incidence: M, (w , hw) ⊨ for some (w , hw) ∈ ¨¨ ¨¨ ¨¨ ¨¨ M, (w, hw) ⊨  ∙ Optimality: M, (w , hw) ⊨ ¬ for no (w , hw) ∈ such that ¨ ¨ ¨¨ ¨¨ (w , hw) ≾v (w , hw)

as nonstrictly v-wise-valuable at which ¬ is true. Simplifying, is true in all the best contextually salient world-pairs. There are critical semantical diﬀerences between  and . The former operates upon any well-formed formula, the latter only upon performative formulas. The former lacks anything resembling the latter’s exception condition. Consequently, ⊤ is a DBWC meta-theorem, but neither ⊤ nor ■x ⊤ are DBWC meta-theorems. The former appeals to relevant possibilities, whereas the latter appeals to relevant abilitive possibilities. The point of  is to express v-value-wise ideality and the point of  is to express what is v-value-wise required of an agent.

3.5.2 Satisfying Marcus’s Constraint

Recall Marcus’s Constraint:

∙ Marcus’s Constraint: The Meinong/Chisholm Thesis must be false in an adequate logic of obligation

The Meinong/Chisholm Thesis is tantamount to the following equivalence claim:

■x ↔ ■x

In eﬀect, the constraint requires that the equivalence claim fails in an adequate praxeo- deontic logic. Plausibly, the equivalence claim should fail in both directions. DBWC satisﬁes Marcus’s Constraint because the equivalence claim fails for each direction. I leave the proofs as exercises for the reader. Countermodels to either direction will exploit the nonaccessibility of ideal world-pairs. In the left-to-right direction, ■x can be true even if the agent lacks abilitive access to any world-pair at which ■x is true, which ensures the absence of obligation. In the right-to-left direction, ■x can be true even if there are better abilitively inaccessible contextually salient possible world-pairs at which the agent does otherwise, which ensures the absence of ideality. Doing the Best We Can 134

3.5.3 Satisfying Urmson’s Constraint

Recall Urmson’s Constraint:

∙ Urmson’s Constraint: An adequate logic of obligation must accommodate the subsidiary deontic statuses.

In effect, an adequate praxeo-deontic logic must recognize a wider corpus of deontic concepts that traditional deontic theorizing allows. The puzzles of expressive inadequacy are a powerful source of motivation for the constraint. Deontic theories that fail to satisfy it are unable to appropriate handle the relevant intuitive data without merely explaining it away. Put differently, the problems of expressive inadequacy arise when deontic theory is theoretically impoverished in such a way that it violates Urmson’s Constraint. Recognizing the wider corpus of deontic notions is a theoretical enrichment that enables a framework to intelligently capture natural language sentences of increasing complexity. DBWC satisfies Urmson’s Constraint. Table 3.5 displays the formal semantics for subsidiary deontic modalities. As a corollary, DBWC is equipped to handle the sorts of sentences that typically reveal the expressive inadequacy of classical deontic logics. McNamara’s first puzzle concerns situations in which the obligatory and the advisable come apart. The six natural language sentences I used to illustrate the point are translated in DBWC as follows:

∙ Damian can stay home, but he ought go check on Regan.

∙ (Damian stays home) ∧ (Damian checks on Regan)

∙ Bill may do whatever he likes, but he should return the books for Albert.

∙ (Bill returns the books) ∧ (Bill returns the books)

∙ It is advisable, but certainly not required, that Dana store her valuables in the safe while she’s away.

∙ (Dana uses her safe) ∧ ¬(Dana uses her safe)

∙ Of course Dominic is permitted to refuse to help Scholastica, but he shouldn’t. 3.5. Adequacy Desiderata Satisﬁed 135

∙ (Dominic helps Scholastica) ∧ (Dominic helps Scholastica)

∙ Lily doesn’t have to go to the meeting, but she really ought to go.

∙ (Lily attends meeting) ∧ (Lily attends meeting)

∙ It is best for Scholastica if she simply buys the research materials she needs, but Dominic also has them and she can get permission to use them.

∙ (Scholastica buys materials) ∧ ▣[](Scholastica borrows materials)

While I take it that the spirit of the method is obvious, it is worth remarking on two points. First, the relevant praxeological operators are suppressed because I take it that they are represented in the natural language portions. Second, I translate ‘ought’ using the maximality operator, but translate ‘should’ using the beyond the call operator, at least in some cases. I am not certain that translating ‘should’ in this way is correct but, to my ear, ‘ought’ and ‘should’ are of a kin but neither implies the other. ‘Ought’ roughly means that the thing is advisable because it indicates that it is best full stop among all the permissible alternatives. ‘Should’ roughly means that the thing is advisable because it is comparatively better without indicating its place in the overall ranking of permissible alternatives. In a word, ‘should’ seems to me to sometimes have interesting contrastive properties that ‘ought’ lacks. Understood in this way,  denotes the deontic ‘ought’ and there are cases in which  denotes the deontic ‘should’. McNamara’s second puzzle concerns situations in which the lower bound of deontic acceptability is salient. The six natural language sentences I used to illustrate the point are translated in DBWC as follows:

∙ The least Damian can do is call to see how Regan is holding up.

∙ (Damian calls Regan)

∙ Bill may do whatever he likes, but he must at least tell Albert whether he’ll return the books for him.

∙ (Bill helps Albert) ∧ (Bill informs Albert) Doing the Best We Can 136

∙ At minimum, Dana should lock the door to her house while she’s away.

∙ (Dana locks her door)

∙ Dominic doesn’t have to help Scholastica, but the least he can do is refuse her politely.

∙ (Dominic helps Scholastica) ∧ (Dominic politely refuses)

∙ Lily doesn’t have to go to the meeting, but she can’t do anything less than work at her desk. She cannot, for instance, call it a day and go home.

∙ (Lily attends meeting) ∧ (Lily works) ∧ (Lily goes home)

∙ (Scholastica forgets) ∧ (Scholastica borrows materials)

As before, I take it that the spirit of the method is obvious and the relevant praxeological operators are again suppressed for the same reason. I have considered but precious few examples. While they fall short of anything of a proof, they are nonetheless important evidence to the eﬀect that DBWC overcomes the problems of expressive inadequacy. In the very least, they suggest that the framework goes far further in the direction of a general solution than traditional deontic theorizing.

3.6 Conclusion

I have sketched a polymodal impossible branching tree framework for obligation, permission, and kin called Doing the Best We Can (DBWC). The framework, and its complexity, is in part motivated by appeal to three adequacy desiderata. First, the distinctions between normative appraisals, and axiological and deontic appraisals in particular, must be maintained. The failure to respect the distinctions means that the formal theory is categorically mistaken. Second, naïve reductions of deontic appraisals to axiological appraisals must fail. While I think that the right is deﬁned from the good, the relation is a complicated one. It is certainly false that the right just is the good. A formal theory of obligation should in some way respect the prescriptive force 3.6. Conclusion 137

that is simultaneously constitutive of deontic modals and lacked by axiological modals. Third, there is a wide corpus of deontic concepts that deserve attention. A formal theory of obligation should make room for these subsidiary deontic statuses lest it succumb to the puzzles of expressive inadequacy. DBWC meets all the adequacy desiderata. DBWC is an elegant deontic framework that can be used to frame and guide substantive theory. It is my aim to employ it to sketch a theory of justiﬁcation ascriptions in general and epistemic justiﬁcation in particular. Part III

Philosophical Theory CHAPTER 4

DEONTIC JUSTIFICATION

Abstract

I sketch the schematic DBWC theory of deontic justification in two phases. First, I characterize the distinction between morphic and praxistic justification. Second, I identify, compare, and contrast the two main competing conceptions of deontic justification: justification-as-permission and justification-as-obligation.

4.1 Introduction

ustification ascriptions are normative appraisals. There are four taxa of normative J appraisals: aretaic, axiological, deontic, and hypological. So, at least in principle, there are four possible taxa of justification ascriptions. In this chapter, I articulate the DBWC theory of deontic justification. Accordingly, justification is a deontic status akin to obligation or permission. In point of fact, justification just is obligation or permission. Having expressed my intention for the chapter, I think it worth contrasting two broad deontic conceptions of justification:

∙ Universal Deontic Conception: All justiﬁcation appraisals are deontic appraisals.

∙ Existential Deontic Conception: Some justiﬁcation appraisals are deontic appraisals.

I defend an existential conception of justification. I do not deny that there are legitimate nondeontic justification ascriptions. Allow me to briefly canvass the other viable normative conceptions and tersely motivate why I think that they are irrelevant in view of my ultimate theoretical ends.

139 Deontic Justiﬁcation 140

Sometimes justification is ascribed to persons. It might be said of a person that they are justifiable or unjustifiable, as when we evaluate them for the way they are moved to act or believe as viewed from their first-person perspective with all the relevant limitations in mind. When ascribed to persons, justification is hypological, tracking excusability or reasonableness. When a person is justifiable, it means that they do not deserve criticism, or that they are reasonable, or that they are worthy of credit; when unjustifiable, they do not deserve praise, or that they are unreasonable, or that they deserve criticism. I leave hypological justification aside because the deontic and the hypological are unrelated. It possible for an agent to be hypologically justifiable but their performance deontically unjustifiable and it is possible for the agent to be hypologically unjustifiable but their performance deontically justifiable. The former is an instance of excusable wrongdoing and the latter an instance of inexcusable rightdoing (e.g., suberogation). Because both are possible, hypological justification is neither necessary nor sufficient for deontic justification. Sometimes justification is ascribed to performances in such a way as to say that they are means of realizing value. It might be said of a performance that its occurrence or nonoccurrence realizes value or disvalue. This is just to say of a certain state of affairs exhibiting certain properties that its occurrence is good or bad for the agent. When ascribed to states of affairs (or performances qua states of affairs), justification is axiological, tracking degree of favor, support, or value. When a state of affairs is justifiable for a person, it means that its occurrence is in some sense and to some degree good for the person; when unjustifiable, its occurrence is in some sense and to some degree bad for the person. Alternatively phrased, a performance is axiologically justifiable if, and only if, realizes value; axiologically unjustifiable if, and only if, it realizes disvalue. I likewise leave axiological justification aside because the relation between the deontic and the axiological is more complicated than the axiological conception allows. That which justifies is one thing, that which is justified another. It is possible for a state of affairs to be axiologically justifiable for an agent but the performance deontically unjustifiable and it is possible for a state of affairs to be axiologically unjustifiable but the performance deontically justifiable. The former is an instance of an insufficient good (e.g., promoting goodness to a degree less than required) and the latter is an instance of a necessary evil (e.g., selecting the least bad option). Axiological justification is neither necessary nor sufficient for deontic justification. I know of no viable aretaic conception of justification. Justification is not typically ascribed to characters in a way that is evocative of virtuousness or viciousness. I leave it to the reader to decide whether this poses a problem for virtue-theoretic accounts of 4.2. The Schematic DBWC Theory of Deontic Justification 141

epistemic justification. The purpose of this chapter is to articulate the DBWC theory of deontic justification and to trace some of its major implications. The structure of this chapter is as follows. In Section 4.2, I sketch the schematic DBWC theory of deontic justification. I distinguish between two kinds of deontic justification, morphic and praxistic justification each definable by two different conceptions of deontic justification, justification-as-permission and justification- as-obligation. The remainder of the chapter is devoted to comparing and contrasting justification-as-permission and justification-as-obligation. In Section 4.3, I observe the ability requirements for deontic justification. In Section 4.4, I argue that deontic conflicts are impossible. In Section 4.5, the DBWC brand of deontic holism is considered. In Section 4.6, I show how DBWC resolves the lottery and preface paradoxes. Finally, in Section 4.7,I conclude by summarizing the findings of the chapter.

4.2 The Schematic DBWC Theory of Deontic Justiﬁcation

In this section, I sketch the schematic DBWC deontic theory of justiﬁcation. There are two possible competing deontic theories of justiﬁcation. The subsections are thematically devoted to comparing and contrasting various aspects of the two deontic conceptions.

4.2.1 Morphic and Praxistic Justiﬁcation

There is a difference between performance types and performance tokens. So, too, should it be correspondingly expected that there is a difference between the normative appraisal of each. I shall respectively call each morphic and praxistic justification. The distinction between morphic and praxistic justification is not unlike what Roderick Firth (1978), and many epistemologists since, respectively call propositional and doxastic justification:

To distinguish between these two epistemic uses of the term [‘justified’] we may adopt the traditional device for separating the “logical content” of a belief from the psychological state of believing. We may distinguish propositional [justification] from doxastic [justification] (Firth 1978: 217–218).

An ascription of doxastic justification tells us something about a belief— whether the belief is justifiably held. An ascription of propositional justification tells us something about a proposition—whether the proposition is such that there is sufficient justification for someone to believe it (Littlejohn 2012: 5). Deontic Justification 142

There is a sense in which you are justified in believing a certain proposition simply by having reasons that support it. Call this propositional justification. There is another sense in which you are justified in believing that only if you base your belief that on those very reasons you have that support it. Call this doxastic justification (Oliveira 2015: 389).

Propositional justification to believe that is supposed to be a positive epistemic property one can have even if one fails to believe that . Accordingly, the relationship between propositional and doxastic justification is, in part, a relationship between a belief type and a belief token. Belief tokens cannot be justified unless there are token beliefs; however, the type can be justified even if it has no corresponding token. For a non-epistemic example, I might have moral justification to kill the one in order to save five in a trolley case even though I don’t kill the one. Here, an action type is deemed morally justified even though it has no corresponding token (Silva 2015b: 371 fn. 2).

Doxastic justification is the justification attributed to an agent’s actual doxastic state in the way that it is actually held. Propositional justification is complicated by two competing conceptions. According to the orthodox view, propositional justification is the justification attributed to a proposition to be taken as the object of belief.1 According to a famous reformational view, propositional justification is the justification attributed to a possible belief or belief type.2 I think that the orthodox view is false and that the reformational view is correct. Epistemic justification is a normative appraisal. There are exactly four types of normative appraisals and none target propositions. So, it is literally false that propositions are targets of normative appraisals, in which case propositional justification cannot be the justification attributed to propositions. If there is supposed to be a tight connection between doxastic and propositional justification, it is better to go with the reformational view. Doxastic justification is a deontic appraisal in the sense that it targets a performance. The kind of propositional justification that is conceptually associated with doxastic justification should

1 This view is often associated with the following conception of doxastic justification: the belief that is doxastically justified if, and only if, the agent’s belief is properly based upon the factors in virtue of which the proposition that is justified for the agent. For proponents, see Rockerick Chisholm (1977, 1989), Marshall Swain (1979), Earl Conee (1980), William Alston (1985), Jonathan Kvanvig and Christopher Menzel (1990), John Pollock and Joseph Cruz (1999), Earl Conee and Richard Feldman (2004), Michael Bergmann (2006), Jonathan Kvanvig (2003, 2014), and Clayton Littlejohn (2012). 2 This view is favored by externalists of a certain breed and often associated with the claim that doxastic justification is theoretically prior to propositional justification such that the latter is defined from the former. For proponents, see Alvin Goldman (1979, 1986), Hilary Kornblith (1980), and John Turri (2010). 4.2. The Schematic DBWC Theory of Deontic Justification 143

also be a deontic appraisal otherwise it is hard to see how doxastic justification could imply propositional justification. If doxastic justification is the justification attributed to a belief token, the natural choice is to think of propositional justification as the justification attributed to a belief type. This preserves the desirable relation between the two types of epistemic justification. So understood, morphic and praxistic justification are the untyped generalizations of propositional and doxastic justification respectively. Morphic justification is attributed to a performance type. It denotes the justifiability of a performance in virtue of there being a right-making way for the agent to make the performance actual. Just as with propositional justification, the attribution of morphic justification does not imply the actualization of the performance. Praxistic justification is attribued to a performance token. It denotes the justifiedness of a performance in virtue of its actualization of a right-making way. Just as with doxastic justification, the attribution of praxistic justification implies the actualization of the performance as well as morphic justification for the performance type. The difference is perhaps best illustrated by appeal to examples:

Example 4.1. Imagine two jurors, Miss Knowit and Miss Not, deliberating about the case of Mr. Mansour. Both jurors have paid close attention throughout the trial. As a result, both have good reason to believe that Mansour is guilty. Each juror goes on to form the belief that Mansour is guilty, which he in fact is. Miss Knowit believes he’s guilty because of the evidence presented during the trial. Miss Not believes he’s guilty because he looks suspicious. Miss Knowit knows that Mansour is guilty; Miss Not does not. Why the diﬀerence? Miss Knowit believes he’s guilty on the basis of the good reasons she has, whereas Miss Not, despite having good reasons at her disposal, believes based on mere suspicion (Turri 2010: 312).

Example 4.2. A toddler is caught in a burning building. The fire and the child’s position are such that even experienced fire personnel might be at serious risk in an attempted rescue. An ordinary pedestrian passes by and, sizing up the situation and its risks, and hearing the fire engines at a considerable distance, enters the building and eventually reaches the infant hoping to rescue the child. The pedestrian waits, trapped in an upper floor until the fire personnel arrive, and then drops the infant to them below (McNamara 2011a: 157).

Example 4.3. A toddler is caught in a burning building. The fire and the child’s position are such that even experienced fire personnel might be at serious risk in an attempted rescue. A black market organ dealer passes by and, sizing up the situation and its risks, and hearing the fire engines at a considerable distance, enters the building Deontic Justification 144

hoping to kidnap the child before the authorities arrive and later harvest its organs. The organ dealer waits, trapped on an upper ﬂoor after eventually reaching the infant. When the ﬁre personnel arrive, the organ dealer drops the infant to them below (Haji 2012: 183–184).3

In Example 5.1, the believing that Mr. Mansour is guilty is morphically justified for both Miss Knowit and Miss Not. In other words, a belief type is accrued deontic status for them both; there is way for either of them to be responsive to their reasons such that their believing is appropriate. Miss Knowit realizes such a way, for she believes for the epistemically decent reasons that relevantly probabilify the proposition for her. Intuitively, her belief token actualizes the belief type in the right way such that her belief is praxistically justified. Miss Not fails to realize any such way, for she believes for epistemically indecent reasons that fail to lend evidential support for the proposition. Intuitively, her belief is praxistically unjustified. In Example 5.2 and Example 5.3, bringing it about that the infant is rescued from the fire is morphically justified for both the pedestrian and the organ dealer. In other words, an action type is accrued deontic status for them both; there is a way for either of them to be responsive to their reasons such that their action is appropriate. The pedestrian realizes such a way and the act is praxistically justified, for the pedestrian brings it about that the infant is rescued for morally decent reasons. The organ dealer’s act is praxistically unjustified, for the organ dealer acts for morally indecent reasons and thereby fails to realize a right-making way. To recapitulate, morphic justification is the justifiability of a performance type. When instantiated, morphic justification roughly means that the agent has all the makings for a justified performance token. It is potential praxistic justification in the sense that it doesn’t entail actual performance. Its indicating locutions express the mere presence of appropriateness: it is appropriate for to perform the performance. Praxistic justification is the justifiedness of a performance token. When instantiated, praxistic justification roughly means that the performance is actual and realizes a right-making way. Its indicating locutions express the actual discharge of appropriateness: appropriately performs the performance. The appeal to a permissible way distinguishes morphic justification from praxistic justification. Morphic justification is mere appropriateness, but praxistic justification is appropriately performed performance or appropriate performance performed in a permissible way. In DBWC, it is easy to describe permissible ways once it is realized that

3 Compare with McNamara (McNamara 2011a: 157). See also Terry Horgan and Mark Timmons (2010) for discussion of “nonmeritorious supererogation”. 4.2. The Schematic DBWC Theory of Deontic Justiﬁcation 145

every performance has a way. How is it that the performance is performed? Is it done for reasons? Which reasons? Is it done from virtue? Which virtues? The way of a performance can be observed in every possible moment/history pair at which the performance occurs. Permissible ways are those that are manifest in the optimific moment/history pair in virtue of which a performance is appropriate. If it is morphically justified for Velma to reach the top of the building, she can achieve praxistic justification bringing it about that Velma reaches the top of the build in a permissible way. If the only way for her to reach the top is to scale the building walls, climb the stairs, or take the elevator, she does one of these in every moment/history pair where she brings it about that Velma reaches the top of the build, in which case at least one of these occurs in some optimific pairs. Any of these ways that occurs in some of the optimific moment/history pairs (and fails to occur in some other moment/history pairs) is a permissible way. Let a blank space ( ) denote some performance, whether being, believing, doing (intentionally or not), intending, or knowing. Pulling the strands together, we get the following schematic deontic analysis of justification:

∙ Morphic Justification (MJ): It is morphically justifiable for agent (at time t) to that (at time t¨) if, and only if, it is (as of t) appropriate for to that (at t¨). ∙ Praxistic Justification (PJ): It is praxistically justified for agent (at time t) to that (at time t¨) if, and only if, that (at t¨) in a way in virtue of which it is (as of t) morphically justified for that (at t¨).

Praxistic justification implies morphic justification because, in some sense, it is successful morphic justification. Morphic justification aspires to be praxistic justification. When morphic justification fails in its aspirations, it is either because there is no performance token to speak of or because the way in which the performance is performed is unlike any in virtue of which the type of performance is appropriate. Believing that Mansour is guilty is a type of belief justifiable for Miss Not, but she doesn’t believe in the right way. Bringing it about that the infant is rescued is a type of action justifiable for the organ dealer, but he doesn’t act in the right way.

4.2.2 Two Conceptions of Deontic Justiﬁcation

I have framed the schematic definitions of morphic and praxistic justification in terms of the language of appropriateness. ‘Appropriateness’ is intended to indicate positive deontic status without indicating specifically obligation or permission. This is because there are two competing deontic conceptions of justification to consider: Deontic Justification 146

∙ Justification-as-Permission (JU/PE): Justiﬁcation is mere permissibility.

∙ Justification-as-Obligation (JU/OB): Justiﬁcation is obligation.

I briefly describe the two conceptions. Let  be the v-value-wise justification operator, where v is the formal concept of agent- and moment/history pair-relativized deontic value. As I use it, ‘deontic value’ is a term denoting whatever evaluative quantity in virtue of which performances are assessed for the presence of right-making features. Whereas an axiology is a theory of value, I use ‘deontic axiology’ for a theory of deontic value. My personal view is that deontic value is value simpliciter: the good (qua axiological appraisal) is prior to the right (qua deontic appraisal). Unfortunately, I am obliged stay the course and omit any explication or defense of my conviction. Justification-as-permission is a thesis that identifies deontic justification with mere permission. It follows that the establishment of permission, or the possession of some of the right kind of reason, suffices for the demonstration of justification. JU/PE interacts with MJ and PJ to generate the following principles:

∙ Morphic Justification-as-Permission (MJ/PE):

∙ Formally:  ■x = ■x . ∙ Informally: It is morphically justiﬁable for agent (at time t) to that (at time t¨) if, and only if, it is (as of t) permissible for to that (at t¨).

∙ Praxistic Justification-as-Permission (PJ/PE):

∙ Formally:  !■x = !■x . ∙ Informally: It is praxistically justiﬁed for agent (at time t) to that (at time t¨) if, and only if, that (at t¨) in a way that discharges ’s (as of t) permission to that (at t¨).

MJ/PE says that morphic justification is a matter of having permission to perform in a certain way. PJ/PE says that praxistic justification is a matter of discharging the permission to perform. If v = r so that v-wise deontic value is nothing more than r-reasons-wise weight, then MJ/PE is equivalent to the claim that morphic justification is some of the right kind of reason and PJ/PE is equivalent to the claim that praxistic justification is performing for the some reasons. Justification-as-obligation is a thesis that identifies justification with obligation. It follows that the establishment of permission, or the possession of some of the right kind of reason, does not suffice for the demonstration of justification. Rather, the establishment of exclusive permission, or the possession of most of the right of kind reason, is required 4.2. The Schematic DBWC Theory of Deontic Justification 147

for the demonstration of justiﬁcation. JU/OB interacts with MJ and PJ to generate the following principles:

∙ Morphic Justification-as-Obligation (MJ/OB):

Formally: x ♠ x ∙  ■ =  ■. ∙ Informally: It is morphically justiﬁable for agent (at time t) to that (at time t¨) if, and only if, it is (as of t) obligatory for to that (at t¨). ∙ Praxistic Justification-as-Obligation (PJ/OB):

∙ Formally:  !■x = !■x . ∙ Informally: It is praxistically justiﬁed for agent (at time t) to that (at time t¨) if, and only if, that (at t¨) in a way that discharges ’s (as of t) obligation to that (at t¨).

MJ/OB says that morphic justification is a matter of being obligated to perform something in a certain way. PJ/OB says that praxistic justification is a matter of discharging the obligation to perform. If v = r so that v-wise deontic value is nothing more than r- reasons-wise weight, then MJ/OB is equivalent to the claim that morphic justification is most of the right kind of reason and PJ/OB is equivalent to the claim that praxistic justification is performing for the most reasons. There is much theoretical overlap between justification-as-permission and justification- as-obligation, but there are also several important differences. One nice way to compare and contrast these views is to observe what implications they share and don’t share. The remainder of the chapter is essentially devoted to doing just that.

4.2.3 The Justiﬁcation Meta-Norm

Among many other things, normative theory of all stripes is interested in the norms that govern the permissibility conditions of aﬀective, cognitive, or conative performances. Timothy Williamson (2000), for instance, investigates the epistemic norm of assertion. In his view, assertion norms are all of a single form:

What are the rules of assertion? An attractively simple suggestion is this. There is just one rule. Where C is a property of propositions, the rule says:

(The C rule) One must: assert only if has C.

In the imperative, assert only if has C. As used here, ‘must’ expresses the kind of obligation characteristic of constitutive rules. The rule is to be parsed Deontic Justiﬁcation 148

as ’One must ((assert ) only if has C)’, with ’only if has C inside the scope of ‘One must’ but outside that of ‘assert’. The rule unconditionally forbids this combination: one asserts when lacks C (2000: 241).

Williamson’s norm schema can be fully generalized in a prescriptively adequate way. Accounts of norms, epistemic, moral, or otherwise, might be more or less complete depending on whether only necessary or only sufficient conditions are specified for the norm. Ideally, however, a norm details all the conditions, both necessary and sufficient, for norms with proper prescriptive force. Norm discussion sometimes uses the deontic language of appropriateness, correctness, or propriety, but the basic underlying structure should always be the same:

∙ Epistemic Norm Schema: It is epistemically permissible for agent to that if, and only if, .

∙ Moral Norm Schema: It is morally permissible for agent to that if, and only if, .

∙ Prudential Norm Schema: It is prudentially permissible for agent to that if, and only if, .

∙ Norm Meta-Schema: It is v-value-wise permissible for agent to that if, and only if, .

I adopt terminology from G. H. von Wright (1963) and Littlejohn (2014). Let ‘norm act’ denote the occupant of the ﬁrst blank. The norm act speciﬁes the performance over which the norm has governance. Possible substitution instances conceivably include any praxeological modal like ‘assert’, ‘be happy’, ‘be indignant’, ‘believe’, ‘bring it about’, ‘intend’, et cetera. Let ‘condition of application’ denote the occupant of the second blank. The condition of application sets the compliance condition(s) for the norm. Possible substitution instances include ‘ has an undefeated duty to make it the case that ’, ‘ knows that ’, ‘it is the case that ’, ‘the occurrence of maximizes deontic value’, et cetera. As I intend them, the norms of present interest are not constitutive, but rather fully prescriptive; they have a kind incumbency—or, beg pardon, “oughtness”—lacked by constitutive norms. DBWC has many norms as theorems, each the instantiation of a general norm schema:

∙ Deontic Meta-Norm (DMN): It is v-value-wise permissible for agent to that if, and only if, that in some of ’s deontically optimiﬁc moment/history pairs. 4.2. The Schematic DBWC Theory of Deontic Justiﬁcation 149

DMN is a semantic consequence of the DBWC analysis of deontic modals. It simply falls out of the theory. As stated, it is not terribly informative. To make better sense of the meta-norm, it is worth invoking the two competing conceptions of deontic justification. Justification-as-permission identifies justification with permissibility. DMN therefore can be equivalently reformulated:

∙ Justification-as-Permission Meta-Norm (JPMN): It is v-value-wise permissible for agent to that if, and only if, it is v-value-wise justiﬁable for to that .

JPMN implies that deontic justification is the norm of performance, for any performance, including action, assertion, belief, and deliberation. The proof is obvious and the meta- norm simply falls out of the formal theory of justification. Strictly speaking, as stated, it is morphic justification-as-permission that is the meta- norm of performance. It goes without saying that a norm act is not permissibly performed unless it discharges the agent’s justification. Consequently, conformity with the norm requires praxistic justification; morphic justification and praxistic justification go hand- in-hand. Insofar as permissibly performed norm acts are the objects of interest, and I take that they are, then JPMN should be qualifiedly understood to require praxistic justification-as-permission as opposed to mere morphic justification. The upshot is that the DBWC conception of justification-as-permission entails that deontic justification is the meta-norm of performance for all normative domains. Justification-as-obligation identifies justification with obligation. Since the Norm Schema is a thesis about epistemic permissibility, justification-as-obligation requires something less than deontic justification with respect to the relevant class of norm acts. This suggests that the justification-as-obligation meta-norm can be equivalently reformulated in a negative fashion:

∙ Justification-as-Obligation Meta-Norm (JOMN): It is v-value-wise permissible for agent to that if, and only if, it is not v-value-wise justiﬁable for to do other than that and it is not nondeontic for to that .

JOMN implies that the absence of alternative deontic justification is the norm of performance, for any performance, including action, assertion, belief, and deliberation. This is apparent once it is remembered that praxeological alternatives are justified if, and only if, the relevant norm act is prohibited. If, for example, doing other than asserting that is epistemically justified (qua justification-as-obligation), then doing other than asserting that is obligatory, in which case it is impermissible (and, hence, not permissible) for Deontic Justification 150

the agent to assert that . So, the absence of justified alternatives is necessary for permissibility. It isn’t sufficient because the absence of contrary justification is consistent with nondeonticality. The proof for the meta-norm simply falls out of the formal theory of justification. Strictly speaking, as stated, it is morphic justification-as-obligation that is the meta- norm of performance. However, and for precisely the same sorts of reasons as before, JOMN should be qualifiedly understood to require praxistic justification-as-obligation as opposed to mere morphic justification. The upshot is that the DBWC conception of justification-as-obligation entails that deontic justification is the meta-norm of performance for all normative domains, at least in the attenuated sense that the agent cannot violate other justifications possessed by the agent. Both JPMN and JOMN are fully specified meta-norms. In both cases, under the appropriate qualifications, v-value-wise justification is both necessary and sufficient for the v-value-wise appropriateness of action, assertion, belief, deliberation, and any other type of performance. Summarily, DBWC entails that deontic justification is the meta- norm of performance for all possible performances in all normative domains. It follows that epistemic justification is the epistemic meta-norm. Moral justification is the moral meta-norm. Prudential justification is the prudential meta-norm. And so on. As a corollary, DBWC entails that all other competing norms are false. If, for example, knowledge and epistemic justification come apart, then, pace Williamson, DBWC entails that knowledge isn’t the norm of assertion—or anything else, for the matter. This opens up two interesting dialectical strategies. On the one hand, a norm exponent can defend their favorite norm by arguing for the equivalence of justification and the relevant condition. For instance, knowledge norms can be defended by arguing that epistemic justification just is knowledge. On the other hand, a norm opponent can demonstrate the falsity of a norm by arguing for the nonequivalence of justification and the relevant condition. In the next chapter, I will seek to rob the competing epistemic norm exponents of their safe havens by showing that epistemic justification is a thing unto its own kind. Though epistemologically framed, the argument generalizes.

4.2.4 Justiﬁcation Principles

Justification-as-permission and justification-as-obligation share most of the justification principles that are DBWC theorems, but there are some key areas of disagreement. In this section, I canvas a number of justification principles. All are DBWC theorems. It is worth noting from the onset that all principles are officially framed in terms of morphic justification. However, the uniform attachment of discharge operator (!) to 4.2. The Schematic DBWC Theory of Deontic Justification 151

all justification operators results in perfect analogues of these principles for praxistic justification. Replicating the principles is unnecessary because the DBWC analysis of  and  ! entails that justification-as-permission and justification-as-obligation either have both versions of each principle as theorems or neither. The first four justification principles impose boundaries on the potential range of justification ascriptions:

∙ Veri/JU:

Formally: x x ∙ ¬ ■⊤, for any ⊤ such that ¬ ▣ ■⊤. ∙ Informally: It is not justiﬁable for that ⊤, for any ⊤ for which cannot that ⊤. ∙ Falsi/JU:

Formally: x x ∙ ¬ ■⊥, for any ⊥ such that ¬ ▣ ■⊥. ∙ Informally: It is not justiﬁable for to that ⊥ for which cannot that ⊥. ∙ ML/JU:

Formally: x x ∗ x ∙ If  ■, then ▣ ■ and ▣ ■. ∙ Informally: If it is justiﬁable for to that , then both can that and can∗ otherwise than . ∙ Deontic/JU:

∙ Formally: If  ■x , then either ■x or ■x . ∙ Informally: If it is justiﬁable for to that , then either it is obligatory for to that or it is permissible for to that .

Veri/JU and Falsi/JU respectively ensure that tautologies and contradictions are not justifiable for an agent if they are not relevantly performable. Both are overdetermined by the other boundary principles because the unperformable cannot be performed by an agent and only performances possible for an agent have deontic status for the agent. ML/JU says that justification requires the relevant dual abilities (subject to the qualification about the excepting ability being logically weaker than the commissive ability, which is indicated by a superscripted asterisk) and Deontic/JU says that justification is either an obligation or a permission. The next five justification principles are distributive, distributing justification over equivalence, disjunction, or conjunction: Deontic Justification 152

∙ Equiv/JU:

∙ Formally: If  ■x and ■x = ■x , then  ■x . ∙ Informally: If it is justiﬁable for to that , and that is identical to that , then it is justiﬁable for to that .

∙ Disint/JU:

∙ Formally: If  ■x ( ∨ ), then  ■x or  ■x . ∙ Informally: If it is justifiable for to that ( ∨ ), then it is justifiable for to that or it is justifiable for to that .

∙ Disjunct/JU:

∙ Formally: If  ■x or  ■x , then  ■x ( ∨ ). ∙ Informally: If it is justifiable for to that or it is justifiable for to that , then it is justifiable for to that ( ∨ ).

∙ Adjunct/JU:

∙ Formally: If  ■x ( ∧ ), then  ■x and  ■x . ∙ Informally: If it is justifiable for to that ( ∧ ), then it is justifiable for to that and it is justifiable for to that .

∙ Agglom/JU:

∙ Formally: If  ■x and  ■x , then  ■x ( ∧ ). ∙ Informally: If it is justifiable for to that and it is justifiable for to that , then it is justifiable for to that ( ∧ ).

Equiv/JU distributes justification over identical performances. The performances must be identical in the strict sense that the performing of the one performance just is the performing of the other. Disint/JU distributes justification over the performative disjuncts of a disjunction and Disint/JU grants justification over the scope of a performative disjunction populated by individually justifiable performances. Adjunct/JU similarly distributes justification over a performative conjunction and Agglom/JU grants justification over the scope of a performative conjunction populated by individually justifiable performances. The last two justification principles are ampliative, closing justification over some nonzero number of properly based performances: 4.2. The Schematic DBWC Theory of Deontic Justification 153

∙ SPC/JU:

Formally: If  ■x ( ∧ ( → )) and ■x ( ∕■x ( ∧ ( → ))), then  ■x . Informally: If it is justiﬁable for to that ( ∧ ( → )) and that on the basis that that ( ∧ ( → )), then it is justiﬁable for to that .

∙ MPC/JU:

Formally: If  ■x and  ■x ( → )) and ■x ( ∕■x ( ∧ ( → ))), then  ■x . Informally: If it is justifiable for to that and it is justifiable for to that ( → ) and that on the bases that that and that ( → ), then it is justifiable for to that .

SPC/JU is the closure of a single justifiable performance taken as a premise over properly based performance, whereas MPC/JU is the closure of multiple justifiable performances taken as just as many premises over properly based performance. In epistemological contexts, a first-personal application of these principles allows an agent to deductively expand their knowledge or otherwise enlarge the domain of justifiable believings. These justification principles are mere restatements of the closure principles discussed in Chapter 2. The proof of these principles is tantamount to a simple set of replacements using the Harmanian meta-theorems. Justification-as-permission and justification-as-obligation agree about most, though not all, of these justification principles. Table 4.1 displays which of the DBWC justification principles are theorems for each conception.

Table 4.1: DBWC Justiﬁcation Principle Theorems

Principle Justification-as-Permission Justification-as-Obligation Veri/JU Yes Yes Falsi/JU Yes Yes ML/JU Yes Yes Deontic/JU Yes Yes Equiv/JU Yes Yes Disint/JU B Yes No Disjunct/JU Yes Yes Adjunct/JU Yes Yes Agglom/JU B No Yes SPC/JU Yes Yes MPC/JU B No Yes

The competing conceptions of justiﬁcation overwhelmingly agree about the principles Deontic Justiﬁcation 154

and feature most as theorems. Only Disint/JU, Agglom/JU, and MPC/JU is held in contention. Justification-as-permission validates the former but rejects the latter two, whereas justification-as-obligation rejects the former but validates the latter two. These areas of contention impinge upon larger debates in substantive philosophy. Before moving on to exploring some of these details, I want to clarify an important limitation of the justification principles. There is a scope distinction between performances and their propositional content. For example, it is possible for an ordinary agent to hold contradictory beliefs. The following conjunctive performance is possible: (believe and believe ¬). So is the following singular performance: believe ( and ¬). Both are possible despite the fact that the conjunction of propositional content ( ∧ ¬) is impossible. All justification principles concern the attachment of justification operators to performances, not the propositional content of performances. This is because deontic justification is the justification of performances, possible or actual. More to the point, propositions are categorically inapt targets of normative appraisal of any kind. To illustrate the scope distinction that I have in mind, consider two simplified versions of a doxastic justification agglomeration principle:

∙ Paraphrased Performance Agglom/JU: If it is justifiable for to believe that and it is justifiable for to believe that , then it is justifiable for to (believe that and believe that ).

∙ Paraphrased Content Agglom/JU: If it is justifiable for to believe that and it is justifiable for to believe that , then it is justifiable for to believe that ( ∧ ).

The former attaches a justification operator to a conjunction of performances, whereas the latter attaches a justification operator to a single performance whose propositional content is the conjunction of propositional contents of all the justifiable performances belonging to the antecedent. The former is an instantiation of a DBWC theorem, and the latter is not. More to the point, it is possible to accept the former but deny the latter. In fact, this is precisely what some fallibilists do for epistemic justification.4 Properly supplemented with a content bridge clause, the content agglomeration principle can be deduced from the performance agglomeration principle. Here is one such possible deduction:

4 See Henry Kyburg (1961) and Richard Foley (1992) for paradigmatic exemplars of the fallibilist strategy. 4.2. The Schematic DBWC Theory of Deontic Justiﬁcation 155

01 Paraphrased Doxastic Agglom/JU: If it is justifiable for to believe and it is justifiable for to believe , then it is justifiable for to (believe and believe ).

02 Content Bridge Clause: If believes and believes , then believes ( ∧ ).

∴ Paraphrased Content Agglom/JU: If it is justifiable for to believe and it is justifiable for to believe , then it is justifiable for to believe ( ∧ ).

An argument of this sort suﬃces in DBWC to deduce Paraphrased Content Agglom/JU from Paraphrased Performance Agglom/JU. As I hope is evident, Content Bridge Clause isn’t terribly plausible—at least not for creatures relevantly like us. We are cognitively limited creatures that do not believe all the logical consequences of what we believe. We even sometimes fail to believe the obvious consequences. Generalizing, if, for the relevant agent, it is abilitively possible for the agent to believe and believe without thereby believing ( ∧ ), then the bridge clause is false for the agent. If, once again, an agent can fail to conjoin the contents of held beliefs, rationally or irrationally, the bridge clause is false. The lottery and preface paradoxes are the locus classicus source of doubt for such content bridge clauses. In general, a content bridge clause allows the distribution of a performance from collections of performances over logical arrangements of their propositional contents. The following set of paradigmatic candidates help illustrate what I have in mind:

∙ Negation Content Bridge Clause (¬CBC): If is in state S with as its object, then is not in S with ¬ as its object.

∙ Disjunctive Content Bridge Clause (∨CBC): is in state S with as its object or is in S with as its object if, and only if, is in S with ( ∨ ) as its object.

∙ Conjunctive Content Bridge Clause (∧CBC): is in state S with as its object and is in S with as its object if, and only if, is in S with ( ∧ ) as its object.

∙ Conditional Content Bridge Clause (→CBC): is in state S with ¬ as its object or is in S with as its object if, and only if, is in S with ( → ) as its object.

∙ Biconditional Content Bridge Clause (↔CBC): is in state S with ( → ) as its object and is in S with ( → ) as its object if, and only if, is in S with ( ↔ ) as its object.

These content bridge clauses, or at least versions of their one-directional derivatives, are required to deduce analogues of the content justiﬁcation principles from the DBWC Deontic Justiﬁcation 156

performance justiﬁcation principles. For example, the above derivation appeals to a version of ∧CBC. The success of such a program depends upon the nature of the states over which the performances range. Strictly speaking, all the content bridge clauses fail for belief, intention, intentional action, and knowledge in DBWC. They all fail for intentional action and knowledge, respectively, because they all fail for belief and intention (and there are no supplementary conditions to pick up the slack). They fail for belief and intention because they are deﬁned over both normal and nonnormal moment/history pairs. Mind-moments are nonnormal; truth assignment is arbitrary. As a consequence, for example, ¬CBC is false because it is possible for the agent to believe that and simultaneously believe ¬ (namely when

both and ¬ are assigned truth value 1 (or truth value 0) by ℑ− in all the relevant accessible mind-moment/mind-history pairs). Parallel remarks apply to the remaining bridge clauses. It is possible to derive the bridge clauses in DBWC by imposing constraints upon the behavior of the nonnormal interpretation function.5 I won’t discuss the details of such constraints except to note that imposition of one or more of them idealizes agents in such a way that they become relevantly logically omnipotent/omniscient. In an effort to avoid this untoward commitment, DBWC does not assume that any of the relevant constraints are imposed. As a consequence, all the content analogues for the performance justification principles strictly speaking fail in DBWC. Formal theory is one thing, empirical adequacy another. In my estimation, human beings aren’t the sorts of critters for whom the content bridge clauses are true. As a matter of fact, I, Ryan Hebert, believe, intend, intentionally do, or know only a very small number of things entailed by what I believe, intend, intentionally do, or know. If ever you, reader, suffer moments of embarrassment stemming from imperfect logical acumen, then you too are a reason to deny the content bridge clauses. If you’re still not convinced, I humbly suggest that you try tutoring struggling logic students.

4.3 Justiﬁcation and Ability

DBWC entails that deontic modals have dual ability requirements. All of the following substantive principles are vindicated by the framework:

∙ Harman’s Law (GL): If it is obligatory for to that , then has most/some reason to that .

5 See Brian Chellas (1980) and Giacomo Sillari (2008) for discussion and citations. 4.3. Justiﬁcation and Ability 157

∙ Haji’s Law (HL): If has most/some reason to that , then is able to that and is able to otherwise than .

∙ Moore’s Law (ML): If it is obligatory for to that , then is able to that and is able to otherwise than .

∙ Kant’s Law (KL): If it is obligatory for to that , then is able to that .

The Harmanian meta-theorems show that all deontic modals are interdefinable with reasons-wise modals. The Hajian meta-theorems show that all reasons-wise modals have dual ability implications. The Moorean meta-theorems show that all deontic modals have dual ability implications. The Kantian meta-theorems are a consequence of the Moorean meta-theorems. They say that all deontic modals have ability implications. Justification-as-permission and justification-as-obligation identify justification with a positive deontic evaluation. Hence the Moorean meta-theorems entail ML/JU.

∙ Moore’s Law/Justification (ML/JU): If it is justiﬁable for to that , then is able to that and is able∗ to otherwise than .

To recapitulate, ML/JU says that justification, morphic or praxistic, has the relevant dual ability implications (subject to the usual qualification), no matter whether justification is obliging or merely a permitting notion. Since knowledge requires the praxistic justification of belief (i.e., doxastic justification), the following is also a DBWC theorem:

∙ Moore’s Law/Knowledge (ML/K): If knows that , then is able to believe that and is able∗ to believe otherwise than .

ML/K says that knowledge has dual doxastic ability implications. The principle is jointly entailed by ML/JU and the doxastic justiﬁcation requirement for knowledge. While all of the above principles have their detractors, KL enjoys the most vibrant discussion, and I take the majority of arguments either for or against that principle to be more or less adaptable for the other principles. Even this claim might be challenged, of course. For example, consider the following principle:

∙ Principle of Alternative Possibilities (PAP): If is able to that , then is able to otherwise than .

PAP is famously contentious. Classical compatibilists and classical incompatibilists alike accept it, but nonclassical compatibilists and nonclassical incompatibilists alike reject it. Deontic Justiﬁcation 158

Jointly, KL and PAP entail ML. Alternatively, GL and PAP entail HL. Some nonclassical theorists might deny ML and HL on the grounds that they deny PAP, but it should be noted that ML and HL are DBWC theorems despite the fact that PAP is not. My point is that PAP is not an essential premise in the proofs for the deontic principles at issue. This should not be surprising. PAP is proposed by classical theorists as a feature of the sorts of abilities indicative of free will. The ability implications of the deontic modals in DBWC are silent on the issue of free will. Belief and knowledge have dual ability implications, for example, but it is doubtful that the cognitive abilities involved are constituted of metaphysical freedom. DBWC defends the view that there are interrelations between ability modals, deontic modals, and reasons. By implication, the deontic principles at issue more or less must together stand or fall. DBWC is committed to the claim that they must stand. Personally, I am satisfied with the substantive defenses of KL in print and regard the issue satisfactorily settled. Rather than repeat what has already been said by Michael Zimmerman (1987, 1996, 1997), Ishtiyaque Haji (2002, 2012, 2016), and Peter Vranas (2007), I will direct the reader to the original sources. Among other things, these defenses of KL (and related principles) suffice to rebut, on the one hand, the objection of self-imposed impossibility as seen in Michael Stocker (1971), Walter Sinnott-Armstrong (1984), and Sharon Ryan (2003) and, on the other hand, the explanatory challenge issued by Peter Graham (2011). They even go some distance toward dealing with the linguistic evidence cited by Moti Mizrahi (2009) (and, to a lesser extent, Sinnott-Armstrong). With this last style of objection, some opponents appeal to true utterances where normative ‘ought’, ‘should’, or the like is employed (e.g., “You ought to do this,” “You shouldn’t do that!”) but the agent lacks the relevant ability. However, normative language of this sort is polysemous and, more to the point, not clearly deontic. Opponents require but lack an argument as to why the normative language in these cases denotes deontic notions as opposed to axiological or hypological ones. It is doubtful that they will find the linguistic argument needed for reasons related to issues investigated by Andrew Jones and Ingmar Pörn (1986) and Paul McNamara (1996c). If there were a plausible deontic theory that implied that deontic modals outstrip ability modals, then I would consider that a genuine and interesting challenge to the deontic principles in question. It would be a debate settled on the basis of theory choice: whether the deontic principles were true or false would depend upon which of the competing theories ultimately prevailed. That said, I know of no such competitive deontic theory in print. After all, the lacuna is precisely why I embarked upon the current project in the first place. Though many deontic logics do not feature the deontic principles as theorems, 4.4. Justification and Deontic Conflicts 159

they are disqualiﬁed because it is the result of conceptual impoverishment or expressive inadequacy, not the product of an insightful analysis of both deontic and ability modals.

4.4 Justiﬁcation and Deontic Conﬂicts

There are two main varieties of deontic conflicts: dilemmas and disagreements. Deontic dilemmas are cases of conflicting obligations for a single agent. Deontic disagreements are cases of multiple normative counterparts whose justifications conflict. In this section, I show that DBWC is unfriendly to the possibility of deontic conflicts. It follows that the DBWC theory of deontic justification is likewise unfriendly.

4.4.1 Deontic Dilemmas

Deontic dilemmas are a single agent species of deontic conﬂict. I take it that deontic dilemmas instantiate the following schema:

∙ Deontic Dilemma Schema:

Formally: x x x x ∙ ■ and ■ and ¬ ▣ (■ ∧ ■ ). ∙ Informally: It is obligatory for to that and it is obligatory for to that but is unable to both ( that and that ).

Broadly, a deontic dilemma is any case where a single agent has two or more obligations but it is impossible for the agent to discharge all of the obligations. The paradigmatic example of a deontic dilemma is the moral dilemma. Plato6 and Jean-Paul Sartre7 are credited with perhaps the two most well-known examples of moral dilemmas. I think the following paraphrase a better candidate:

Dale ﬁnds himself in a Buridan’s ass-type moral dilemma in which not both of two identical twins (of identical moral status) can be saved from being crushed to death by a heavy rock. The twins are pinned down in such a way that only one can be pulled free at a time. If nothing is done the rock will soon kill both, but if either twin is removed, the weight shift will immediately kill the other. The dilemma impinges upon Dale, who has accepted responsibility to act as guardian of both twins, may naively think he is obligated to save twin Bill, and obligated not to save Bill. This is because he is also obligated to save twin Ted,

6 See Book I 331c of the Republic. 7 See Jean-Paul Sartre for the famous passage about the young man torn between caring for his mother and joining the war eﬀort against the Nazis (1957: 295–296). Deontic Justiﬁcation 160

he cannot save both, and his obligation to save Ted under the circumstances obligates him not to save Bill. By similar token, Dale is apparently obligated to save Ted and obligated not to save Ted (Jacquette 1991: 44).8

Of course, the opponent of deontic dilemmas will hold that Dale’s dual obligations are merely apparent. It is literally false that Dale both has the obligation to save Bill and the obligation to save Ted when it is impossible for Dale to save both Bill and Ted. Rather Dale has the obligation to save one but, given that, ex hypothesi, there are no moral grounds whatever to prefer one over the other, it is his terrible option to choose between them. The only thing that he must do is choose. DBWC entails that deontic dilemmas are impossible. The impossibility of deontic dilemmas is overdetermined by the framework’s theorems. To make good on this claim, I sketch two syntactical arguments for the impossibility of deontic conﬂicts. They are not the only syntactical arguments that DBWC makes available, but they are the most germane given the above discussion concerning the relation between justiﬁcation and ability.

The First Syntactic Argument

Table 4.2 displays the first syntactic argument. It is an indirect argument that appeals to an axiom meta-schema and an interaction theorem. The first syntactic argument is valid. There are only two controvertible premises, the fourth and fifth, all other premises being elementary operations of propositional logic. The fourth premise instantiates the DBWC meta-axiom C■x . The fifth premise instantiates the DBWC Kantian meta-theorem OB/KL. The exponent of deontic dilemmas must give up C■x or OB/KL. (Both are provable in DBWC, so the exponent of deontic dilemmas must also deny DBWC.) Both options have their takers, but, as I have already indicated, the denial of KL (or its formal counterparts)

8 Though he doesn’t say so, it seems pretty clear that Dale Jacquette (1991) is making good on a suggestion offered more than a decade earlier by Ruth Barcan Marcus (1980): Setting aside the casuistic logical claim that a single principle can always be derived by conjunction from a multiplicity, it can be seen that the single-principle solution [to the problem of deontic inconsistency] is mistaken. There is always the analogue of Buridan’s ass. Under the single principle of promise keeping, I might make two promises in all good faith and reason that they will not conflict, but then they do, as a result of circumstances that were unpredictable and beyond my control. All other considerations may balance out. The lives of identical twins are in jeopardy, and, through force of circumstances, I am in a position to save only one. Make the situation as symmetrical as you please. A single-principled framework is not necessarily unlike the code with qualifications or priority rule, in that it would appear that, however strong our wills and complete our knowledge, we might be faced with a moral choice in which there are no moral grounds for favoring doing x over y (1980: 125). 4.4. Justification and Deontic Conflicts 161

Table 4.2: First Syntactic Argument

x x x x 01 ¬((■ ∧ ■ ) → ▣ (■ ∧ ■ )) assumption

x x x x 02 ■ ∧ ■ ∧ ¬ ▣ (■ ∧ ■ ) from 01

03 ■x ∧ ■x from 02

04 (■x ∧ ■x ) → (■x ∧ ■x ) C■x

x x x x 05 (■ ∧ ■ ) → ▣ (■ ∧ ■ ) OB/KL

x x 06 ▣ (■ ∧ ■ ) from 03–06

x x 07 ¬ ▣ (■ ∧ ■ ) from 02

08 ⊥ from 06, 07

x x x x ∴ (■ ∧ ■ ) → ▣ (■ ∧ ■ ) from 01–08

is a nonstarter. This leaves only the denial of C■x as an option. John Horty (2014), for example, aims to retain KL and kin while rejecting all versions of C■x . Actually, Horty offers two accounts of obligation in a default logic formalism, one in which a version of C■x is a theorem, one in which no version of C■x is a theorem. His personal preference is for the latter because he is persuaded that deontic dilemmas are possible. Of course, I am asking why deontic dilemmas should be thought possible. Horty will not accept the first syntactic argument because he rejects C■x . But I am asking for independent motivation for the rejection of the axiom meta-schema apart from the citation of deontic conflicts. I am not moved by the intuitive cases on offer. I am inclined to say, as I did for Jacquette’s case, that the agent does not have any conflicted obligations at all. While it is obligatory for the agent to perform one of the relevant options, as it is obligatory for Dale to either save Bill or save Ted, each of the relevant alternatives is optional. Luckily, the issue can be bypassed. Not all arguments for the impossibility of deontic dilemmas require C■x , as demonstrated the second syntactic argument.

The Second Syntactic Argument

Table 4.2 displays the second syntactic argument. It is an indirect argument that appeals to the generalized version of OB/KL. The argument is valid and the only controvertible premise is the fourth, all other Deontic Justiﬁcation 162

Table 4.3: Second Syntactic Argument

x x x x 01 ¬((■ ∧ ■ ) → ▣ (■ ∧ ■ )) assumption

x x x x 02 ■ ∧ ■ ∧ ¬ ▣ (■ ∧ ■ ) from 01

03 ■x ∧ ■x from 02

x x x x 04 (■ ∧ … ∧ ■ ) → ▣ (■ ∧ … ∧ ■ ) G/OB/KL

x x 05 ▣ (■ ∧ ■ ) from 03, 04

x x 06 ¬ ▣ (■ ∧ ■ ) from 02

07 ⊥ from 05, 06

x x x x ∴ (■ ∧ ■ ) → ▣ (■ ∧ ■ ) from 01–07 premises being elementary logical operations. G/OB/KL is the DBWC meta-theorem that says that, for any number of obligations incumbent upon an agent, the agent is able to discharge each and every obligation. Its proof is a generalization of the proof for OB/KL. The dialectical purpose of the second syntactic argument is to highlight that the genuine issue at heart concerns the ability requirements for deontic modals. Attempts, like Horty’s, to obviate the issue by rejecting other premises in other arguments are ineﬀectual in the face of the second syntactic argument. While it is in principle possible to endorse KL (and its formal counterparts) while denying its generalized version, the core set of arguments and intuitions typically cited in favor of—or against—KL generalize. If, for example, it is unfair that an agent would have one obligation such that is impossible for the agent to discharge, it is no less unfair that an agent has two obligations such that it is impossible for the agent to discharge them both, and so on. The possibility of deontic dilemmas hinges upon the denial of KL and kin. But, again, since that tactic is a nonstarter, I take the possibility of deontic dilemmas to be refuted. A fortiori, the DBWC theory of deontic justiﬁcation rules out the possibility of deontic dilemmas.

4.4.2 Deontic Disagreements

Deontic disagreements are a multiagent species of deontic conflict. I take it that deontic disagreements instantiate the following schema: 4.4. Justification and Deontic Conflicts 163

∙ Deontic Disagreement Schema:

Formally: x x ¨ x x ∙  ■ for and  ■ for and ¬ ▣ ( ■ ∧  ■ ) for both and ¨. ∙ Informally: It is justifiable for to that and it is justifiable for ¨ to that but, for each agent, it is impossible that both performances are justifiable.

Broadly, a deontic disagreement is any case where two or more agents are justified in performing competing performances but it is impossible for more than one of the performances to be simultaneously justifiable for each individual agent. Richard Feldman (2007) popularized the question of deontic disagreement. The paradigm example is the disagreement between two experts, one an atheist, the other a theist, who are both equally well-appraised of all the relevant information and both equally competent theologians. Both equally well know that they cannot both be right. Each accepts what the other denies and denies what the other accepts. Neither party can both justifiably believe and justifiably disbelieve that God exists. Feldman wants to know whether both parties can have justifiable beliefs about the existence of the divine:

But how exactly can there by reasonable disagreements? And how can there be reasonable disagreements when the parties to the disagreement have been confronted with a single body of evidence? And can they sensibly acknowledge, as I have suggested they do, that the other side is reasonable as well? To sharpen these questions, I will introduce some terminology. Let’s say that two people have a disagreement when one believes a proposition and the other denies (i.e., disbelieves) that proposition. Let’s say that two people have a reasonable disagreement when they have a disagreement and each is reasonable (or justiﬁed) in his or her belief. Let’s say that people are epistemic peers when they are roughly equal with respect to intelligence, reasoning powers, background information, and so on. When people have had a full discussion of a topic and have not withheld relevant information, we will say that they have shared their evidence about that topic (2007: 201).

To be clear, the question concerns the justificatory status of the disagreeing parties’ beliefs. Given two or more epistemic peers who share all epistemically relevant factors, is it possible that each party has a justifiable belief in the face of genuine disagreement? Can the atheist justifiably endorse atheism while the theist justifiably endorses theism (and vice versa) given that they share all of each others’ relevant reasons? The question of deontic disagreement in epistemic contexts is merely an instance of a more general puzzle. Take any number of counterparts who are alike in all the normatively Deontic Justification 164

relevant respects. Exactly the same set of possible options is available to each counterpart. All counterparts are equally able to perform any of the options. It isn’t possible for any particular counterpart to justifiably perform more than one of the available options in the circumstances. With these constraints in mind, is it possible for one counterpart to justifiably perform one option, another counterpart justifiably perform a different option, and so on and on for any number of counterparts? Are deontic disagreements between normative counterparts possible? Famously, Richard Feldman answers in the negative. DBWC agrees. It does not matter whether justification is a permitting or obliging notion, deontic disagreements between normative counterparts is impossible. Allow me to explain. I prefer the term ‘normative counterpart’ to ‘epistemic peer’ as it lacks the epistemic denotation, but it is supposed to capture the very same essence. Two or more agents are normative counterparts if, and only if, they are indiscernible in all the normatively relevant respects. Normative counterparthood is constituted by two elements. The first element is evaluative and it represents something akin to shared evidence. ¨ Formally, if and are normative counterparts, and v and v ¨ are the relevant formal notions of deontic values respectively indexed to and ¨ at the relevant moment/history

pair, then v = v ¨ . Plainly, whatever it is in virtue of which something has deontic value for in the circumstances is also the thing in virtue of which something has deontic value for ¨ in the circumstances. If there is evidence relevant to the issue, they have the same evidence; if the agent’s practical interests are relevant to the issue, they have the same stakes; if there are reasons relevant to the issue, the same reasons implinge upon them both; and so on. The second element is abilitive and it represents peerhood. Formally, if and ¨ are normative counterparts, then, for all contextually salient possible world-moment/world- ¨ ¨ ¨ ¨ ¨ history pairs, (w, hw)ℜ(w , hw) for just in case (w, hw)ℜ(w , hw) for . Plainly, normative counterparts have abilitive access to all the same contextually salient possible world-pairs. This ensures that the agents have all of the same abilities and disabilities that are relevant in the circumstances. If being able to perform certain deductions is relevant to the issue, they are both equally apt logicians; if there are certain powers of imagination relevant to the issue, they can equally well imagine the pertinent states of the world; and so on. Normative counterparts are both normatively and abilitively indiscernible. Agents that fail to satisfy either element do not, strictly speaking, qualify as counterparts in the

relevant sense. It follows that normative counterparts have indiscernible ≾r-wise orderings over exactly the same set of contextually salient possible world-pairs. Deontic modals

are defined by appeal to the ≾r-wise orderings of world-pairs. So, it seems, normative 4.4. Justification and Deontic Conflicts 165

counterparts have indiscernible justificatory states. The argument can be made more perspicuous. Suppose that there is some set of options available to all the relevant parties. Suppose that  ■x is true for . From the Deontic Disagreement Schema, it is true ex hypothesi for all the relevant parties that at most one relevant alternative is justifiable for each agent. No other relevant alternative is justifiable for . Since  ■x is true for , it must be the case that, roughly, ■x ¨ is true for in all/some of ’s v -value-wise optimific world-pairs. But and are normative counterparts, which means that ¨ has abilitive access to exactly the same sorts of contextually salient world-pair and all relevant possible moments are ordered x ¨ in exactly the same sort of way. So, roughly, ■ is true for in all/some of the v ¨ - value-wise optimific world-pairs. It follows that  ■x is true for ¨. By implication, no other relevant alternative is justifiable for the agent. In sum, DBWC entails that normative counterparts have exactly the same justifications in the relevant circumstances. A performance is justificatory status for one counterpart if, and only if, it has the very same justificatory status for every other counterpart. Deontic disagreements are cases in which normative counterparts have justifications for disagreeing performances in the relevant circumstances. Therefore, deontic disagreements are impossible. A fortiori, the DBWC theory of deontic justification precludes the possibility of deontic disagreements. In episemic contexts, it is false that epistemic peers can justifiably disagree. Ultimately, the negative verdict is a consequence of how I have spelled out what it is for agents to be normative counterparts. Perhaps some will balk. As of yet, I have failed to discern a method by which the formulation could be improved to yield a different verdict. Perhaps such a method exists, but I would want to see it. Epistemic peers who have shared the evidence are, as Richard Feldman says, agents who, roughly, have all the same information and comparable abilities to assess and use the information. Sameness of information is what I have called the evaluative element. Sameness of ability is what I have called the abilitive element. As I have framed them, the elements of counterparthood are abstract away from any specifically epistemological details. Normative counterparts satisfy both elements but, in doing so, preclude the possibility that they justifiably disagree on the relevant issue. If normative counterparts indeed genuinely disagree about something, at least one counterpart does so unjustifiably. Deontic Justification 166

4.5 Justiﬁcation and Deontic Holism

As I use it, ‘deontic holism’ is the view that the deontic status attributable to individual performances depends not upon the good-making features exhibited by the performance, but rather upon its place in a whole system of performances exhibiting complex arrays of good-making properties. DBWC is a holistic theory of deontic modals. By implication, the DBWC theory of deontic justification is a deontically holistic theory too. A performance is justifiable—obligatory or permissible—for an agent in virtue of its occurrence at some relevant number of optimific moment/history pairs. Roughly, a performance is obligatory for an agent if, and only if, the agent performs the performance in all their best accessible world-pairs; permissible if, and only if, the agent performs the performance in some of their best accessible world-pairs. World-moment/world-history pairs are formal devices that can be understood as the exhaustive system of beings, believings, doings, intendings, intentional doings, knowings, et cetera, performed by the agent at coarse-grained point in time. Simplifying, pair-pairs are supersets of the agent’s action, belief, intention, knowledge, et cetera, performance sets at a coarse-grained moment in time. As such, actions are justifiable for an agent because they are members of the agent’s best performance superset. Beliefs are justifiable for an agent because they are members of the agent’s best performance superset. And so on. Deontic values are formal devices that act as placeholders for the evaluative criteria for states of affairs and world-pairs. Every world-pair is assigned a deontic value. All possible world-pairs are ranked according to their deontic value. The best possible world-pairs are such that no other abilitively possible world-pairs are strictly deontically better. Since world-pairs are merely formal devices for complex performative wholes, the deontic ranking of possible world-pair is equivalent to the deontic ranking of complex performative wholes. The best possible performative sets, no whether for action, belief, intention, or anything else, are such that no other possible performative set is strictly deontically better. The DBWC theory of deontic justification is correspondingly holistic. It is possible for an individual performance to be justifiable for an agent even if that performance lacks any good-making properties and fails to contribute any deontic value to the whole. Morally bad acts can be morally justifiable. Epistemically bad beliefs can be epistemically justifiable. Prudentially bad assertions can be prudentially justifiable. The list goes on. The upshot is that justification attributable to single performances does not in any way supervene upon the good-making features exhibited by that individual performance. Justification is solely a matter of a performance’s membership in an optimific performative whole. This is not to 4.6. Justification and the Paradoxes of Agglomeration 167

say that the value of individual performances has no bearing whatsoever. I take it that the value of a world-moment/world-history pair is a function of the value of the performances that occur there. All things being equal, the best possible world-pair will be those in which the agent has the most reliable tendency to perform value-contributing performances. DBWC enjoins agents to make actual the best possible world. The framework tolerates deontic badness only insofar as it is an ineliminable feature of the best abilitively possible world-pairs. In this sense, DBWC borrows from the Leibnizian theodicy that deontically bad actions, assertions, beliefs, intentions, et cetera, are justifiable, when they are, because it is impossible for agents to do any better. Deontic holism has sweeping consequences. In the next chapter, I show that the DBWC theory of epistemic justification falsifies all competing theories of epistemic justification and lays the groundwork for the refutation of skepticism.

4.6 Justiﬁcation and the Paradoxes of Agglomeration

Paradoxes of agglomeration generate contradictions by agglomerating a number of independently plausible premises. Perhaps the two most famous examples are the lottery and preface paradoxes. In recent years, philosophers, especially epistemologists, have taken renewed interest in these paradoxes. In this section, I argue that the DBWC theory of deontic justiﬁcation vindicates the two main methods of resolution.

4.6.1 The Lottery Paradox

Henry Kyburg (1961) is responsible for contemporary formulations of the lottery paradox. Here’s a simplified version. Imagine a fair lottery with n number of tickets. There will w be exactly one winner. Everyone knows all these things about the lottery. Let x represent l the proposition that ticket x is a winner and let x represent the proposition that ticket x is a loser. On the one hand, it isn’t intuitively justifiable to believe that all the tickets are losers. Very little cognitive effort is required to figure out that not all tickets are losers given the ex hypothesi knowledge that there is exactly one winner. On the other hand, it is intuitively justifiable to believe, of each ticket, that the ticket is a loser. The odds of any ticket’s being a loser are astronomically high. Rarely do ordinary beliefs enjoy such a high degree of support, but they are nonetheless justified. These intuitions can be marshaled into an argument that derives a contradiction. Table 4.4 displays one version of the lottery paradox. The argument is deductively valid. The contradiction is derived from the first and fifth premises. The fifth premise is derived from a chain of applications of modus ponens on the Deontic Justification 168

Table 4.4: A Formal Variant of the Lottery Paradox l l 01 ¬ [ ]( 1 ∧ … ∧ n) given all lottery tickets 1, … , n l 02  [ ]( m), for each arbitrary ticket m l l l 03 If  [ ]( m), for each arbitrary ticket m, then  [ ]( 1)∧…∧ [ ]( n) given all lottery tickets 1, … , n

l l l 04 If  [ ]( 1) ∧ … ∧  [ ]( n) given all lottery tickets 1, … , n, then  [ ]( 1 ∧ l … ∧ n) given all lottery tickets 1, … , n

l l 05  [ ]( 1 ∧ … ∧ n) given all lottery tickets 1, … , n

∴ ⊥ second, third, and fourth premises. The fourth premise is a justification principle. The third premise is a logical consequence of the second premise. The second premise is a substantive assumption. The first premise is nearly uncontestable. Allow me to unpack these claims. The first premise says that it isn’t justifiable to believe that all the tickets are losers. In typical treatments of the lottery paradox, it is simply taken for granted. Indeed this makes a lot of sense when a knowledge operator is used instead of a justification operator: no one can know that a contradiction is true. While I don’t intend to fuss about the premise, it should be noted that it isn’t entirely beyond contention.9

9 Intuitively, it is supported by an argument of the following kind:

w 01  [ ]( x) for some lottery ticket x w l l 02 If  [ ]( x) for some lottery ticket x, then  [ ]( 1 ∧ … ∧ n) given all lottery tickets 1, … , n l l l l 03 If  [ ]( 1 ∧ … ∧ n) given all lottery tickets 1, … , n, then ¬ [ ]( 1 ∧ … ∧ n) given all lottery tickets 1, … , n

l l ∴ ¬ [ ]( 1 ∧ … ∧ n) given all lottery tickets 1, … , n

The ﬁrst premise of this supporting argument can be granted because it is true ex hypothesi that the agent knows all the relevant facts about the lottery, including that there is exactly one winning ticket. However, the conclusion goes through only if the right content bridge clauses obtain for belief. In particular, the argument requires both of the following:

∙ Consequence Content Bridge Clause (CCBC): If is in state S with p as its object, and p entails q, then is in state S with q as its object. 4.6. Justiﬁcation and the Paradoxes of Agglomeration 169

The second premise states that it is justifiable to believe, of each ticket, that it is a loser. This premise is rejected by some epistemologists who impose various substantive conditions on justification. For example, if epistemic justification is factive, then premise two is false because there is a ticket—the winning ticket—for which it is false that it is a losing ticket, in which case belief that it is a loser isn’t justifiable. DBWC doesn’t impose substantive conditions like factivity upon justification, so it doesn’t endorse this maneuver. And while the framework is technically neutral on such matters, it is implicitly unfriendly to all such views. An argument to this effect is produced in the next chapter. The third premise states that if it is justifiable to believe, of each ticket, that it is a loser, then it is justifiable to believe that that ticket #1 is a loser and . . . and it is justifiable to believe that ticket #n is a loser. This strikes me as an instantiation of Equiv/JU. The belief, apportioned to each ticket, that it is a loser is just to simultaneously believe that ticket #1 is a loser and . . . and believe that ticket #n is a loser. As such, the premise is accepted by both justification-as-permission and justification-as-obligation. The fourth premise states that if it is justifiable to believe that ticket #1 is a loser and . . . and it is justifiable to believe that ticket #n is a loser, then it is justifiable to believe that all the tickets are losers. This premise is an instantiation of the content agglomeration principle previous discussed. It is not a DBWC theorem. Both justification-as-permission and justification-as-obligation reject this premise. The latter would accept it if, again, ∧CBC were true in DBWC. It isn’t. To sum up, both justification-as-permission and justification-as-obligation crucially deny the fifth premise of the lottery paradox. This squares nicely with the traditional fallibilist solution proposed by Kyburg (1961) and Richard Foley (1992). DBWC isn’t problematized by the lottery paradox.

∙ Negation Content Bridge Clause (¬CBC): If is in state S with p as its object, then is not in S with ¬p as its object.

The second premise says that if it is justifiable to believe that there’s a winning ticket, then it is justifiable to believe that it isn’t the case that all the tickets are losers. This premise is false if there is no acceptable variant CCBC for belief. The third premise says that if it is justifiable to believe that it isn’t the case that all the tickets are losers, then it isn’t justifiable to believe that all the tickets are losers. This premise is false if there is no acceptable variant of ¬CBC for belief. Maybe there is a shorter deduction than what I’ve suggested, but that too requires an acceptable variant of a content bridge clause. If there aren’t any, and I doubt there are, then it seems that the first premise of the lottery paradox can be rejected, depending on the background information. Having said that, the reason I don’t intend to fuss over the premise is that this maneuver isn’t a promising general solution. I see no reason why the background cannot be buffed up to secure the assumption that it isn’t justifiable to believe that all the tickets are losers. Deontic Justification 170

4.6.2 The Preface Paradox

D. C. Makinson (1965) is responsible for the preface paradox. Here’s a simplified version. Imagine a scholar in the process of fact checking a very large book that asserts a huge number of propositions on the basis of evidence. Owing to human limitations, it is overwhelmingly likely that the book contains at least one erroneous sentence. In fact, grant that it does and that the scholar knows this about the e book. Let x represent the proposition that sentence x is erroneous. It isn’t intuitively justifiable to believe that not all sentences aren’t erroneous. However, it is intuitively justifiable to believe, of each sentence, that the sentence isn’t erroneous. Every claim is backed by excellent evidence. These intuitions can be marshaled into an argument that derives a contradiction. Table 4.5 displays one version of the lottery paradox.

Table 4.5: A Formal Variant of the Preface Paradox e e 01 ¬ [ ](¬ 1 ∧ … ∧ ¬ n) given all sentences 1, … , n e 02  [ ](¬ m), for each arbitrary sentence m e e e 03 If  [ ](¬ m), for each arbitrary sentence m, then  [ ](¬ 1)∧…∧ [ ](¬ n) given all sentences 1, … , n

e e e 04 If  [ ](¬ 1) ∧ … ∧  [ ](¬ n) given all sentences 1, … , n, then  [ ](¬ 1 ∧ e … ∧ ¬ n) given all sentences 1, … , n

e e 05  [ ](¬ 1 ∧ … ∧ ¬ n) given all sentences 1, … , n

∴ ⊥

So understood, the preface paradox is structurally identical to the lottery paradox and invokes the same inference rules. Both DBWC conceptions of deontic justiﬁcation reject the fourth premise and for exactly the same reasons. DBWC isn’t problematized by the preface paradox. It is especially interesting to note that MPL/JU fails to support belief in the conjunction of all the relevant propositions. With respect to both paradoxes, the multi-premise justiﬁcation closure principle is consistent with the denial of the fourth premise. This is, again, because the relevant content bridge clauses are not DBWC theorems. This accords with intuition. It is false that belief exhibits the logical properties required to make good on the principle. 4.7. Conclusion 171

Justification doesn’t close the nonfactive propositional content of its performances. Belief is a nonfactive state. So, justification doesn’t close the propositional content of belief. If knowledge closes its content, the difference in closure principles suffices to show that knowledge and belief justification are two different phenomena. As a corollary, since justification is the meta-norm, it follows that knowledge isn’t the norm of anything.

4.7 Conclusion

I have sketched the schematic DBWC theory of justification both for justification-as- permission and justification-as-obligation. The two deontic conceptions were compared and contrasted by investigating a slew of issues of philosophical interest to ethics and epistemology. Among other things, the schematic theory says that justification is the meta-norm of performance and that deontic conflicts are impossible. In the next chapter, I apply the schematic DBWC theory of justification to the epistemological domain. I sketch and defend value-first epistemology. CHAPTER 5

VALUE-FIRST EPISTEMOLOGY

Abstract

I operationalize the schematic DBWC theory of deontic justification to articulate and defense a value-first epistemology. I explore two interesting implications stemming from the falisification of any view that assumes that justification requires the exem- plification of epistemic goodness. The first is that the letter of existing theories of justification must be false. The second is that skepticism is refuted.

5.1 Introduction

DBWC is a teleological theory of deontic modals. The theory is teleological in the sense that it substantiates the following thesis:

∙ Teleological Deontism: All deontic modals are teleological.

Every class of deontic modal is defined from the relevant notion of deontic value. In an effort to maintain theoretical neutrality, I am unfortunately compelled to invoke ‘deontic value’ as a technical term to denote whatever evaluative quantity it is in virtue of which a performance is deontically appraisable. It is an attenuated notion of value that does not, strictly speaking, denote an axiological appraisal. Its referent is something to be decided by deontic axiology. In this sense, the DBWC defense of teleologism is sadly trivialized despite my personal view that deontic value really should be understood as value proper. I will not presently attempt to defend my conviction, so, with this attenuated qualification in mind, DBWC defines moral deontic modals from the morally good, prudential deontic

172 5.1. Introduction 173

modals from the prudentially good, and so forth. So, too, are epistemic deontic modals deﬁned from the epistemic good. The last remark suggests a further thesis:

∙ Epistemic Deontism: All epistemic modals are deontic modals.

The phrase “epistemic deontic modal” is a pleonasm. All epistemic modals are deontic modals—not in a moral or prudential sense, but in an epistemic sense. All epistemic modals are deontic in the sense that they are defined by appeal to the epistemic good being realized under certain conditions. This is no less true for knowledge, the paradigmatic epistemic modal. Knowledge is belief whose justification tracks truth across all the relevant abilitively accessible epistemically optimific world-moment/world-history pairs. Epistemic justification is an essential ingredient for knowledge and is likewise a deontic modal. To the point, DBWC entails the following pair of theses:

∙ Knowledge Deontism: Knowledge is a deontic modal.

∙ Epistemic Justification Deontism: Epistemic justiﬁcation is a deontic modal.

Both theses are entailments of Epistemic Deontism and interderivable from the DBWC analyses of knowledge and justification. My primary aim has been the elaboration of the deontic theory of justification. All deontic justification ascriptions are either permissions or obligations. Epistemic justification is, a fortiori, either epistemic permissibility or epistemic obligation. DBWC is a teleological theory of deontic modals. Pulling all the details together, DBWC entails all of the following theses:

∙ Epistemic Teleologism: All epistemic modals are teleological.

∙ Knowledge Teleologism: Knowledge is teleological.

∙ Epistemic Justification Teleologism: Epistemic justiﬁcation is teleological.

Epistemic modals are both deontic and value-theoretic concepts. Accordingly, then, epistemic value is the most fundamental theoretical notion for epistemological theorizing. DBWC secures—an attenuated sense of—value-ﬁrst epistemology. Broadly, the DBWC style of epistemological theorizing may be fairly termed teleological deontism. The purpose of this chapter is to articulate DBWC value-ﬁrst epistemology and to defend its consequences. The structure of this chapter is as follows. In Section 5.2,I defend DBWC against three of the most popular objections to teleological deontism. There Value-First Epistemology 174

are other objections that merit consideration, but I can do only so much in a chapter. In Section 5.3, I defend the DBWC theory of knowledge. In Section 5.4, I argue for the possibility of unhinged justification—viz., a performance may be justifiable even if it fails to realize any of the relevant kind of goodness. Unhinged justification is a consequence of deontic holism. In Section 5.5, I show that the possibility of unhinged justification grounds a novel refutation of epistemological skepticism. Finally, in Section 5.6, I conclude by summarizing the findings of the chapter.

5.2 Against Objections to Teleological Deontism

In this section, I answer a few famous objections to both epistemological deontism and epistemological teleologism. My goal is not to canvass all the possible objections, nor even most of the objections in print. Rather my aim is to elucidate and typify the sorts of rebuttals that DBWC permits.

5.2.1 Doxastic Voluntarism Objection

William Alston (1988, 1989) oﬀers perhaps the most famous objection to deontism. The thrust of the argument is as follows:

Table 5.1: Doxastic Voluntarism Objection

01 Deontism entails doxastic voluntarism.

02 Doxastic voluntarism is false.

∴ Deontism is false.

The argument is valid. I intend to deny only the ﬁrst premise. Doxastic voluntarism, roughly, is the thesis that some doxastic attitudes are under the voluntary control of some agents some of the time, which is to say that some doxastic states are the products of the agent’s will.1 In favor of the second premise, Alston asks his readers to try to believe various propositions at will (1988: 263–264). He reports that he cannot and indeed it seems precisely the sort of control we lack over our doxastic states. Not everyone agrees, but I am happy to grant that doxastic voluntarism is false because it’s irrelevant.

1 For discussion and defense, see, among others, Margery Bedford Naylor (1985), James Montmarquet (1986), Matthias Steup (2000), Sharon Ryan (2003), and Pamela Hieronymi (2009). 5.2. Against Objections to Teleological Deontism 175

The first premise is equivalent to the claim that deontic justification requires voluntary control over some doxastic attitudes. Alston supports the premise by appeal to two considerations.2 The first consideration adduced in favor of the first premise is the suggestion that deontism is justification-as-permission:

To say that is justiﬁed in believing that p at time t is to say that the relevant rules or principles do not forbid ’s believing that p at t. In believing that p at t, is not in contravention of any relevant requirements. Again, it is not to say that is required or obligated to believe that p at t, thought that might also be true (1988: 258).

I should quickly note that Alston also famously claims that deontism is tied hypological appraisals.3 I will turn to address this element of Alston’s discussion in the next subsection. The second consideration adduced in favor of the ﬁrst premise is the suggestion that deontic statuses—and hypological statuses—require voluntary control:

Now [the deontic] conception of epistemic justification is viable only if beliefs are sufficiently under voluntry control to render such concepts as requirement, permission, obligation, reproach, and blame applicable to them. By the time honored principle that ‘ought’ implies ‘can’, one can be obligated to do p only if one has an effective choice as to whether to do p. It is equally obvious that it makes no sense to speak of ’s being permitted or forbidden to do p if lacks an effective choice as to whether to do p. And it seems even more obvious, if possible, that cannot be rightly blamed for doing (not doing) p if is incapable of effectively deciding whether or not to do p. Therefore the most fundamental issue raised by [deontic justification] is whether belief is under voluntary control (1988: 259).

To be clear, Alston understands voluntary control as follows:

[O]ne has control over a given type of state only if one also has control over some ﬁeld of incompatible alternatives. [. . . ] Voluntary control necessarily extends to contraries; the power to choose p at will is the power to determine at will whether it shall be p or (some form of) ¬p (1988: 261).

2 See Alston (1988: 258; 259; 261–262) and (1989: 118). 3 See, for example, Alston (1988: 259; 284–285). Value-First Epistemology 176

The purpose of the last quote is to show that Alston’s invocation of KL is not an accurate representation of his view. Rather Alston assumes a principle closer to ML. From these two considerations, Alston infers that deontism requires the dual ability to voluntarily believe. If deontism is justification-as-permission, then, strictly speaking, neither KL nor ML support the inference because both principles concern obligation. Of course, Alston thinks that it is “equally obvious” that permissions have the same ability requirements as obligations. While, ultimately, DBWC agrees with him, the attitude cavalierly disregards that the matter is contentious. Nevertheless whether deontism is justification-as-obligation or justification-as-permission, epistemic justification requires that the agent is able to believe and able to not believe. Even with this concession, however, the implicit argument for the first premise is unsound. KL links obligations with an ability to live up to the obligation. ML links obligation with the relevant dual abilities. The Moorean meta-theorems link the relevant dual abilities with all deontic modals. None of these principles, formal or substantive, specify the nature of the required abilities. Broadly, deontic appraisals are performance appraisals. Roughly, a performance is the output of a reasons-responsive power. Performativity does not ipso facto implicate choice, control, freedom, voluntariness, or anything of the kind. Plausibly, and Alston agrees, affective and cognitive performances are not indicative of voluntariness. So, even if conative performances are freedom-implicating, it doesn’t say anything about affective and cognitive performances. Since the ability implications of deontic modals is a function of the nature of the performances appraised, the deontic modals applicable to affective and cognitive performances are not freedom-implicating regardless of whether the deontic modals applicable to conative performances are freedom-implicating. The upshot is that, by granting Alston the falsity of doxastic voluntarism, it simply falls out of the framework that neither the performativity constitutive of believings nor the deontic appraisal of believings is voluntaristic. In a word, it is a trivial consequence of the DBWC theory of deontic justification that deontism doesn’t require doxastic voluntarism. In general, deontic appraisability does not ipso facto imply control, freedom, or anything of the kind. Nowhere in the framework is the concept of control invoked to explain the truth-conditions of deontic modals.4 Consequently, DBWC isn’t threatened by the doxastic voluntarism objection. In point of fact, it is doubtful that any bona fide deontism is threatened by any version of this objection because deontism isn’t conceptually tied to either doxastic voluntarism or free will.

4 Having said that, I ﬁnd it highly plausible that the deontic modals applicable to conative performances require control. Presumably, this is because conative performativity is constitutive of the relevant notion of control. The moral evaluation of action, for example, has freedom requirements precisely because the acts of principal interest to moral appraisal just are those acts that agents can freely perform. 5.2. Against Objections to Teleological Deontism 177

5.2.2 Isolation Objection

Alston op. cit. oﬀers another famous ancillary argument against deontism. It may be summarized as follows:

Table 5.2: Isolation Objection

01 Epistemic justiﬁcation is truth-conducive.

02 Deontic justiﬁcation isn’t truth-conducive.

∴ Epistemic justiﬁcation isn’t deontic.

The argument is valid because essential properties are closed under logical equivalence. Each premise merits further attention, but I should note that Clayton Littlejohn (2012) offers a nice rebuttal. However, there is a line of response more decisive than what Littlejohn offers. The first premise is more or less incontrovertible. Epistemic justification is truth- conducive in the sense that its role is to position the agent to know truths and avoid falsehoods. It is—typically—epistemically probabilifying, where an attitude is justified when the agent’s reasons makes the attitude sufficiently probable; or, at least, not a detriment to the agent’s epistemic aims. The aim of my remarks in not to settle on the details of what constitutes truth-conduciveness is or what Alston thinks it consists in. Rather my goal is to make clear that the most fundamental requirement for an adequate theory of epistemic justification is that it respects the role that justification plays in the achievement of knowledge and the satisfaction of properly epistemic aims. The second premise suggests that deontic justification fails the most fundamental requirement for an adequate theory of epistemic justification. What is the support for this premise? At bottom, it is an appeal to the possibility that an agent can be hypologically justified in having certain beliefs that aren’t held in a truth-conducive way:

has lived all his life in an isolated primitive community where everyone unhesitantly accepts the traditions of the tribe as authoritative. These have to do with alleged events distant in time and space, about which and his fellows have no chance to gather independent evidence. has never encountered anyone who questions the traditions, and these traditions play a key role in the communal life of the tribe. Under these conditions, it seems clear to me that is in no way to blame for forming beliefs on the basis of the traditions. Value-First Epistemology 178

He has not failed to do anything he could be reasonably expected to do. His beliefs about, e.g., the origins of the tribe stem from what, so far as he can see, are the best grounds one could have for such beliefs. And yet, let us suppose, the traditions have not been formed in such a way as to be a reliable indication of their own truth. is deontologically justiﬁed, but he is not believing in a truth-conducive way (1988: 286).5

Alston’s case of cultural isolation does not support the second premise. The target of the case is hypological justification, what Alston elsewhere6 calls freedom from blame, but the second premise of the isolation objection concerns deontic justification. Unless Alston can show that the hypological and the deontic are somehow related, the considerations adduced in favor of the premise are irrelevant. The only way, to wit, in which hypological justification can be made relevant is if the right deontic appraisals are assumed to be a necessary condition. In particular, Alston needs the following principle:

∙ Blameworthiness Requires Impermissibility (BRI): Agent deserves blame/criticism for that only if it is impermissible for to that .

BRI makes negative deontic appraisals a necessary condition of negative agent appraisals. Despite its intuitive appeal, this principle is false. Less contentiously framed, there are, as far as I am aware, no actual arguments for it in print but several against it.7 I will not devote space to rehearsing these arguments. Anyone who wishes to employ BRI is obliged to deal with its problems. Since no defense is forthcoming, it seems that Alston’s motivation for the second premise is a non sequitur. Perhaps a more direct route is available. The new evil demon argument purports to oﬀer cases in which it is impermissible for the agent to believe that even though is true. Consider the following passage from Stuart Cohen (1984):

5 Reprinted in Alston (1989: 145). 6 See Alston (1988: 286; 287; 294). 7 Anthony Robert Booth (2012) claims to motivate this principle, but his argument is seriously problematic. In its entirely, his argument is that an agent must deserve blame for violating an overall obligation because an agent cannot deserve blame for violating a pro tanto duty (2012: 511). The argument is invalid because the fact that an agent doesn’t deserve criticism for violating a pro tanto duty doesn’t in any way show that an agent deserves criticism for violating an overall duty. To secure his conclusion, Booth needs the disjunctive premise that negative agent appraisals supervene on either pro tanto or ultima facie negative deontic appraisals. But this is precisely the matter under contention. Fixing the argument results in begging the question. For another response, see Scott Stapleford (2015). For arguments against BRI, see Roderick Chisholm (1963b, 1964), Alvin Goldman (1986, 1988), Julia Driver (1992), Michael J. Zimmerman (1997, 2002, 2004), Paul McNamara (1996b, 2011a, 2011b), Ishtiyaque Haji (1998, 2002, 2006, 2012, 2013, 2014, 2016), Gregory Mellema (2005), and Justin Capes (2012). 5.2. Against Objections to Teleological Deontism 179

Imagine that unbeknown to us, our cognitive processes (e.g., memory, perception, inference) are not reliable owing to the machinations of the malevolent demon. It follows on a Reliabilist view that the beliefs generated by those processes are never justified. Is this a tenable result? I maintain that it is not. [. . . ] [W]e would have every reason for holding our beliefs that we have in the actual world. Moreover since we actually have reason to believe that our cognitive processes are reliable, it follows that in the demon world we would have every reason to believe that our cognitive processes were in fact reliable. . . It strikes me as clearly false to deny that under these circumstances our beliefs could be justified. If we have every reason to believe e.g., perception, is a reliable process, the mere fact that unbeknown to us it is not reliable should not affect its justification-conferring status. . . My argument hinges on viewing justification as a normative notion. Intu- itively, if ’s belief is appropriate to the available evidence, he is not to be held responsible for circumstances beyond his ken (1984: 281–282).

Summarily, Cohen postulates that the ordinary beliefs had by our counterparts who are victims of skeptical devices are equally well justified as our beliefs even though our counterparts’ beliefs aren’t reliably formed and ours are. By implication, reliabilism is false, or so Cohen argues. Perhaps deontism has similarly untoward results. Extending Cohen’s argument, it might be suggested that it is impermissible for the victims of skeptical hypotheses to believe that they are victims, or that they are tricked by the evil demon, et cetera. Yet that is the truth of the matter. Alarmingly, the deontically justified beliefs are radically mistaken, totally and sytematically unconnected with the facts. So, the objection goes, it seems that deontic justification isn’t truth-conducive after all. If it were, it wouldn’t be possible for agents to have systematically mistaken yet justified beliefs. I wish to offer three independent lines of response. My first rebuttal is that Cohen’s evil demon case makes exactly the same mistake as Alston’s cultural isolation case.8 As Cohen says, his argument hinges upon viewing justification in such a way that agents cannot deserve criticism (“held responsible”) if their beliefs are justified (“appropriate to the available evidence”). In a word, BRI is taken as an implicit premise in the argument. To see this, ask: why do agents and their skeptically victimized counterparts have equally well- justified beliefs? It seems that Cohen’s answer is that none of the relevant parties deserve

8 Compare with Kent Bach (1985), Mylan Engel, Jr. (1992), and Clayton Littlejohn (2012). Value-First Epistemology 180

criticism for believing as they do. Put another way, because normal and victimized agents are all hypologically justified in having all the same beliefs for all the same reasons, Cohen infers that the normal agents’ and victimize counterparts’ beliefs must be deontically justified. But the inference is fallacious; BRI is false. The fact that all the relevant parties believe in equally responsible ways given the available information in no way shows that their actual beliefs are deontically justified. The new evil demon argument equivocates between hypological justification and deontic justification. My second rebuttal is the deontism is not committed to the claim that it is impermissible for victims of skeptical hypotheses to believe that they are victims, or that they are tricked by the evil demon, et cetera. In point of fact, deontism isn’t explicitly committed in any claims about what is obligatory, permissible, impermissible, or anything else for the matter, in these cases. The DBWC theory of deontic justification requires input from epistemic axiology. On some epistemic axiologies, impermissibility is predicted. Evidentialism, for example, holds that all and only belief apportioned to the evidence realizes epistemic value; all and only belief disproportioned to the evidence realizes epistemic disvalue. Pairing DBWC with evidentialism entails that the evil demon’s victims must have the ordinary beliefs shared by their normal counterparts. This is because no other belief set does a better job of proportioning belief according to degree of evidential support. On other epistemic axiologies, impermissibility isn’t predicted. Veritism, for example, holds that all and only true belief realizes epistemic value; all and only false belief realizes epistemic disvalue. Pairing DBWC with veritism entails that the evil demon’s victims must believe that they are so victimized. This is because no other belief set does a better job of attaining truth and avoiding falsehood. Other axiologies offer other predictions when paired with DBWC. My point is that it is simply false that deontism per se is committed one way or the other to claims about what is justifiable or not in these cases. At worst, the new evil demon cases should be understood as objections to implausible axiologies. My third and final rebuttal is that the argument lacks bite. Even if sound, all it shows that some false beliefs are deontically justifiable. So what? This just means that deontism agrees with the popular view that epistemic justification isn’t factive. Alston’s and Cohen’s favorite theories of justification aren’t factive either. If this is grounds enough to reject deontism, then I think epistemology has got bigger problems. DBWC isn’t threatened by the isolation objection and neither is deontism in any of its guises. The cases employed to show that deontic justification isn’t truth-conducive succumb to two different fatal flaws. On the one hand, they attack the wrong target. It can be granted that hypological justification isn’t truth- or knowledge-conducive because it needn’t, and doesn’t, bear any interesting relation to deontic justification. On the 5.2. Against Objections to Teleological Deontism 181

other hand, it is simply false that deontism alone makes the relevant deontic predictions. Deontism must be supplemented with axiology for the theory to make predictions about what is obligatory, permissible, or impermissible. This means that deontism can always in principle jettison problematic deontic predictions.

5.2.3 No Positive Obligations Objection

There is an oft repeated argument against various forms of deontism in the literature. It is roughly as follows:

Table 5.3: No Positive Obligations Objection

01 Deontism entails that there are positive epistemic obligations.

02 There are no positive epistemic obligations.

∴ Deontism is false.

The argument is obviously valid. The contentiousness of the argument is divided among its premises. First premise ﬁrst. A positive epistemic obligation is typically understood to mean a requirement to commit something, such as having a certain doxastic attitude. Positive epistemic obligations are contrasted with negative obligations, which I understand to be prohibitions. A paradigmatic evidentialist prohibition is the requirement to refrain from believing without adequate evidence. A paradigmatic knowledge primitivist prohibition is the requirement to refrain from believing what isn’t known. A paradigmatic veritist prohibition is the requirement to refrain from believing falsehoods. And so on. Littlejohn (2012) and Jonathan Kvanvig (2014) argue deontism doesn’t entail the existence of positive epistemic obligations. Their skepticism is well-warranted. A theory of right action doesn’t entail that there are any moral obligations per se. It circumscribes the conditions under which obligations, positive or negative, exist. If the conditions aren’t met, there are no obligations whatever by the lights of the theory. The same goes for deontism. It circumscribes the conditions under which epistemic obligations, positive or negative, exist. Whether the conditions are met is a contingent matter beyond the scope of deontic theory proper. So while DBWC is consistent with there being positive epistemic obligations, it doesn’t entail that there are any. Even so, positive epistemic obligations are unproblematic. I am therefore inclined to reject the second premise despite the interesting arguments in its favor. I will consider Value-First Epistemology 182

some momentarily. Before I do, I want to register a point underappreciated by opponents of positive epistemic obligations. Formally framed, deontic modals are interdefinable. Substantively framed, the imposition of enough negative obligations entail a positive obligation. If the agent is prohibited from disbelieving that , and prohibited from withholding that , it can be inferred, given KL or ML, that the agent is obligated to believe that . To illustrate what I have in mind, consider the evidentialist prohibition to refrain from believing without sufficient evidence. What should be said when there is sufficient evidence? Is merely optional to believe or is it obligatory, given the evidence? If the former, then what should be said when the evidence overwhelmingly and conclusively supports belief? Is it still merely optional or does it finally become obligatory? If insufficient evidence triggers obligations about what not to believe, why can’t sufficient evidence ever trigger obligations about what to believe? In moral contexts, when an option is overwhelmingly and conclusively better than any other (across the relevant states of the world), it is obligatory. In prudential contexts, when an option is overwhelmingly and conclusively nets more utility than any other (across the relevant states of the world), it is the best response strategy. So, in epistemic contexts, when evidence is overwhelming and conclusively supports one belief better than any other (across the relevant states of the world), belief should likewise be obligatory. Not everyone is moved by this line of reasoning. Some still insist that there are no such things as positive epistemic obligations. Consider a pair of arguments from Littlejohn:

First, it is hard to see what wrong you could be guilty of if you do not bother to draw some of the obvious conclusions from your evidence. If you do not form beliefs concerning the obvious consequences of things you believe, what of it? Not forming these beliefs is not like not bothering to lift a ﬁnger to save a life that could easily be saved (2012: 46). Second, it is hard to imagine what a plausible account of positive epistemic obligation would look like. If there were positive epistemic obligations, there should be some principle that identiﬁes some condition, C, and says that you ought to form C-beliefs. What might that condition be? Suppose the condition is truth. Since we cannot believe all the true propositions, the principle violates [KL]. The same problem arsies for other principles in the neighborhood (e.g., the principle that says that you ought to believe all the obvious consequences of what you know) (2012: 47).

Littlejohn’s ﬁrst objection demands a substantive account of epistemic wrongdoing. DBWC doesn’t give this because it doesn’t commit to substantive axiology, but I hope 5.2. Against Objections to Teleological Deontism 183

the style of answer is clear enough. An evidentialist account of epistemic wrongdoing is, roughly, the disrespect of evidence. A responsiblilist account of epistemic wrongdoing is, roughly, irresponsible belief. A reasons-theoretic account of epistemic wrongdoing is, roughly, insensitivity to good epistemic reasons. A virtue-theoretic account of epistemic wrongdoing is, roughly, vicious belief. Not lifting a finger to save a life is just like any of these accounts of epistemic wrongdoing in the sense that it is a moral wrongdoing because the agent disrespects the value of the needy person, or the agent is insensitive to the good moral reasons that they have, or the agent irresponsibly does nothing to help, et cetera. The accounts of epistemic versus moral wrongdoing are comparable enough. It doesn’t matter if moral wrongdoing somehow feels more momentous than epistemic wrongdoing. The issue isn’t about intuitive badness, especially if, as it is usually thought, moral evaluations override epistemic evaluations. Rather the issue is about whether the accounts of moral and epistemic wrongdoing are comparable and DBWC answers in the affirmative. Ultimately, however, the adequacy of the comparison is a matter borne out by the relevant axiologies, moral and epistemic, not the deontic theory. My point is that this isn’t an objection to deontism per se. Littlejohn’s second objection is a challenge to develop an account of positive epistemic obligations that respects KL. DBWC meets this challenge. Accordingly, an agent must believe the best that they can; that is, an agent must have all and only the doxastic attitudes that they do in their epistemically best abilitively accessible world-moment/world-history pairs. On this view, all deontic—and, a fortiori, epistemic—modals supervene on the relevant class of praxeo-abilitive modals. If an agent is relevantly unable to have the relevant belief, the agent is not obligated to have it. KL is a theorem of the formal theory, not an ad hoc supplementation. Essentially the same point suffices to deal with a pair of arguments from Kvanvig:

Such a view is seriously problematic, however. For one thing, it imposes impossible demands upon us. If correct, we have to take an attitude toward every proposition whatsoever, and that is impossible for a finite mind. For another, there is a problem of cognitive overload. For any belief we have that our state of information tells us is true, that state of information also tells us that either that claim is true or it is true. But the proposition p is not the same proposition as p ∨ q, so we’d have an additional obligation of a sort, that if generalized, requires way too much cognitive overload (even if we grant that there is some way to avoid the application of this line of argument to infinity). There is no reason to require an attitude toward everything confirmed by our state of information (2014: 20). Value-First Epistemology 184

Deontism does not require that an agent has more beliefs that they are able to have given any body of information had by the agent. DBWC says that the agent must believe the best that they can, meaning that an agent’s epistemic obligations are a function of the agent’s cognitive limitations and whatever it is in virtue of which a belief realizes epistemic value. If, for example, proportioning belief to the evidence realizes epistemic value, then an agent must have all and only the beliefs that are members of the best belief sets, where the value of the belief set is roughly a function of the agent’s tendency to proportion belief according to the evidence. Deontism does not impose a larger number of obligations than the agent is able to discharge. This is a consequence of the Kantian and Moorean meta-theorems.9 Littlejohn gives a third argument against positive epistemic obligations:

What if instead the principle said that you ought to form as many C-beliefs as you can? This principle cannot violate [KL], but it still seems problematic. Suppose you have two options. You can head to the library to study history or you can head to the laboratory to do chemistry experiments. You can acquire C-beliefs in either place, but they are easier to come by in the library. Thus, the number of C-beliefs you could form in the library is greater than the number of C-beliefs you could form in the lab. Suppose you head to the lab. The beliefs you form constitute knowledge, but forming those beliefs prevents you from forming a greater number of C-beliefs in the library. Thus, you would not satisfy the principle that says that you ought to form as many C-beliefs as you can even if your beliefs constitute knowledge. I think this means the alleged principle is not a principle since you justiﬁably believe what you come to know in the lab. Acting in such a way as to acquire fewer justiﬁed beliefs is not like acting in such a way as to save fewer lives (2012: 47).

Littlejohn’s objection is remarkably similar to one from Keith DeRose (2000):

Suppose that Henry firmly believes that p—it doesn’t matter much what p is— and has excellent evidence for p (evidence that’s strong enough to adequately support the firm and confident attitude Henry has adopted toward p). Suppose further that Henry doesn’t possess evidence against p, so the attitude toward p that fits all the evidence Henry possesses is the confident belief that p which Henry in fact holds. But suppose that Henry doesn’t believe p on the basis of the excellent evidence for it that he possesses. Indeed, Henry hasn’t even

9 Mark Nelson (2010) makes yet another argument in this vein. The DBWC response is, once more, essentially unchanged. 5.2. Against Objections to Teleological Deontism 185

considered p in the light of this excellent evidence, and the fact that he possesses good evidence for p is no part of the explanation for why Henry believes that p (2000: 697). Suppose then that there is some evidence Henry very easily could have, and should have, gathered, but that he negligently never encountered. This would have been very strong evidence against p. So strong that, despite the excellent evidence Henry possesses in favor of p, this negative evidence that Henry should have gathered would have completely outweighed the positive evidence he actually possesses, such that disbelief of p would have been the attitude that would have best suited Henry’s evidence, had he gathered this negative evidence (2000: 699).

Littlejohn going to the lab to perform experiments is like DeRose’s Henry failing to gather the evidence he should have gathered against p. In both cases, the agent would have realized more overall value by doing something else instead and, supposing that this is the only relevant factor, it would have been obligatory for them to have different beliefs than they in fact do end up with. In both objections, this is a problem for positive epistemic obligations. Littlejohn thinks his beliefs in the lab are nonetheless justified. DeRose thinks that Henry’s belief that p is unjustified. This is allegedly inimical to deontism because deontism implies the opposite. Except that these cases aren’t problematic. Those acquainted with the paradoxes of deontic logic will quickly recognize that these cases are instances of Chisholm’s paradox. In Chisholm’s original cases, there is an agent that acquires various contrary-to-duty obligations in virtue of the violation of the original set of obligations.10 The challenge was to develop a deontic logic that could account for such changes in such a way that didn’t result in contradiction. Massachussettsian theory is one among many that resolved the paradox before Littlejohn’s and DeRose’s objections were in print.11 I won’t bother to rehearse all the poignant details. Briefly, DBWC suggests that the agent has various absolute and conditional obligations that change over time as the agent fulfills or fails to fulfill the initial set of obligations. If acquiring new knowledge is all that matters, Littlejohn should have gone to the library, but the beliefs he will acquire after investing time at the lab, given that he goes to the lab, will nevertheless end up justified. If following the evidence is all that matters, Henry should have gathered more evidence but, given that he didn’t, his belief that p is justified. If it is insisted that such cases make positive

10 See Roderick Chisholm (1963a). 11 See Fred Feldman (1986, 1990) and Michael Zimmerman (1987, 1996). Value-First Epistemology 186

epistemic obligations impossible, then positive obligations of any kind are impossible because the cases instantiate a paradox schema. One ﬁnal remark that brings my defense of DBWC full circle. An agent’s obligations are, again, a function of the agent’s abilities and the realization of the good. It follows that bad deontic predictions can be avoided by making the appropriate changes to the theory of the good. If, for example, Littlejohn thinks that it is optional to go to the laboratory or the library, then he should look for the epistemic axiology that bears out his intuitions. So, too, for DeRose and his intuitions. As such, the cited cases aren’t objections to deontism per se. They’re objections to implausible epistemic axiologies.

5.3 Disarming Counterfactual Worries About Knowledge

In this section, I clarify and defend the DBWC theory of knowledge. Though I am not entirely persuaded that I’d settle on its current form, it a promising starting place. In the very least, it helps make plausible the thought that epistemology should be seen as an outgrowth of ability theory. Counterfactual theories of knowledge are inﬂuential. Fred Dretske (1970, 1972, 1981) and Robert Nozick (1981) argue that knowledge is sensitive true belief. Keith DeRose (1995) conjoins sensitivity with contextualism. Ernest Sosa (1999, 2007, 2009) argues that knowledge is safe true belief. The DBWC treatment of sensitivity and safety may be rendered as follows:

∙ Sensitivity: ⊡( → [ ]) and ⊡(¬ → ¬[ ])

∙ Safety: ⊡([ ] → )

The belief that is sensitive if, and only if, were true, the agent would believe that and were false, the agent wouldn’t believe that . In effect, an agent wouldn’t believe if it were easily false. The belief that is safe if, and only if, were the agent to believe that , then would be true. In effect, an agent’s safe belief wouldn’t easily be false. The DBWC analysis of knowledge is fairly comparable. It holds that knowledge is modalized justified true belief; or, belief whose justification tracks truth. The justification and epistemic connections each impose modal conditions upon knowledge. The belief that is justifiedly held if, and only if, the agent’s belief that is a member of an optimific belief set. Justification connection is as follows:

∙ Epistemic Connection: ▣( ![ ] → [ ]!) 5.3. Disarming Counterfactual Worries About Knowledge 187

The belief that is epistemically connected if, and only if, the agent justifiedly believes that only if the agent accurately believes that in all contextually salient abilitively accessible world-moment/world-history pairs; or, in every optimific world-pair, the agent’s belief is part of an optimific belief set only if it is true. Subjunctively framed, the agent’s justified belief wouldn’t easily be a false belief. According to the sensitivity theorist, a true belief fails to instantiate knowledge if, and only if, it is insensitive. According to the safety theorist, a true belief fails to instantiate knowledge if, and only if, it is unsafe. By the same token, DBWC holds that a justified true belief fails to instantiate knowledge if, and only if, it is epistemically unconnected. The epistemic connection condition can fail in but one way:

∙ Unsafe Justification: ▣ ( ![ ] ∧ ¬[ ]!)

DBWC holds that a justified true belief fails to instantiate knowledge if, and only if, it is justificationally unsafe. Though influential, counterfactual theories of knowledge are not without problems. Though I would not classify DBWC as a counterfactual theory, it might be thought that DBWC succumbs to the same sorts of problems that usually plague counterfactual theories. In this section, I attempt to allay a few of such worries.

5.3.1 A Closer Look at the Formal Features of Knowledge

The DBWC theory of knowledge is not easily problematized by the standard objections to counterfactual theories of knowledge. But before making that argument, I want to make the formal features of knowledge as perspicuous as possible.

Suppose that an agent knows that at the normal moment/history pair (w, hw). Conse-

quently, at (w, hw) is true, the agent justiﬁedly believes that , and the agent’s belief is epistemically connected.

Justiﬁed belief that at (w, hw) means that the agent believes that at w, the agent ¨ ¨ has abilitively access to another contextually salient world-pair, (w , hw), at which the agent doesn’t believe that , and there exists no abilitively accessible contextually salient ¨¨ ¨ world-pair (w , hw), epistemically comparable to (w, hw) at which the agent doesn’t believe

that . In other words, the agent’s belief set at (w, hw) is epistemically optimiﬁc. It follows that the conditional between the agent’s justiﬁed belief that and true belief that is

satisﬁed at least one contextually salient world-moment, namely (w, hw) itself.

Epistemically connected belief that at (w, hw) means that the agent justiﬁedly believes that just in case the agent accurately believes that at every contextually salient ¨ ¨ world-pair accessible from (w, hw),m including (w, hw) itself. It follows that if (w , hw) is Value-First Epistemology 188

contextually salient and abilitively accessible from (w, hw), then the agent has a true belief ¨ ¨ that at (w , hw) if, and only if, the agent’s belief set—which includes the belief that —is ¨ ¨ epistemically optimiﬁc at (w , hw). The robustness of the epistemic connection condition is a function of how the set of contextually salient world-moment/world-history pair is populated. The DBWC distinction between simple and competent praxeological modals applies equally well to propositional knowledge.

Simple knowledge quantiﬁes over the original world-pair of evaluation alone, (w, hw), or all those world-moments that are in perfect agreement about all the well-formed formulas

true at (w, hw). Since, as previously observed, the conditional between the agent’s justiﬁed

belief that and the true belief that is satisfied at (w, hw), justified true belief trivially satisfies the epistemic connection condition. In effect, simple knowledge is nothing over and above justified true belief. I suspect that a sizable portion of testimonial knowledge fits the bill.12

Competent knowledge quantifies over the original moment of evaluation, (w, hw), in addition to some number of other moments that are dissimilar enough in the relevant respects. Intuitively, the contextually salient world-moments differ in environmental hospitality. Justified true belief will be easier to achieve in some world-pairs, harder in others. Competent knowledge is justified true belief across all these variably difficult accessible world-pairs. The result is something very close to the picture of creditworthy knowledge often painted by virtue epistemologists.13 The upshot is that the set of contextually salient world-moment/world-history pairs must be fixed before any assessments can be made about what DBWC implies about what the agent knows. Simple knowledge is defined by appeal to Simple Parameterization and competent knowledge is defined by appeal to Competent Parameterization.

5.3.2 Knowledge of Necessity

Counterfactual theories of knowledge do not fare well when it comes to tautologies and other necessary truths. Allow me to explain. A tautologous well-formed formula is necessarily true at every possible world-pair. The belief that ⊤ is sensitive if, and only if, were ⊤ false at some world-pair, the agent wouldn’t believe that ⊤. Since it is impossible for ⊤ to be false at any world-pair, what is

12 Compare with Keith DeRose (2009). Jennifer Lackey (2007, 2009) argues against the popular virtue- theoretic claim that agents deserve credit for achieving knowledge. I take it that the sorts of cases that she evokes to pump the relevant intuitions are those in which the agent comes to simply know something from testimony without correspondingly competently knowing. 13 Compare with Wayne Riggs (2002, 2009), John Greco (2010), and Ernest Sosa (2011, 2015). 5.3. Disarming Counterfactual Worries About Knowledge 189

the status of the counterfactual? It is either trivially true or trivially false. Both options are equally bad. If trivially true, then the belief that ⊤ is sensitive by default, in which case it is impossible for a belief that takes a tautology as its object to fail to be knowledge. If trivially false, then the belief that ⊤ is insensitive by default, in which case it is impossible for a belief that takes a tautology as its object to be knowledge. Safety doesn’t fare any better. The belief that ⊤ is safe if, and only if, were the agent to believe that ⊤, it would be the case that ⊤. Since ⊤ must be true at every possible world-pair, every belief that ⊤ is safe by default, in which case it is impossible for a belief that takes a tautology as its object to fail to be knowledge. Mathematical and logical propositions are the paradigmatic examples of necessary truths. Since counterfactual theories of knowledge stumble about when it comes to necessary truths, they will not handle mathematical knowledge well. Sensitivity makes mathematical knowledge either impossible full stop or impossibly easy to acquire. Safety makes mathematical knowledge impossibly easy to acquire. Even on charitable readings, both radically overestimate agents’ cognitive abilities. The DBWC theory of knowledge is not so easily troubled. Epistemic connection is the knowledge-making feature added to justified true belief. The agent must justifiedly believe that ⊤ if, and only if, the agent believes that ⊤ in all abilitively accessible contextually salient world-pair. So while ⊤ is true in all world-moments and therefore, a fortiori, all abilitively accessible contextually salient world-pair, there remains the question of whether the agent believes and, if so, whether the belief is praxistically justified. The agent’s belief must be part of an optimific belief set, which is to say that the agent’s actual belief set must be epistemically better than any salient accessible belief set lacking the tautological belief. What makes the agent’s actual belief set optimific is that a sufficiently large number of the agent’s actual beliefs realize epistemic good or have epistemically good-making properties going for them, such as being coherent, being proportioned to the evidence, being reliably formed, et cetera. My point is that if the belief that ⊤ is in some way stupid, then, ceteris paribus, it won’t be justifiedly held because it won’t part of an optimific belief set—the seemingly salient and accessible belief set alike in all respects except lacking the stupid tautologous belief is epistemically better.14 DBWC implies neither that mathematical knowledge is impossible full stop nor that it is impossibly easy to acquire. Rather it suggests that an agent achieves mathematical

14 I am assuming that the comparable belief set lacking the stupid tautologous belief is epistemically better on any plausible epistemic axiology. To wit, the only epistemic axiology that falsiﬁes the assumption is naïve doxastic conservativism, which holds that all beliefs whatever realize an equal amount of epistemic value. Ultimately, naïve doxastic conservativism enjoins agents to realize epistemic value by having the largest possible belief set. I leave it to the reader to judge the plausibility of the axiology. Value-First Epistemology 190

knowledge in fundamentally the same sort of ways as any other kind of knowledge: roughly, by the agent’s believing the truth by manifesting cognitive powers in ways that reliably realize epistemic value.

5.3.3 Justiﬁcationally Unsafe Belief

The epistemic connection condition is unsatisfied if belief is justificationally unsafe. Schematically, a belief is justificationally unsafe if, and only if, there is some abilitively accessible contextually salient world-moment/world-history pair such that the agent’s justified belief is false. Formally, justification is unsafe when the following is true:

∙ Unsafe Justification: ▣ ( ![ ] ∧ ¬[ ]!)

Gettier cases are the paradigm examples of justiﬁcationally unsafe belief. As such, DBWC agrees with intuition that Gettier cases don’t instantiate—competent—knowledge. It is helpful to run through a few examples to see why. Begin with a famous case originated by Edmund Gettier (1963):

Suppose that Smith and Jones have applied for a certian job. And suppose that Smith has strong evidence for the following conjunctive proposition:

(d) Jones is the man who will get the job and Jones has ten coins in his pocket.

Smith’s evidence for (d) might that the president of the company assured him that Jones would in the end be selected and that he, Smith, had counted the coins in Jones’s pocket ten minutes ago. Proposition (d) entails:

(e) The man who will get the job has ten coins in his pocket.

Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e) on the grounds of (d), for which he has strong evidence. In this case, Smith is clearly justiﬁed in believing that (e) is true. But imagine, further, that unknown to Smith, he himself, not Jones, will get the job. And, also, unknown to smith, he himself has ten coins in his pocket. Proposition (e) is then true, though proposition (d), from which Smith inferred (e), is false. In our example, then, all of the following are true: (i) (e) is true; (ii) Smith believes that (e) is true; and (iii) Smith is justiﬁed in believing that (e) is true. But it is equally clear that smith does not know that (e) is true; for (e) is true in virtue of the number of coins in Smith’s pocket, while Smith does not know how many coins are in Smith’s pocket, and bases his belief in (e) on 5.3. Disarming Counterfactual Worries About Knowledge 191

a count of the coins in Jones’s pocket, whom he falsely believes to be the man who will get the job (1963: 122).

Smith has a justified true belief that the man who will get the job has ten coins in his pocket that fails to instantiate knowledge. Gettier seems to suggest that Smith doesn’t know because the right relation between what it is in virtue of which his belief is justified and the truth fails to obtain. Subjunctively framed, Smith’s justified belief is too easily mistaken to count as competent knowledge; were it false that Smith had ten coins in his pocket, he would nevertheless justifiedly believe that the man who will get the job has ten coins in his pocket. Consider another famous case due to Alvin Goldman (1976):

Henry is driving in the countryside with his son. For the boy’s edification, Henry identifies various objects on the landscape as they come into view. “That’s a cow,” says Henry, “That’s a tractor,” “That’s a silo,” “That’s a barn,” etc. Henry has no doubt about the identity of these objects; in particular, he has no doubt that the last-mentioned object is a barn, which indeed it is. Each of the identified objects has features characteristic of its type. Moreover, each object is fully in view, Henry has excellent eyesight, and he has enough time to look at them reasonably carefully, since there is little traffic to distract him. Given this information, would we say that Henry knows that the object is a barn? Most of us would have little hesitation in saying this, so long as we were not in a certain philosophical frame of mind. Contrast our inclination here with the inclination we would have if we were given some additional information. Suppose we are told that, unknown to Henry, the district he has just entered is full of papier mâché facsimiles of barns. These facsimiles look from the road exactly like barns, but are really just facades, without back walls or interiors, quite incapable of being used as barns. They are so cleverly constructed that travelers invariably mistake them for barns. Having just entered the district, Henry has not encountered any facsimiles; the object he sees is a genuine barn. But if the object on that site were a facsimile, Henry would mistake it for a barn. Given this new information, we would be strongly inclined to withdraw the claim that Henry knows the object is a barn (1976: 772–773).

Henry has a justiﬁed true belief that that’s a barn (where the ‘that’ is accompanied by the appropriate demonstrative) that fails to instantiate knowledge. Goldman suggests that Henry doesn’t know because the right relation between what it is in virtue of which his Value-First Epistemology 192

belief is justified and the truth fails to obtain. In particular, the characteristic perceptual information responsible for the judgment that that’s a barn in normal environments is finicky in fake barn country. While belief formed on the basis of this information suffices to make it justified, it is false that justified belief will be appropriately sensitive to truth. Subjunctively framed, were it a papier mâché facsimile, the agent would nonetheless justifiedly believe that it is a barn. Finally, consider the following case from Ernest Sosa (1999):

A VCR-driven screen ﬂeetingly becomes a window allowing a good view of the scene beyond. If you are under the impression that it is a window all the while, giving you access to the scene beyond, do you know when it ﬂeetingly becomes one? Suppose, conversely, that the VCR were turned on for an instant and a scene were put randomly on the window/screen by the VCR for that randomly selected instant, where the scene on the screen just happened to match the jerkily changing scene beyond (say you’re in a train traversing rapidly changing terrain). Here again, “looking at the window” seems in general a reliable method (the present instant being randomly selected as the one instant ever when the VCR is attached and turned on). Intuitively you do not know about the scene beyond, despite the perfect accuracy of your beliefs (1999).15

Ernie has a justified true belief that the landscape is such-and-such (where ‘such-and-such’ accurately describes whatever scene the agent is apt to perceive) that fails to instantiate knowledge. Sosa suggests that Ernie doesn’t know doesn’t because the accuracy of the belief is accidental. Were the images upon the false window different, the agent’s beliefs would reflect what was depicted upon the false screen rather than describe the actual landscape beyond. The agent would justifiedly believe that the landscape is such-and-such even if the screen radically misrepresented the actual state of the landscape.16 There are plenty of other Gettier cases, but I see no reason why the diagnosis should not generalize. DBWC agrees with Gettier, Goldman, and Sosa that the agents’ justified true beliefs are too much a matter of luck to count as instances of competent knowledge. More specifically, their beliefs are epistemically unsafe. In some abilitively accessible contextually salient world-pairs, Smith justifiedly believes that the man who will get the job has ten coins in his pocket and Henry justifiedly believes that that’s a barn and

15 Compare with Chisholm (1966), especially with the Gettier case of the sheep-shaped rock. 16 By similar lights, the agent who gazes out into the distance and acquires the justified true belief that there is a sheep in the field but whose belief is caused by the perception of a sheep-shaped rock is too accidental to count as knowledge. The agent would have the justified belief even if there were no sheep hiding behind the sheep-shaped rock. 5.3. Disarming Counterfactual Worries About Knowledge 193

Ernie justifiedly believes that the landscape is such-and-such despite the fact that all three propositions are false. Smith would justifiedly believe even if he had a different number of coins in his pocket. Henry would justifiedly believe even if it were a fake barn. Ernie would justifiedly believe even if the screen were wildly inaccurate. The reason, then, that Gettierized agents don’t know is that they fail the epistemic connection condition for—competent—-knowledge. Gettier cases are paradigmatic, but not exhaustive. I briefly want to turn attention to another class of epistemically unsafe beliefs. Jonathan Vogel (1990) and John Hawthorne (2004) popularized what I shall here call the lottery puzzle. Hawthorne famously describes the structure of the puzzle as follows:

In each of these cases, the structure of the problem is the same. There is what we might all the ordinary proposition, a proposition of a sort that we ordinarily take ourselves to know. There is, on the other hand, a lottery proposition, a proposition that we would be intuitively disinclined to know. And in each case the ordinary proposition entails the lottery proposition (2004: 5–6).17

Hawthorne illustrates the puzzle with a slew of diﬀerent cases, some more persuasive than others, but the opening passage of his book highlights the problem rather nicely:

Suppose someone of modest means announces that he knows he will not have enough money to go on an African safari this year. We are inclined to treat such a judgment as true, notwithstanding various far fetched possibilities in which that person suddenly acquires a great deal of money. . . However, were that person to announce that he knew that he would not win a major prize in a lottery this year, we would be far less inclined to accept

17 Hawthorne goes on to explain why biting the bullet and claiming to know lottery propositions is in general an unpromising strategy:

[P]hilosophers who see their way to embracing the claim to know the relevant lottery proposition will find themselves quickly embarrassed by conjunction introduction. Suppose I hang tough and claim that since I know I will be spending part of the sumer living in Syracuse, I know I will not be one of the unlucky heart attack victims, and that since I know I will not be able to afford a safari, I know I will not win the lottery. Well, if I can know such things about myself, I can presumably know such things about my friends as well. Consider 1, 000 such friends. If I know of each of them that they will lack sufficient resources to go on an African safary, then I can know of each of them that they will not lottery a lottery. But assuming that I can extend my knowledge by conjunction introduction, I can now know of all of them that they will lose. But that is crazy: soon enough, by such methods, I will take myself to know of a large chunk of lottery tocket-holders that they will all lose and of a sizable chunk of the population that they will all be free from fatal attacks (2004: 6). Value-First Epistemology 194

his judgment as true. We do not suppose that people know in advance of a lottery drawing whether they will win or lose. But what is going on here? The proposition that the person will not have enough money to go on an African safari this year entails that he will not win a major prize in a lottery. If the person knows the former, then isn’t he at least in a position to know the latter by performing a simple deduction (2004: 1–2)?

At bottom, the question raised is this: how can an agent have ordinary knowledge given that ordinary propositions have lotteryesque entailments that the agent doesn’t actually know but can easily deduce? Put another way, if agents have ordinary knowledge, then either they must also have lotteryesque knowledge or knowledge isn’t closed over competent deduction. Neither option is particularly attractive, but neither is the denial of ordinary knowledge. The options seem to be: Moorean dogmatism, skepticism, or closure denialism.18 Of course, there are another options on the table. In recent decades, epistemology has borne witness to a surge in what Jeremy Fantl and Matthew McGrath (2012) call shifty epistemology:

Sometimes it is true to say that you know that p even though it is false to say that some other person, , knows that p. In many such cases, the reasons for the diﬀerence are not suprising. Perhaps you have stronger evidence for p than does, or p is true when you are said to know it, but false when is said to know it, or is Gettiered and you are not. Shifty epistemologists allow that the truth value of “knowledge”-ascriptions can vary not merely because of such diﬀerences, but because of factors not traditionally deemed to matter to whether someone knows, like salience of error possibilities and practical stakes (2012: 55).

Broadly, shifty theories allow epistemic modals to vary in light of nonepistemic situational factors. Contextualism and subject-sensitive invariantism are the two main exemplars of contemporary shifty epistemology. Epistemic contextualism, roughly, is the view that epistemic modals are sensitive to linguistic factors salient in the context of utterance.19 Subject-sensitive invariantism, roughly, is the view that epistemic modals are sensitive to

18 G. E. Moore (1922, 1939) advocates dogmatism. Peter Unger (1975) advocates skepticism. Dretske and Nozick deny closure. 19 See Gail Stine (1971, 1976), Stewart Cohen (1986, 1988), David Lewis (1990), and Keith DeRose (1995, 2002, 2009), among others, for statements and defenses of epistemic contextualism. 5.3. Disarming Counterfactual Worries About Knowledge 195

practical factors cognitively salient to the subject.20 Shifty epistemology, roughly, splits the difference between dogmatism and skepticism: in ordinary situations, the agent has ordinary and antiskeptical knowledge; in extraordinary situations, the agent lacks both ordinary and antiskeptical knowledge. While DBWC vindicates shifty epistemology, I rather want to focus upon the judgment that agents do not know the lotteryesque entailments of their ordinary beliefs. Intuitively, agents do not know that won’t win the lottery; or, that they won’t be struck by lightning; or, that they won’t suffer a fatal heart attack. Agents do not seem to know lottery propositions despite the overwhelming probability, objective and epistemic, that the lottery proposition is true. Interestingly, Hawthorne notes in passing that many popular analyses of knowledge “do especially bad at predicting our reactions to the lottery case” (2004: 9). This includes safety theory. Beliefs that take lottery propositions as their objects are typically safe. In all the contextually salient world-pairs, the life is exactly as it appears to be: the agent isn’t struck by lightning, doesn’t suddenly suffer a fatal heart attack, doesn’t win the lottery, et cetera. Were the agent to believe any of these things, the belief wouldn’t easy be false. Maybe not all lotteryesque beliefs are safe, but most are, and that’s plenty enough to worry that safety theory is too much a Moorean dogmatism. Sensitivity theory at least gets this one right, but at the cost of denying closure. Arguably the biggest cost of denying closure is what Keith DeRose (1995) calls abominable conjunctions:

Accepting [sensitivity theory] involves embracing the abominable conjunction that while you don’t know you’re not a bodiless (and handless!) [brain-in-a-vat], still, you know you have hands. Thus, while his account does quite well on the relevant particular intuitions regarding what is and isn’t known, it yields an intuitively bizarre result on the comparative judgment [about epistemic closure] (1995: 28).

Saul Kripke (2011) makes essentially the same complaint:

Let us suppose that the barn is red. Suppose further that any counterfeit erected in its place would have been green. (We can suppose, if we wish, that for some chemical reason the cardboard in the counterfeit barns cannot be painted red. Alternatively, those who erected counterfeit barns deﬁnitely preferred green

20 See Jeremy Fantl and Matthew McGrath (2002, 2007, 2009), John Hawthorne (2004), Jason Stanley (2005), and John Hawthorne and Jason Stanley (2008), among others, for statements and defenses of subject-sensitive invariantism. Value-First Epistemology 196

ones, or even definitely preferred a green one in this particular location.) Now consider Henry’s true belief (thus satisfying the first two conditions) that there is a (genuine) red barn in the field. Now the third condition is satisfied. If there had not been a red barn in the field, then there would have been a green counterfeit, and Henry would not have believed that there was a red barn in the field. There is no trouble with the fourth condition. So according to Nozick’s criterion, although Henry may not know that there is a genuine barn in the field, he does know that there is a genuine red barn there! Surely even someone who follows Nozick (and others mentioned before) in rejecting deductive closure in general cannot be very comfortable with this particular result. Notice that it is not essential that in the absence of a real barn a counterfeit definitely would have been erected—all that is required is that had any counterfeit been erected, it would not have been red. (If no object resembling a barn is in the field, clearly Henry will not believe that there is a red barn there.) Notice also that there would have been no problem with the result (and no failure of deductive closure) if Henry had been aware that redness is a distinguishing mark of real, as opposed to counterfeit, barns. The problem is that Nozick’s theory says that Henry knows there is a red barn there even if he is entirely unaware of the connection of genuineness with color, or even of the danger that the barn might be counterfeit (2011: 186).

Summarily, it is bad if a theory knowledge permits a fully epistemically responsible agent to say, “I know full well that and I know full well that entails ,” but, in the very same breath, “I’m not in any sort of a position to know that .” If an agent knows that that’s a red barn and competently deduces that’s a barn thereby, the only reason the agent should fail to know that that’s a barn is that the agent is flouting good epistemic practice or otherwise indulging irrationality. Yet sensitivity theory condones abominable conjunctions as instances of good epistemic practice. Happily, DBWC agrees with intuition. Generally, agents do not know lottery propositions even if true and the lotteryesque belief is justified because they are difficult to make epistemically connected—when, that is, the possibility of error is salient. There are abilitively accessibly contextually salient world-pairs such that the agent justifiedly believes a lottery proposition and the proposition is false. The agent would justifiedly believe that they won’t win the lottery even if they had a winning ticket. The agent would justifiedly believe that they won’t be stuck by lightning even if they will. The agent would justifiedly believe that they won’t suffer a fatal heart attack even if they will. The factors in virtue of which the lotterysque belief is justified do not hook up with truth in the right 5.4. Schematic Argument for Unhinged Justification 197

way; they fail the epistemic connection condition on knowledge when the possibility of error is salient. When salient, there are abilitively accessible contextually salient world-pairs at which the agent’s justiﬁed belief is false. By the same token, if the error possibility isn’t salient, the belief is justiﬁcationally safe.

5.4 Schematic Argument for Unhinged Justiﬁcation

The DBWC theory of epistemic justification finds itself at a strange crossroads. On the one hand, qua formal theory, it is not a competitor to substantive theories of epistemic justification. Theorists of all stripes can retain the spirit of their theories while adopting the DBWC framework when the core intuitions are conceptualized as a doxastic axiology. Insofar as the epistemic properties P , … , P ¨ are understood to be good-making features of belief, the justified beliefs will tend to be those that exhibit properties P , … , P ¨. On evidentialist axiologies, the class of justified beliefs will tend to be just those that are apportioned to the evidence. On reliabilist axiologies, the class of justified beliefs will tend to be just those that are reliably formed. On vertistic axiologies, the class of justified beliefs will tend to be just those that are true. The same goes for any other specification of the good-making epistemic properties P , … , P ¨. On the other hand, qua deontic theory, DBWC is a competitor to the letter of all theories whatever of epistemic justification. A theory of epistemic justification identifies some set of epistemic properties, P , … , P ¨, the exhibition of which a belief is justified qua deontic status. DBWC implies that no set of epistemically good-making properties P , … , P ¨, for any set of good-making properties, are either necessary or sufficient for epistemic justification. DBWC entails that the sole justification-making feature of any belief, for any doxastic axiology, is membership in an epistemically optimific belief set. While a great many of epistemically justified beliefs will have one or more of these good-making features, as determined by the reader’s favorite doxastic axiology, it is possible that some are justificationally unhinged—viz., lacking any good-making properties of any kind. This is precisely what traditional theories of epistemic justification all say is impossible. This is precisely why they are all false. The argument for unhinged justification is surprisingly straightforward, given the universality of its conclusion. In brief, it exploits the difference between the axiological (the good) and the deontic (the right). Though DBWC defines the right in terms of the good, not everything right is good and not everything good is right. Unhinged justification is merely an instance of a category things that are right but not good. First some background for sake of clarity. Let ‘doxastic axiology’ denote, broadly, any Value-First Epistemology 198

theory of what it is in virtue of which a belief is epistemically valuable or disvaluable, which is represented by the notion of v-wise-value or v-wise-disvalue. Every plausible axiology must meet certain basic minimum constraints on pane of incoherence. A doxastic axiology is no diﬀerent. Recall the basic value theory schema:

∙ Property P , … , P ¨ Axiology: All and only states of aﬀairs exhibiting properties P , … , P ¨ realize any v-wise-value. More precisely:

Recall that, at minimum, an axiology identifies all the things the realize either value or disvalue and specify how they relate to the valuation of a world-moment/world-history pair as a whole. The axiology schema assigns value of quantity n to states of affairs exhibiting properties P , … , P ¨ and disvalue of quantity m to states of affairs failing to exhibit properties P , … , P ¨. It is possible that n is greater than, equal to, or less than m. Deontic value and disvalue can benefit from, or be penalized by, various situational modifiers or multipliers, but I omit any such inclusions for sake of simplicity. The deontic value of a world-pair is a function of the deontic values of the relevant formulas representing the relevant states of affairs occurring there, but I say nothing about the nature of this function. It might be merely additive or it might be something else entirely. Whatever the exact nature of the function, it takes as inputs all the deontic value atoms that occur at a world-pair and outputs the deontic value for the world-pair as a whole. All that DBWC requires of an axiology is that it can be used to impose a total deontic value-wise ordering over the domain of possible world-pairs. Doxastic axiology concerns the epistemic value realized by believings, treating the beliefs that exhibit the relevant good-making epistemic properties P , … , P ¨ as value atoms. The best belief sets are those had by the agent in the epistemically optimific world- pairs, which are the world-moment/world-history pairs such that no competing belief set is strictly better from the perspective of the relevant doxastic axiology. More explicitly, the best world-pairs are those that have a sufficient number of beliefs that exhibit properties P , … , P ¨ over beliefs that lack said properties. Pulling all these details together, and conjoining them with the DBWC analysis of epistemic justification, the schematic argument for unhinged justification is stated thusly: 5.4. Schematic Argument for Unhinged Justification 199

Table 5.4: Schematic Argument for Unhinged Justiﬁcation

01 Property P , … , P ¨ Axiology enjoins agents to realize epistemic value by having all and only beliefs exhibiting epistemic properties P , … , P ¨.

02 The epistemic value of a world-pair for an agent is a function of the number of beliefs exhibiting epistemic properties P , … , P ¨ in that world-pair.

03 The deontic status of an individual belief at a world-pair is a function of its occurrence in the relevant number of abilitively accessible contextually salient epistemically optimiﬁc world-pairs.

04 So, the deontic status of an individual belief at a world-pair is a function of its occurrence in an abilitively accessible contextually salient world-pair such that there exists no other abilitively accessible contextually salient world-pair where the agent fails to have the belief but the agent has a suﬃcient number of other beliefs exhibiting properties P , … , P ¨ in that world-pair.

05 It is possible for a belief to occur at an abilitively accessible contextually salient epistemically optimiﬁc world-pair without exhibiting properties P , … , P ¨.

∴ The epistemic justiﬁcation of belief neither implies, nor is implied by, a belief’s exhibiting epistemic properties P , … , P ¨.

The argument is valid: the conclusion is entailed by the fourth and fifth premises. The fifth premise is tantamount to the claim that something can part of a valuable whole without contributing value to the whole. The fourth premise is entailed by the first three premises. The first two premises are motivated by the background information. The third premise is the DBWC analysis of epistemic justification. All in all, then, the argument looks solid. Allow me to bolster the argument by disarming the most obvious objections to the two key premises. I won’t attempt to assuage all possible worries. The defenses are thematically divided among various subsections.

5.4.1 Objections to the Fourth Premise

Some might wish to deny the fourth premise. If the fourth premise is false, the deontic status of a belief is not a function of whether there are abilitively accessible contextually salient world-moment/world-history pairs at which the agent doesn’t have the belief that are deontically better—in the sense that the agent has a suﬃcient number of beliefs exhibiting epistemic properties P , … , P ¨. The fourth premise is an entailment of the ﬁrst Value-First Epistemology 200

three premises, so denying it entails the denial of at least one of these three. Which should be given up? The first premise is incontrovertible. It is merely a statement of some doxastic axiology. Denying the premise is tantamount to denying that there are any true doxastic axiologies, a position which may be termed epistemic value nihilism. This is an absurd view. The second premise notes that the overall deontic value of a world-pair is a function of the value of its parts. It does not specify the nature of the function. It does not say that every part must contribute value to the whole. It does not say that the function is a summative one. As stated, it is consisted with, say, Moorean organic unities. It might be the case that, as Moore thought, the value of a world-pair might sometimes be greater, and other times lesser, than the sum of its value atoms. The point remains that, even so, once the nature of the relation between the value atoms and the value whole is determined, there should be some critical mass where some number of value atoms (standing in the relevant value-enabling relation) suffice to make a world-moment optimific. The denial of the second premise, then, is tantamount to the claim that value atoms bear no relation whatsoever to the value of a whole world-pair, which is absurd. Even a world-pair value holism, according to which all and only world-pairs have value, denotes a functional relationship between value atoms and world-pairs, albeit a very simple one. It simply makes world-pair the value atoms. If it is still insisted that this premise is false, I think the burden of proof lies upon its opponent to come up with a plausible axiological function that bears out the contention. The third premise is a summary of the DBWC analysis of deontic modals. I won’t attempt to defend DBWC in one fell swoop. Instead I will issue a challenge to its detractors: propose a theoretically superior formal framework that defines and analyzes the array of praxeo-abilitive, deontic, and epistemic modals that DBWC does. It is doubtful that any competitor is forthcoming. Worse, it isn’t enough that there is a theoretically superior competitor. It must be the case that unhinged justification is impossible in the competitor theory, otherwise all is for naught. It is worth tersely denying one easy attempt to meet the challenge just issued. Suppose that my opponent adopts the essentials of the DBWC framework, but changes the formal semantics in such a way that only performances that contribute value to the world-pair of evaluation are obligatory or permissible. Such a change would have the implication that a performance is positively deontically appraisable only if it is good. If the proposed revision is adopted, then the fourth premise is false in such a way that a belief is justifiable, roughly, just in case it both occurs in and contributes value to the optimality of the relevant world-moment. 5.4. Schematic Argument for Unhinged Justification 201

As a general strategy, I think the proposed revision to DBWC is unpromising. What happens if the agent ﬁnd themselves in the unfortunate situation of having to pick between only bad options? What happens if, as a matter of course, there is no possible way for the agent to avoid the realization of disvalue? In comparable moral and prudential contexts, a bad option is obligatory for an agent when, roughly, it is the least bad of them all. There is nothing to credit the principle that only morally good things are morally obligatory or morally permissible. Nor is there anything to credit the principle that only prudentially good things are prudentially obligatory or prudentially permissible. Yet both principles are entailments of the proposed revision. My point is that the revised version of DBWC will make systematically mistaken deontic predictions in unfortunate cases where the realization of disvalue is unavoidable. It is on this basis that I reject the proposed revision. Perhaps it might still be insisted that the fourth premise is false. Moore knew the skeptic’s conclusion was wrong, even if he couldn’t tell which of the skeptic’s premises were at fault. So, too, might it be insisted that the fourth premise is false even if it’s hard to tell which of its jointly entailing premises are faulty. Moore had the intuitive appeal of ordinary knowledge to rely upon. No such luck for the imagined opponent. W. D. Ross (1930) proposed the infamous two worlds objection. Maybe the opponent will appeal to it. Some think that it constitutes an excellent objection to teleological theories, and DBWC is a such theory. Ross is a pluralist about the good. His objections to monistic hedonism are as follows:

And if any one is inclined to doubt this and to think that, say, pleasure alone is intrinsically good, it seems to me enough to ask the question whether, of two states of the universe holding equal amounts of pleasure, we should really think no better of one in which the actions and dispositions of all the persons in it were thoroughly virtuous than of one in which they were highly vicious (1930: 134). If we compare two imaginary states of the universe, alike in the total amounts of virtue and vice and of pleasure and pain in the two, but in one of which the virtuous were all happy and the vicious miserable, while in the other the virtuous were miserable and the vicious happy, very few people would hesitate to say that the ﬁrst was a much better state of the universe than the second (1930: 138).

In the ﬁrst case, in comparing two worlds equal in the amount of pleasure contained therein, the world where everyone is virtuous is better than the world in which everyone is vicious. In the second case, in comparing two worlds equal in the amount of pleasure Value-First Epistemology 202

and virtue contained, the world where everyone enjoys pleasures according to its just desert is better than the world where no one enjoys pleasures according to its just desert. This shows that simple monadic hedonism is false and since it is false, and perhaps so too are all forms of value monism, any deontic theory that essentially appeals to simple monistic hedonism is likewise false. Benthamian utilitarianism, for example, entails it is optional for an agent to realize either of the two worlds in either of the two cases. Insofar as intuition agrees with Ross, and my intuitions do, Benthamian utilitarianism will make systematically mistaken moral claims in various virtue- and desert-laden contexts. So, Benthamian utilitarianism is ruled out. The Rossian two worlds objection can be epistemicized. Take any set of epistemic good-making properties P , … , P ¨. Compare two worlds exactly alike in their amount of epistemic value by virtue of the relevant exhibition of properties P , … , P ¨. Even so, the world filled with epistemically responsible for virtuous agents is better than the world filled with epistemically irresponsible or vicious agents. Moreover, the world where beliefs exhibiting properties P , … , P ¨ is enjoyed by agents according to their responsibility or virtue is better than the world in which the beliefs exhibiting properties P , … , P ¨ is accidentally enjoyed by agents who are epistemically irresponsible or vicious. Insofar as intuition agrees with Ross, any teleological theory essentially committed to a thusly problematized doxastic axiology is false. How can the epistemicized Rossian two worlds objection ground the denial of the fourth premise? To wit, by claiming that DBWC is committed to an axiology susceptible to the Rossian objection. But that is clearly false. DBWC is a pure deontic theory utterly silent on issues of substantive axiology. Personally, I fundamentally agree with the Rossian objection and think that a plausible axiology must adjust its notion of the good in concordance with considerations of desert or fit or the like. A normatively complete theory would pair DBWC with an adequate desert- or fit-adjusted axiology. I do not claim that DBWC alone is normatively complete. The only way, then, in which the Rossian two worlds objection could threaten DBWC is if it was thought that the objection showed that an adequate axiology is impossible. Apart from being a bad interpretation of the objection, this maneuver is tantamount to denying the first premise, which is, again, absurd.

5.4.2 Objections to the Fifth Premise

Some might wish to deny the fifth premise. If the fifth premise is false, it is impossible for a belief to occur in an abilitively accessible contextually salient epistemically optimific world-pairs without exhibiting epistemically good-making properties P , … , P ¨. As far as I can tell, there are two main strategies for approaching the denial of the premise. 5.4. Schematic Argument for Unhinged Justification 203

Both nonskeptical and skeptical strategies aim to show that justified belief requires the exhibition of the good-making properties, but the former grants that there are in fact justified beliefs and the latter insists that agents must in fact suspend judgment on all matters. Presently, I focus solely upon the former strategy. I’ll pick up discussion on the latter strategy in the next section. As far as the nonskeptical argument strategy is concerned, I think the denial of the fifth premise is demonstrably mistaken. If the premise is false, then a performance is obligatory or permissible only if it is good. By implication, it is impossible for neutral doxastic attitudes to be justifiable and it is impossible for bad doxastic attitudes to be justifiable. I have already argued against this implication on the grounds that, in general, deontic modals don’t require goodness. But additional problems lurk. It is obvious that the suspension of judgment is sometimes justifiable for agents with respect to certain matters. But does the suspension of judgment always realize epistemic value? A survey of the prima facie plausible doxastic axiologies on offer definitively answers in the negative. Just run through the candidates: coherentism enjoins the suspension of judgment when neither belief nor disbelief coheres with the agent’s belief set; conservatism when either belief or disbelief would cause the loss of too many other beliefs; evidentialism when neither belief nor disbelief fits the evidence; foundationalism when the neither belief nor disbelief would either be basic or inferentially related to basic beliefs; knowledge primitivism when neither belief or disbelief would instantiate knowledge; reliabilism when neither belief or disbelief would be reliable; and so on and on. Generalizing, doxastic axiology enjoins the suspension of judgment not as a means of realizing epistemic value, but rather as a means of avoiding disvalue. Consequently, on any nonskeptical doxastic axiology on offer, the suspension of judgment is sometimes justifiable for agents on certain occasions but typically fails to exhibit any epistemically good-making properties P , … , P ¨. Justifiable withholding is possible precisely because the fifth premise is true. By implication, the denial of the fifth premise means denying all the doxastic axiologies on offer. While I think this suffices as a defense of the premise, more should be said in its favor. In particular, I want to defend the possibility of epistemically justified beliefs that realize epistemic disvalue. Begin by considering a simple summative valuation function. It makes the value of a world-pair the sum of its value atoms. The optimific world-pairs will therefore be those that have the largest belief sets with the best overall balance of beliefs exhibiting epistemically good-making properties P , … , P ¨. The same goes for other valuation functions. It is a simple arithmetic fact that the disvalue realized by a single belief failing to exhibit properties P , … , P ¨ is washed out by acquiring some sufficient number of new beliefs with properties P , … , P ¨. Value-First Epistemology 204

It isn’t merely possible that epistemic value can be washed out or swamped by other instances of intratheoretic value. Good epistemic practices depends upon this fact. It is exemplified by the common scientific practice of employing empirical models known to be false for the experimental purposes. So, too, is the universal practice of deciding between epistemically imperfect theories an exemplar. These practices, and others like them, fall under the general heading of reflective equilibrium. Given the epistemological legitimacy of methodological reflective equilibrium, it is possible for beliefs failing to exhibit epistemically good-making properties P , … , P ¨ to occur in optimific belief sets. If it were impossible, then it wouldn’t ever be appropriate to adopt or employ epistemically imperfect theories. The fact that a theory or view is epistemically imperfect means that some elements of the theory realize epistemic disvalue, which is to say that not all of its components exhibit good-making properties P , … , P ¨. Reflective equilibrium would always be epistemologically improper. So, again, denying the fifth premise means holding that it is impossible for a world- pairs to be epistemically optimific unless every belief in the belief set exhibits epistemically good-making properties P , … , P ¨. This is logically equivalent to the claim that it must be impossible for realized epistemic value to be washed out or swamped. Slightly rephrased, the occurrence of a nonvaluable belief must guarantee that there are other contextually salient competing world-pairs both abilitively accessible to the agent and strictly epistemically better for the agent such that every belief had by the agent exhibits epistemically good-making properties P , … , P ¨. As such, the denial of the fifth premise must be sub- stantiated by a plausible doxastic axiology. The axiology must entail that an agent always, from every possible world-pairs, has abilitive access to some special moment/history pair at which all and every belief in the special moment exhibits epistemically good-making properties P , … , P ¨ and, furthermore, that the special moment/history pair is strictly better than all other salient accessible world-pairs where there is even a single belief lacking properties P , … , P ¨. In a word, it must rule out the possibility that there are ever expectable gains for taking on epistemic disvalue. As far as I can tell, all prima facie plausible doxastic axiologies allow for the possibility that there are expectable gains for taking on epistemic disvalue. Just run through the list of candidates again: coherentism enjoins agents to take on epistemic disvalue if, by doing so, it nets a larger, more coherent belief set than otherwise possible; conservatism if it nets a larger belief set than otherwise possible; evidentialism if it nets a larger belief set where more beliefs are better apportioned to the evidence than otherwise possible; foundationalism if it nets a larger belief set where more beliefs are either basic or better inferentially related to basic beliefs than otherwise possible; reliabilism if it nets a larger 5.4. Schematic Argument for Unhinged Justification 205

belief set where more beliefs are reliably formed than otherwise possible; veritism if it nets a larger belief set where more beliefs attain truth and avoid falsehood than otherwise possible; and so on. Generalizing, doxastic axiology enjoins enjoins agents to take on epistemic disvalue if, by doing so, the realized disvalue is relevantly outweighed by all the epistemic value its inclusion enables. So, once again, the denial of the fifth premise means denying all the prima facie doxastic axiologies on offer. Summarizing, the nonskeptical strategy aimed at denying the fifth premise fails. Firstly, it isn’t supported by any of the prima facie plausible doxastic axiologies on offer. All weigh in favor of the premise. Secondly, and perhaps more importantly, denying the fifth premise has skeptical consequences. We would be required to give up on legitimate epistemic practices and, by extension, all the beliefs dependent upon those practices. Reflective equilibrium—and anything relevantly like it—would be condemned as methodologically inappropriate for the achievement of epistemic aims. The centrality of such methods suggests sweeping skepticism.

5.4.3 Brute Objections to the Conclusion

All the premises for the argument for unhinged justification are both defensible and plausible. They jointly entail that unhinged justification is possible. This is, again, tantamount to the claim that something can be right without also being good. To deny the possibility of unhinged justification is to deny the conclusion of my argument. But denying the conclusion entails that something is right only if it is good. There is nothing to credit such a principle. Moral rightness does not imply moral goodness. Sometimes agents are obliged to perform bad acts when it is the only way to avoid far greater evils. Prudential rightness does not imply prudential goodness. Sometimes agents are obliged undesirable acts when it is the only way to avoid far greater disutility. So, to the extent that epistemology is comparable to ethics and rational choice, the same can be expected for epistemic justification. After all, the argument for unhinged justification generalizes and its possibility isn’t at all surprising for ethics or rational choice. Why should it be so surprising for epistemology? If it is still insisted that unhinged justification is impossible in epistemology, the burden of proof firmly rests upon the objector. What makes epistemological prescriptivity so special that epistemic justification requires epistemic goodness when it is so clearly false for literally every other normative domain? The question is especially pressing once it is remembered that DBWC demolishes many of the usually cited differences between ethics and epistemology. I have already shown that differences in control requirements for moral justification and epistemic justification doesn’t problematize the comparison. Nor is there Value-First Epistemology 206

a principled difference in the types of possible obligations, positive or negative, between ethics and epistemology. Nor does it have anything to do with issues involving deontic conflicts because DBWC entails that they are universally impossible. So, why think that epistemic justification requires epistemic goodness? I think the answer to the question is obvious: it doesn’t. But that is because justificationally unhinged performances are possible full stop. And so all traditional theories of epistemic justification are false: coherentism, foundationalism, and infinitism are false; counterfactual theories of justification are false; internalism is false; empiricism is false; evidentialism and reliabilism are false; responsibilism and virtue epistemology are false; and so on. Whatever the theory of epistemic good-making properties (except, perhaps, naïve doxastic conservatism), it is possible for a belief to lack the property but nevertheless be epistemically justified. Though the spirit of epistemological tradition is retained by understanding it in terms of doxastic axiology, the letter of tradition (qua theory of justified believings) is something best forgotten. Justificationally unhinged beliefs are justifiably beliefs that do not realize epistemic value. DBWC alone cannot predict which beliefs are justificationally unhinged because it does not assume a theory of value. Having said that, it isn’t difficult to image the possibilities. Just run through the list of doxastic axiologies on offer: for coherentism, justificationally unhinged belief is any justifiable belief that does not cohere; for evidentialism, any justifiable belief that does not fit the evidence; for foundationalism, any justifiable belief that both is not basic and is not inferentially related to any basic beliefs; for knowledge primitivism, any justifiable belief that is not knowledge; for reasons primitivism, any justifiable belief not backed by sufficient reason; for veritism, any justifiable belief that is not true; and so forth. Admittedly, some renditions of justificationally unhinged belief are quite jarring. I will try to make them seem more palatable.

5.4.4 A Corollary for Epistemic Norms

The possibility of unhinged epistemic justification entails that epistemic justification is a thing unto its own kind. Strictly speaking, epistemic justification is discernible from evidential support, epistemic probabilification, knowledge, reasonableness, reliable causal history, truth, virtuousness, and everything else for the matter. An action, assertion, belief, or deliberation is epistemically justifiable even if it lacks any conceivable plausible epistemically good-making property. In the previous chapter, I demonstrated that the DBWC theory of deontic justification entails that justification is the meta-norm of performance. A fortiori, epistemic justification is the epistemic meta-norm of performance. So, whatever is discernible from epistemic 5.5. Speculative DBWC Refutation of Skepticism 207

justification cannot be the epistemic norm of anything. It immediately follows that all competing epistemic norms are false. Knowledge isn’t the epistemic norm of anything. Reasonableness isn’t the epistemic norm of anything. Truth isn’t the epistemic norm of anything. Neither is anything else apart from epistemic justification. Competing norm defenders cannot find reprieve for their favorite norms by arguing that epistemic justification is identical to their favorite condition. The possibility of unhinged justification eliminates that reprieve.

5.5 Speculative DBWC Refutation of Skepticism

In this section, I put the possibility of justiﬁcationally unhinged belief to work with the aim of refuting skepticism. In particular, I address both of the following skeptical theses:

∙ Justificational Skepticism: No one has any epistemically justiﬁable beliefs. ∙ Knowledge Skepticism: No one has any knowledge.

Justificational Skepticism entails Knowledge Skepticism. Importantly, there are two main ways in which the former is satisfiable. On the one hand, it might be the case that only the suspension of judgment is justifiable for agents. If it is, then neither belief nor disbelief is justifiable for the relevant agents because they are unjustifiable. On the other hand, it might be the case that all doxastic attitudes are nondeontic. If it is, then no doxastic attitude has any justificatory status of any kind for the relevant agents. The latter possibility is realized when agents are situated in environments that violate the ability requirements for epistemic justification. For example, if brains-in-vats are directly fed their doxastic states in such a way that it in principle robs them of any cognitive ability to be responsive to counterinformation, then all their doxastic states are nondeontic; neither belief, nor disbelief, nor suspending judgment is justifiable or unjustifiable for such brains-in-vats. I fully concede that skepticism is unavoidably true in certain epistemologically hellish environments. By the same token, though, skepticism is unavoidably false in certain epistemologically heavenly environments. My point is the philosophical arguments for or against skepticism shouldn’t essentially appeal to the agent’s epistemic environment. It takes very little imagination to contrive logically possible worlds where skepticism is trivially true or trivially false. Skepticism is trivially true in worlds where epistemic agents don’t exist ex hypothesi. Skepticism is trivially false in worlds where all epistemic agents are omniscient ex hypothesi. I intend to ignore tactics that essentially appeal to the epistemological environment because they are philosophically frivolous. Value-First Epistemology 208

5.5.1 Sketching the Strategy

DBWC vindicates justificationally unhinged performances. It might be thought that this is too big a bullet to bite and opt to simply deny DBWC. But before panic sets in, I want to beg the reader’s indulgence. If there are justificationally unhinged performances, what are they and why? I suspect that making room for them affords theory the ability to accommodate otherwise recalcitrant philosophical conundrums. As is, DBWC is a formal theory too abstract to identify what things will in fact be justificationally unhinged. To be clear, then, I aim to engage in considered speculatation rather than provide rigorous proofs. But careful speculation can be fruitful. Justificationally unhinged performance are all and only those performances that occur in the relevant number of best abilitively accessible world-moment/world-history pairs lacking the relevant good-making properties. A performance is justificationally unhinged from an epistemic point of view just in case it is epistemically justifiable but doesn’t have anything good going for it, so to speak. In point of fact, it might have plenty bad going against it. It just has to be the case that its realized disvalue is washed out or swamped in the overall evaluation of the performative whole to which it is a member. Think of a belief set as a world-view. It is filled with a huge number of beliefs, each varyingly supported by the agent’s relevant total information. On any common sense conception of human cognitive life, a large number of the beliefs in a normal belief set realize value even though plenty realize disvalue. Just run through the doxastic axiologies: our normal beliefs tend to accord well enough with our evidence, tend to be reliably formed, tend to be true enough, et cetera. Obviously not all ordinary beliefs and not all the time. But lots and often enough. So while ordinary beliefs about the people, places, and things that we take an active interest in tend to do fairly well in realizing epistemic value, many theoretical commitments don’t provided that most people don’t give them serious thought and because it is very difficult to get sufficiently good information on their behalf. And yet the best world-views will nevertheless feature these theoretical commitments because whatever disvalue they realize is washed out—perhaps even by all the good beliefs that they enable or are otherwise parasitic upon. What kinds of theoretical commitments do I have in mind? All the classic targets of skeptical attack: that there is an an external world; or, that there are other minds; or, that there is a remote past; and so on. My suggestion is that such theoretical commitments are features, implicitly or explicitly, of a typical belief set, for nearly all possible belief sets that most people have the genuine ability to acquire at any given moment. If so, then such theoretical commitments will expectably occur in most agents’ epistemically optimific 5.5. Speculative DBWC Refutation of Skepticism 209

belief sets. Perhaps not everyone and certainly not all the time. But for most of us, and for most of the time, these commitments will typically be epistemically justiﬁably regardless of whether they have anything going for them from an epistemic point of view. In a word, I speculate that exactly those beliefs that skeptics argue lack any epistemic good-making properties belong to the class of justiﬁcationally unhinged beliefs.

5.5.2 A Defense of Epistemically Justiﬁed Belief

In this subsection, I refute Justificational Skepticism. Many argument forms have been attributed to the skeptic, but the closure-based template is among the most enduring, at least in recent literature.21 Following the usual presentation, let o denote any arbitrary ordinary proposition and let h denote the corresponding skeptical hypothesis. The basic argument schema has the following form:

Table 5.5: Schematic Closure-Based Argument for Justiﬁcational Skepticism

01 If has a justiﬁable belief that o, then has a justiﬁable belief that ¬h.

02 does not have a justiﬁable belief that ¬h.

∴ does not have a justiﬁable belief that o.

The argument is obviously valid. The conclusion denies ordinary justification. The first premise is a simplified instantiation of a justification closure principle. The second premise denies that the agent justifiably believes that the relevant hypothesis doesn’t obtain. Consider an illustration. If an agent justifiably believes that here’s a hand, then, assuming the agent has the relevant logical acument, the agent justifiably believes that I’m not a handless brain-in-a-vat. But the agent doesn’t justifiably believe that I’m not a handless brain-in-a-vat. How could they? So, it seems, the agent doesn’t have justification for the ordinary belief that they thought they did. Keith DeRose (1999) names the incredulity that skeptical hypotheses often garner the “Aw, come on!” reaction. Perhaps such a reaction is warranted. Luckily, whether it is warranted is irrelevant. John Hawthorne (2004) famously observes that the closure-based skeptical argument schema is that it is satisfied by the lottery puzzle. The skeptical hypothesis may be substituted out for a lottery proposition to achieve the very same result.

21 Compare with the presentations of skepticism as seen in, among others, Robert Nozick (1981), Keith DeRose (1995, 1999), Ernest Sosa (1999), Jonathan Vogel (1999), and Duncan Pritchard (2005). Value-First Epistemology 210

The upshot is that the force of the skeptical argument isn’t essentially dependent upon far-fetched error possibilities. Mundane error possibilities suﬃce to motivate skepticism. Previously, when discussing the lottery problem, I noted four available responses: Moorean dogmatism, skepticism, closure denialism, and shifty epistemology. The same is true here. Skepticism endorses the argument. If skepticism is to be avoided, which option should be picked and why? Closure denialism rejects the ﬁrst premise. I take it that the problems associated with denying closure are many, prominent, and decisive. Moorean dogmatism rejects the second premise. I think this option too dogmatic. Robert Nozick (1981) does too:

The skeptic asserts that we do not know his possibilities don’t obtain, and he is right. Attempts to avoid skepticism by claiming we do know these things are bound to fail. The skeptic’s possibilities make us uneasy because, as we deeply realize, we do not know they don’t obtain; it is not surprising that attempts to show we do not know these things leave us suspicious, strike us even as bad faith (1981: 201).

I, like Nozick, ultimately agree with the skeptic that many of our theoretical beliefs lack the good-making epistemic properties that our ordinary justifiable beliefs seemingly possess. When the skeptic says that we merely took them for granted, the skeptic is exactly right. We genuinely did take them for granted. So when Moorean dogmatism says that we didn’t really take them for granted, that our antiskeptical theoretical beliefs really had all the relevant good-making properties all along, I am suspicious. Happily, my suspicion is vindicated by shifty epistemology. But I don’t want to lean on that option just yet. Rather I want to explore the unique contribution that DBWC has to offer. Looking at the framework, it validates closure principles, but it also seems that, on the one hand, our ordinary and antiskeptical commitments are justifiable but, on the other hand, the skeptic is nevertheless correct that we can’t produce good reasons for our antiskeptical commitments. But how can the framework say this? Allow me to explain. What is the skeptic’s motivation for the second premise? Why think that agents cannot justifiably deny that skeptical hypotheses obtain? The skeptic appeals to salient error possibilities that are not ruled out by the agent’s epistemic grounds. Presumably, beliefs exhibit epistemically good-making properties P , … , P ¨ for an agent in virtue of standing in the right relation to the agent’s epistemic grounds. The skeptic points out that it is consistent with our ordinary epistemic grounds that the relevant skeptical hypotheses and lottery propositions obtain. It isn’t merely that our antiskeptical commitments are 5.5. Speculative DBWC Refutation of Skepticism 211

underdetermined by our ordinary epistemic grounds. It’s that our ordinary epistemic grounds in no way favors the antiskeptical commitments over the salient error possibilities. As such, our antiskeptical commitments cannot be said to realize epistemic value or exhibit epistemically good-making properties P , … , P ¨ because they do not stand in the appropriate relation to our ordinary epistemic grounds. To borrow a turn of phrase from Fred Dretske (1970), the epistemic value realized by ordinary belief does not fully penetrate to the entailed antiskeptical commitments. The reason, then, that the denial of skeptical hypotheses and lottery propositions is unjustiﬁable is that all such beliefs fail to realize epistemic value. The skeptic relies upon the following principle:

∙ Justification Requires Goodness (JRG): It is v-value-wise justiﬁable for agent to that only if ’s that realizes v-value-wise.

JRG states that justifiable performances requires that the performance realizes deontic value. A fortiori, a belief is justifiable for an agent only if the agent’s believing realizes epistemic value. In actuality, it seems that the skeptic endorses something stronger. The skeptic shouldn’t deny that our ordinary beliefs realize any epistemic value. The rationale for this claim is evident; just run through the doxastic axiologies on offer. Rather the skeptic should insist that our ordinary beliefs are unjustifiable because they in principle cannot realize the sufficient quantity of epistemic good. In a word, the skeptic seems beholden to the principle that belief is justifiable only if it is sufficiently good; or, it realizes a certain amount of epistemic value above some relevant threshold. Such a principle permits the skeptic to concede that we indeed have some ordinary grounds in virtue of which our ordinary beliefs realize an appreciable quantity of epistemic value, but ultimately deny that the goodness thusly realized suffices to make ordinary belief epistemically justifiable. The DBWC rebuttal is clear, regardless of the version of JRG employed. Justificationally unhinged belief is possible; or, equivalently, the epistemic justifiably of belief does not require of the belief that it realizes any epistemic value; or, simply, JRG is false. As I see it, the skeptic demonstrates that some of the most important beliefs that we have lack any epistemically good-making features. I agree. However, it cannot be validly inferred from this basis that our most important beliefs are unjustifiable. The skeptic requires this inference, but I object because justificationally unhinged beliefs are possible. My speculative DBWC refutation of skepticism is thusly rendered: Value-First Epistemology 212

Table 5.6: The DBWC Refutation of Justiﬁcational Skepticism

01 If justiﬁcationally unhinged belief is possible, then Justificational Skepticism is false.

02 Justiﬁcationally unhinged belief is possible.

∴ Justiﬁcational skepticism is false.

The argument is obviously valid. The first premise is true because skepticism requires that the absence of good-making epistemic properties entails that the belief is unjustifiable. The entire strategy of every skeptical argument is to somehow frustrate or undermine the instantiation of these good-making properties. The skeptic takes this as conclusive proof that the relevant beliefs are unjustifiable. In fact, the premise is trivially true because justificationally unhinged beliefs are justifiable, which is precisely what the skeptic denies. The second premise therefore does all the heavy lifting for my argument. The skeptic denies the possibility of justifiable belief full stop, and so, a fortiori, denies the possibility of justificationally unhinged belief. Consequently, the skeptic is obliged to deny at least one of the premises in my argument for unhinged justification. In particular, the skeptic must deny whatever premises are inconsistent with JRG. To wit, the skeptic must deny the third and fourth premises. Since the fourth premise is entailed by the first three premises, the skeptic must focus attention on the third premise. Allow me to briefly buttress the premise against skeptical attack. The third premise is a summary of the DBWC analysis of deontic modals. Accordingly, and applied to deontic justification, a doxastic attitude is justifiable only if it occurs the abilitively accessibly contextually salient epistemically optimific world-pairs. In order to easily meet the theoretical challenge issued in defense of the framework—and, hence, the premise—the skeptic will presumably appeal to the tweaked version of DBWC where the belief must realize epistemic value in order to be an apt target of deontic appraisal. This tweaked version of DBWC entails JRG. I have already argued against the proposed revision. Two independent considerations militate against it. The first is that the revised analysis is systematically mistaken about the extensions of ‘obligation’ and ‘permission’. It is false that morally, prudentially, et cetera, obligatory or permissible performances are ipso facto good in the relevant sense. I won’t belabor the point. The second is that none of the prima facie plausible doxastic axiologies on offer vindicate JRG. Each is consistent with the possibility that justifiable performances are epistemically neutral and each is consistent with the possibility that 5.5. Speculative DBWC Refutation of Skepticism 213

justifiable performances are epistemically bad. The former is especially important because it rules out the first method of satisfying Justificational Skepticism. More explicitly, the suspension of judgment is justifiable, when it is, as a means of avoiding the realization of disvalue, not as a means of realizing epistemic value. On any of these doxastic axiologies, suspending judgment realizes zero epistemic value. If it turns out that only the suspension of judgment is justifiable for every given proposition for an agent, then the corresponding world-pairs has exactly zero total epistemic value and all other abilitively possible world- pairs have total epistemic value less than zero. This happens precisely when the agent is situated in an epistemologically hellish environment, which is, as I said from the onset, disqualified as a legitimate philosophical argument for skepticism. Even so, the point stands that justifiable doxastic attitudes needn’t realize epistemic value.

Perhaps the skeptic will propose a skeptical axiology such that all and only suspension of judgment realizes epistemic value; all else realizes epistemic disvalue. Pairing DBWC with the skeptical axiology obviates both problems noted above. What are the prospects for this maneuver? I think there are two insuperable diﬃculties for this strategy.

The first new problem is that the skeptic loses the plausible error theory previously at their disposal. Why is it at all tempting to think, as we in fact do, that our ordinary beliefs are justifiable? By remaining neutral on doxastic axiology, the skeptic could plausibly say that our ordinary beliefs in fact realized epistemic value but not enough to count as epistemically justifiable. But with the skeptical axiology, what is there to help explain our natural antiskeptical inclinations? No error theory is corroborated by the skeptical axiology. Rather it suggests that we shouldn’t be tempted by the thought that our ordinary beliefs are justifiable, which doesn’t square with the facts.

The second new problem is damning. Simply put, skeptical axiology doesn’t rule out the possibility that there are justifiable beliefs. Skeptical axiology enjoins agents to take on new beliefs if, by doing so, the agent is able to suspend judgment on more things than otherwise possible. So, in comparing all the abilitively possible belief sets, if there is one much better than all others in virtue of the agent’s intelligently suspending judgment on a whole slew of matters, but only because the agent takes on certain background beliefs that psychologically enables the agent to entertain the sorts of questions that are absent in other abilitively possible belief sets, then, on the skeptical axiology, there are some justifiable beliefs. To reiterate, then, the possibility of unhinged justification entails the falsity of skepticism on any axiology, even skeptical axiology.

DBWC offers a novel refutation of Justificational Skepticism. Justification in general is possible because unhinged justification in particular is possible. Value-First Epistemology 214

5.5.3 Extending the Defense to Knowledge

In this subsection, I refute Knowledge Skepticism. In doing so, I aim to make the relation between DBWC and shifty epistemology perspicuous. As before, begin with the closure-based argument template. Let o denote, again, any arbitrary ordinary proposition and let h denote, again, the corresponding skeptical hypothesis. The basic argument schema has the following form:

Table 5.7: Schematic Closure-Based Argument for Knowledge Skepticism

01 If knows that o, then knows that ¬h.

02 does not know that ¬h.

∴ does not know that o.

The argument is replaces instances of justification for knowledge. The first premise is a simplified instantiation of a knowledge closure principle. The second premise denies that the agent knows that the relevant hypothesis doesn’t obtain. The conclusion that denying ordinary knowledge obviously follows. The lottery puzzle satisfies this argument schema too, so skeptical hypotheses may be substituted out for lottery propositions. Mundane error possibilities still suffice to motivate skepticism. There are, once more, four available responses: Moorean dogmatism, skepticism, closure denialism, and shifty epistemology. The prospects of the nonskeptical options are the same as before. More explicitly, closure denialism and Moorean dogmatism are nonstarters and for the same sorts of reasons. The option is between shifty epistemology and skepticism. It is worth taking stock of the dialectical situation. As I see it, knowledge is modalized justified true belief; or, belief whose justification tracks truth across the epistemically optimific world-moment/world-history pairs. If Knowledge Skepticism is true, it is because one of the conditions for knowledge is unsatisfiable. It can’t be the belief or truth conditions. We certainly have many beliefs and certainly some of them are true. Nor can it be that the justification condition is unsatisfiable. Justification Skepticism is tantamount to the thesis that the justification condition for knowledge is unsatisfiable, but I have already shown that it is false because justificationally unhinged belief is possible. Consequently, the skeptic must argue that no one knows anything because the epistemic connection condition is unsatisfiable. It follows that Knowledge Skepticism is true if, and only if, every possible belief is justificationally unsafe. 5.5. Speculative DBWC Refutation of Skepticism 215

DBWC vindicates shifty epistemology. All epistemic modals are deontic modals and all deontic modals have at least two shifty parameters. On the one hand, all deontic modals are defined over parameterizations of the domain. It is possible for deontic modals to variably quantify over world-pairs. There is, for example, the distinction between simple knowledge and competent knowledge. Knowledge is simple when defined by appeal to the Simple Parameterization; competent otherwise. Intuitively rendered, knowledge is the exemplary manifestation of cognitive powers aimed at adapting mind to world. The adaptation is more or less competent to the extent that the agent’s cognitive powers are successful over a larger, more diverse arrangement of possible world-pairs. In this sense, knowledge can be rated along a spectrum, where simple knowledge is the pole of least competent cognitive success. Competent knowledge is any degree of cognitive success more competent than simple knowledge, where some instances of competent knowledge may be more or less competent than others. On the other hand, all deontic modals are defined by deontic value orderings over the domain. All deontic value orders are indexed to agents and moment/history pairs. In principle, it is possible for orderings to differ between agents and pairs. Resultingly, differences in e.g. practical stakes can affect how a fixed set of world-pairs is deontically ordered for agents (depending on the specification of the deontic axiology). Summarily, DBWC is a shifty theory because the relevant set of world-pairs and the orderings over those world-pairs can shift agent to agent, world-pair to world-pair. DBWC shiftiness is the undoing of skepticism. Begin with the easy case. I have already shown that simple knowledge trivially satisfies the epistemic connection condition. Consequently, simple knowledge is justified true belief. So, if justifiable belief is possible, simple knowledge is possible. It immediately follows that Knowledge Skepticism is false because justificationally unhinged belief is possible. Relatedly, there is no lottery puzzle for simple knowledge. DBWC entails that agents can easily have simple knowledge of lottery propositions. Strictly speaking, the possibility of simple knowledge falsifies Knowledge Skepticism. I need say nothing more about the topic. Nonetheless I think it worth briefly turning attention to competent knowledge, in part because it is vexing. Roughly, ceteris paribus, the possibility of competent knowledge is inversely proportional to the salience of the possibility of error. Salient error possibilities are represented as contextually salient world-pairs where the relevant belief is false. If the possibility of error is salient, the agent lacks competent knowledge because the belief is justificationally unsafe; if not salient, the agent has competent knowledge; if salience is vague, then so too will be the attribution of competent knowledge. The point is that competent knowledge of ordinary Value-First Epistemology 216

propositions, antiskeptical commitments, and lottery propositions all vary together over the relevant parameterizations of the domain. When an agent competently knows ordinary propositions, then, assuming the appropriate logical acumen, the agent also competently knows lottery propositions and the falsity of skeptical hypotheses. When an agent doesn’t competently know lottery propositions or the falsity of skeptical hypotheses, then, assuming the appropriate logical acumen, the agent also doesn’t competently know ordinary propositions. A number of additional factors complicate the attribution of competent knowledge. How are the possible world-pairs deontically ordered? Perhaps world-pairs where error possibilities are realized rank so poorly as to be idle. Just how excellent are the agent’s cognitive faculties? Perhaps the agent is so competent that error possibilities pose no trouble at all. Overall, the better the epistemic grounds, the more able the agent, the more competently does the agent know. In any case, there is no substantive reason why the epistemic connection is unsatisfiable for competent knowledge. In order to secure the skeptical conclusion, it must be the case that the agent is an epistemologically hellish environment where error possibilities are always robustly salient in such a way that they are realized in all the relevantly accessible epistemically optimific world-pairs. But, again, that is precluded as legitimate argument for skepticism. DBWC offers a novel refutation of Knowledge Skepticism. Simple knowledge is possible because unhinged justification is possible. Competent knowledge is possible because simple knowledge is possible and there is no principled reason to suppose that error possibilities are always robustly salient. Just because competence-robbing error possibilies can be made salient does mean that they are in fact salient. This is confuse possibility with actuality.

5.6 Conclusion

I have elucidated and defended DBWC value-first epistemology. I have shown that it is not easily problematized by the literature’s standard objections to either teleological deontism or counterfactual theories of knowledge. I have also argued for the possibility of justificationally unhinged belief. It is an instantiation of the class of performances that are right but not good. The possibility of justificationally unhinged belief was brought to bear against both traditional theories of epistemic justification and skepticism. All are false because they mistakenly assume that justificationally unhinged belief is impossible. BIBLIOGRAPHY

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236 Part IV

Appendices APPENDIX A

ELEMENTARY MATHEMATICAL CONCEPTS

Abstract

This appendix serves as a glossary for deﬁnitions of some introductory mathematical concepts. It is intended as a quick reference guide and refreshment tool for nonmathematicians.

This appendix is intended as a primer for nonmathematicians, nothing more. Interested readers should consult other resources for further information. Paul Halmos (1960), Brian Chellas (1980), and Karel Hrbacek and Thomas Jech (1999) all oﬀer nice glimpses into the formalism. To be clear, I am in no way the author of the ideas presented below.

A.1 A Sprinkle of Elementary Set Theory

In this section, I cover some basic set theory concepts.

Definition A.1.1. A set is any collection of objects.

Sets are denoted by enclosed braces {…}. The notation m ∈ S means that m is a member of set S. A set without members is the empty set, denoted {}, ç, or {ç}. In what follows, I use {ç} to denote the empty set. Importantly, a set is not strictly deﬁned by the order or the plurality of its members. This means that {1, 2} = {2, 2, 1} = {1, 2, 1, 2, 1, 2, 1, 2, 2, 1}. There are elegant ways of describing sets. If, for example, S is the set of prime numbers, then S = {m ∣ m is prime} = {2, 3, 5, 7, 11, 13, …}. More generally, the notation S = {m ∣ m has property p} is understood to mean that the members of set S are such that they have property p. The ∣ symbol can

238 A.1. A Sprinkle of Elementary Set Theory 239

be read as “such that” or “so that”. The ∶ symbol can replace the ∣ symbol and is read the same way.

Definition A.1.2. The intersection of two sets, X ∩ Y , is the set containing all objects that belong to both sets X and Y . Formally, X ∩ Y = {m ∣ m ∈ X or m ∈ Y }.

Definition A.1.3. The union of two sets, X ∪ Y , is the set containing all objects that belong to either sets X or Y . Formally, X ∪ Y = {m ∣ m ∈ X and m ∈ Y }.

Definition A.1.4. The diﬀerence of two sets, X ⧵ Y or X − Y , is the set containing all objects that belong to set X but don’t belong to set Y . Formally, X ⧵ Y = X − Y = {m ∣ m ∈ X and m ∉ Y }.

Definition A.1.5. A subset of a set, X ⊆ Y , is a set X containing all the members of a set Y or fewer.

Definition A.1.6. A proper subset of a set, X ⊊ Y , is a subset X containing fewer members of the set Y than Y .

Definition A.1.7. A superset of a set, Y ⊇ X, is a set Y containing all the members of a set X or more.

Definition A.1.8. A proper superset of a set, Y ⊋ X, is a superset Y containing more members than the set X.

Definition A.1.9. A powerset of a set, P (X) or 2X, is the set of all the set X’s subsets (including the empty set and X itself).

Definition A.1.10. A complement of a set, XC , is the set of all objects that don’t belong to the set X. Formally, XC = {m ∣ m ∉ X}.

Definition A.1.11. A Cartesian product of two sets, X × Y , is the set of all ordered pairs, (x, y), such that x ∈ X and y ∈ Y . Formally, X × Y = {(x, y) ∣ x ∈ X and y ∈ Y }.

It’s worth illustrating these concepts with a straightforward example. Let X = {1, 2} and Y = {2, 3} and Z = {1}. If so, then:

∙ Intersections: X ∩ Y = {2} and X ∩ Z = {1} and Y ∩ Z = {ç}.

∙ Unions: X ∪ Y = {1, 2, 3} and X ∪ Z = {1, 2} and Y ∪ Z = {1, 2, 3}.

∙ Diﬀerences: X ⧵ Y = {1} and X ⧵ Z = {2} and Y ⧵ X = {3} and Y ⧵ X = {2, 3} and Z ⧵ X = {ç} and Z ⧵ Y = {1}. Elementary Mathematical Concepts 240

∙ Subsets: Z ⊊ X but Z ⊈ Y .

∙ Supersets: X ⊋ Z but Y ⊉ Z.

∙ Powersets: P (X) = 2X = {{ç}, {1}, {2}, {1, 2}} and P (Y ) = 2Y = {{ç}, {2}, {3}, {2, 3}} and P (Z) = 2Z = {{ç}, {1}}.

∙ Complements (where 1, 2, 3 are all objects): XC = {3} and Y C = {1} and ZC = {2, 3}.

∙ Cartesian Products: X × Y = {(1, 2), (1, 3), (2, 2), (2, 3)} and X × Z = {(1, 1), (2, 1)} and Y × X = {(2, 1), (2, 2), (3, 1), (3, 2)} and Y × Z = {(2, 1), (3, 1)} and Z × X = {(1, 1), (1, 2)} and Z × Y = {(1, 2), (1, 3)}.

Because it is important for the discussion of neighborhood structures, it is worth noting that powerset operations can be iterated. Whereas the powerset of a set, X, contains 2X number of elements, the powerset of a powerset of X contains 22X number of elements. To illustrate, let X = {1, 2} as before. If so, then P (X) = 2X = {{ç}, {1}, {2}, {1, 2}} and P (P (X)) = 22X is as follows:

X P (P (X)) = 22 = {{ç}, {{ç}}, {{1}}, {{2}}, {{1, 2}}, {{ç}, {1}}, {{ç}, {2}}, {{ç}, {1, 2}}, {{1}, {2}}, {{1}, {1, 2}}, {{2}, {1, 2}}, {{ç}, {1}, {2}}, {{ç}, {1}, {1, 2}}, {{ç}, {2}, {1, 2}}, {{1}, {2}, {1, 2}}, {{ç}, {1}, {2}, {1, 2}}, } A.1. A Sprinkle of Elementary Set Theory 241

I wish to turn now to discuss properties of sets, such as closure, especially when paired with special sets of subsets. Roughly, a set, S, is closed under an operation when the application of that operation on elements of S outputs an object that is also a member of S. For a silly example, consider all the books ever written. Some receive film adaptations, some don’t, but having been adapted to film doesn’t disqualify a book from having been written. So, the set of all books ever written is closed under the film adaptation operation. Setting the example aside, let ⟨, ⟩, where  is a nonempty set and  ⊆ P ().

Definition A.1.12. A set, , is consistent when  ≠ {ç} and {ç} ∉ .

Definition A.1.13. A set, , is contains the unit when  ∈ .

Definition A.1.14. A set, , is contains its core when ⋂ X ∈ , where ⋂ X is the  X∈  X∈ core of , deﬁned from the intersection of all the sets that are elements of .

Definition A.1.15. A set, , is closed under intersections when if X∩Y ∈ , then X ∈  and Y ∈ .

Definition A.1.16. A set, , is closed under unions when if X ∈  and Y ∈ , then X ∪ Y ∈ .

Definition A.1.17. A set, , is closed under supersets (or: supplemented, monotonic) when, for all X ⊆ , if X ∈  and X ⊆ Y ⊆ , then Y ⊆ .

Definition A.1.18. A set, , is closed under complements when, for all X ⊆ , if X ∈ , C then X ∈ .

Definition A.1.19. A set, , is a quasiﬁlter when  is closed under intersections and is closed under supersets.

Definition A.1.20. A set, , is a ﬁlter when  is a quasiﬁlter and contains the unit.

Definition A.1.21. A set, , is augmented when  contains its core and is closed under supersets.

Many of the deﬁned notions and properties are interestingly related to one another. A number of these interrelations importantly bear upon modal logics. Interested readers may consult Chella (1980: 214–229) for discussion. Elementary Mathematical Concepts 242

A.2 A Sprinkle of Elementary Order Theory

In this section, I cover some basic order theory concepts. Let D be the nonempty domain of objects, where D = {, ¨, ¨¨, …}. Let < and ⩽ respectively denote some strict and nonstrict ordering relations over D.

Definition A.2.1. The relation, <, is a strict order over a set, D, if, and only if, < is irreﬂexive, transitive, and asymmetrical. The following conditions hold for all , ¨, ¨¨ ∈ D: ∙ Irreﬂexivity: < . ∙ Transitivity: If < ¨ and ¨ < ¨¨, then < ¨¨. ¨ ¨ 1 ∙ Asymmetry: If < , then < .

Definition A.2.2. The relation, ⩽, is a preorder (or: quasiorder) over a set, D, if, and only if, ⩽ is reﬂexive and transitive. The following conditions hold for all , ¨, ¨¨ ∈ D: ∙ Reﬂexivity: ⩽ . ∙ Transitivity: If ⩽ ¨ and ¨ ⩽ ¨¨, then ⩽ ¨¨.

Definition A.2.3. The relation, ⩽, is a partial order over a set, D, if, and only if, ⩽ is an antisymmetrical preorder. The following conditions hold for all , ¨, ¨¨ ∈ D: ∙ Reﬂexivity: ⩽ . ∙ Transitivity: If ⩽ ¨ and ¨ ⩽ ¨¨, then ⩽ ¨¨. ∙ Antisymmetry: If ⩽ ¨ and ¨ ⩽ , then = ¨.

Definition A.2.4. The relation, ⩽, is a nonstrict total order over a set, D, if, and only if, ⩽ is comparable partial order. The following conditions hold for all , ¨, ¨¨ ∈ D: ∙ Reﬂexivity: ⩽ . ∙ Transitivity: If ⩽ ¨ and ¨ ⩽ ¨¨, then ⩽ ¨¨. ∙ Antisymmetry: If ⩽ ¨ and ¨ ⩽ , then = ¨. ∙ Comparability: ⩽ ¨ or ¨ ⩽ .

Definition A.2.5. The relation, <, is a strict total order over a set, D, if, and only if, < is comparable strict order. The following conditions hold for all , ¨, ¨¨ ∈ D: ∙ Irreﬂexivity: < . ∙ Transitivity: If < ¨ and ¨ < ¨¨, then < ¨¨. ¨ ¨ ∙ Asymmetry: If < , then < . ∙ Comparability: < ¨ or ¨ < .

1 The asymmetry condition is is entailed by the irreﬂexivity and transitivity conditions. Though its inclusion is superﬂuous, it is mentioned for sake of completeness. APPENDIX B

MODAL LOGIC CRASH COURSE

Abstract

This appendix provides a terse overview of the basics of modal logic. Its intended role is to act as a quick reference guide and refreshment tool for nonlogicians.

This appendix is intended as a primer for nonlogicians, nothing more. Interested readers should consult Brian Chellas (1980), Graham Priest (2008), Johan van Benthem (2010), and James Garson (2013). The Garson text is superb guide for the mathematically squeamish and the Priest text oﬀers a superbly simple look at nonnormal modal logics, but the Chellas text is a classic for good reason and should not be overlooked.

B.1 The Base Language ℒ

I assume familiarity with propositional logic. Let the language ℒ be some propositional language fragment. The set of all atoms, Atom, is composed of propositional constants, ⊤ (tautology), and ⊥ (contradiction). All other well-formed formulas are deﬁned recursively.

ℒ ∶= Atom | ( → )

The ﬁrst entry says that all atomic formulas are well-formed formulas in the language ℒ. The second entry says that if and are well-formed formula in the language ℒ, then so is ( → ). I want to emphasize that ℒ contains all propositional tautologies as this will become important momentarily.

243 Modal Logic Crash Course 244

In fact, I’ll help myself to all the familiar Booleans, but all those not part of the oﬃcial grammar should be considered abbreviations. This is possible because all Booleans are interdeﬁnable.

Abbreviation Definition ¬ ( → ⊥) ∧ (( → ) → ⊥) ∨ (( → ⊥) → ) ↔ ((( → ) → ( → )) → ⊥)

In typical presentations, every Boolean is paired with an introduction and elimination rule. It can be said that a typical propositional logic is closed under the Boolean introduction and elimination rules, meaning that it contains all the conclusions of all the premises of all the arguments satisfying the forms of the rules. For example, a set of formulas,

ℒ∗, is closed under conditional introduction (or: modus ponens) if, and only if, whenever

( → ) ∈ ℒ∗ and ∈ ℒ∗, then ∈ ℒ∗. In the interest of space, I shall present only a single rule appealing to the notion of tautological consequence.

Definition B.1.1. The formula ∈ ℒ is a tautological consequence of the formula ∈ ℒ if follows from in virtue of the truth-functional connectives; or, if, and only if, every row of their joint truth table that assigns true to also assigns true to .

Oﬃcially, the language ℒ is closed under TC.

Rule Name Rule Schema

TC 1, … , n ⊢ , where is a tautological consequence of 1, … , n

The rule TC is a generalization of all propositional inference rules.1 In English, it can

be interpreted to mean that the conclusion is provable from the premises 1, … , n

(provided, obviously, that is a tautological consequence of 1, … , n). Following Chellas (1980), a standard modal logic is deﬁned as follows:

Definition B.1.2. A standard modal logic is a set, ℒ∗, of well-formed formulas closed under the inference rule TC.

From this deﬁnition it straightforwardly follows that the propositional language ℒ is a

standard modal logic. In fact, the language of all propositional tautologies, ℒ⊤ ⊊ ℒ, is the smallest standard modal logic.

1 See Chellas (1980: 15–16; 45–46) for discussion. B.2. Relational Structures 245

B.2 Relational Structures

Now to introduce some modal operators. Let ℒK be an extension of ℒ augmented with a

single modal operator. (I use the subscripted K for ℒK because relational structures are sometimes called Kripkean structures.)

ℒK ∶= Atom | ( → ) | □

In a word, ℒK extends ℒ by adding □ to the primitive grammar. The □ symbol is the necessitation operator. As such, the formula □ reads “necessarily ” or “ is necessarily true” under an alethic interpretation.

Definition B.2.1. A relational frame, FK , is the ordered tuple

FK = ⟨, ℜ⟩ where each element is deﬁned as follows:

∙  = {w, w¨, w¨¨, …} is the nonempty domain of all possible worlds.

∙ ℜ ⊆  ×  is a binary accessibility relation that relates one moment to another. The notation wℜw¨ expresses that w¨ is accessible from w, which is true if (w, w¨) ∈ ℜ.

A relational structure is a relational frame, which consists of a domain and some number of accessibility relations. A domain is a nonempty set of objects (e.g., moments, nodes, points, states, worlds, et cetera). Accessibility relations are nothing more than one-object-to-one-object relations on the domain. Presently, as I construe everything worlds-theoretically, accessibility relations are mappings from one world to another.

Definition B.2.2. A relational model, MK , is an ordered tuple

MK = ⟨FK , ℑ⟩ where each element is deﬁned as follows:

∙ FK = ⟨, ℜ⟩ is a relational frame. ∙ ℑ ∶  × Atom ↦ {1, 0} is an interpretation function assigning truth-values into worlds

and atom pairs for all atoms, Atom, belonging to the language ℒK .

A relational model is a relational frame plus an interpretation function. Interpretation functions are sometimes called valuation functions. Its job is to assign truth values to all Modal Logic Crash Course 246

atomic formulas of the ℒK at all the worlds in the domain. Because everything is deﬁned

recursively, the interpretation function gets the semantics of ℒK oﬀ the ground. How do we ﬁnd out whether an atomic formula is true at world w (relative to a model)? By asking the interpretation function given by the model.

Operator Definition

MK , w ⊨ (w, ) = 1

In other words, the atomic formula is true at world w in model MK if, and only if,  outputs value 1 when fed the input (w, ). By outputting 1, the interpretation function

decides for us that is true at w in MK . The interpretation function decides that is false

at w in MK by outputting 0. Booleans are truth functional, meaning that they inherit their truth values from their component formulas, so they behave in the usual and unsurprising way.

Operator Definition MK , w ⊨ ¬ (w, ) = 0; or, MK , w⊨ MK , w ⊨ ( ∧ ) MK , w ⊨ and MK , w ⊨ MK , w ⊨ ( ∨ ) MK , w ⊨ or MK , w ⊨ MK , w ⊨ ( → ) MK , w ⊨ ¬ or MK , w ⊨ MK , w ⊨ ( ↔ ) MK , w ⊨ ( → ) and MK , w ⊨ ( → )

In English, the formula ¬ is true at world w in model MK if, and only if,  outputs value

0 when fed the input (w, ); or, isn’t true at w in MK . The formula ( ∧ ) is true at w in

MK if, and only if, is true at w in MK and is true at w in MK . The formula ( ∨ ) is

true at w in MK if, and only if, is true at w in MK or is true at w in MK . The formula

( → ) is true at w in MK if, and only if, ¬ is true at w in MK or is true at w in MK .

The formula ( ↔ ) is true at w in MK if, and only if, ( → ) is true at w in MK and

( → ) is true at w in MK . Notice that the accessibility relation isn’t used to give the truth conditions for atomic or Boolean formulas. It is, however, essential for the semantics the necessitation operator.

Operator Definition ¨ ¨ ¨ MK , w ⊨ □ , w ⊨ for all w ∈  such that wℜw

In English, the formula □ is true at world w in model MK if, and only if, for all worlds ¨ ¨ w accessible from w, the formula is true at w in MK . Plainly, to decide whether □ is true at world w, check whether is true at all worlds w¨ such that wℜw¨. If is true at all worlds accessible from w, then □ is true; false otherwise. B.2. Relational Structures 247

Possibility is the dual of necessity and a possibilation operator can be deﬁned from the necessitation operator. It, too, should be considered an abbreviation.

Abbreviation Definition ◇ ¬□¬

Since the ◇ symbol is the necessitation operator, the formula ◇ reads “possibly ” or “ is possibly true” under an alethic interpretation. Whereas necessity behaves like a universal quantifier, quantifying over all accessible worlds, possibility behaves like an existential quantifier in that it quantifies only some accessible worlds.

Operator Definition ¨ ¨ ¨ MK , w ⊨ ◇ MK , w ⊨ for some w ∈  such that wℜw

In English, the formula ◇ is true at world w in model MK if, and only if, for some world ¨ ¨ w accessible from w, the formula is true at w in MK . Plainly, to decide whether ◇ is true at world w, check whether is true at some world w¨ such that wℜw¨. If is true in at least one world accessible from w, then ◇ is true; false otherwise. Generalizing, the formal semantics speciﬁes the satisfaction conditions for the various well-formed formulas of the formal language.

Definition B.2.3. A well-formed formula ∈ ℒ∗ is satisﬁable (or: true) at a world, w,

in model, M∗, if M∗, w ⊨ for some w ∈ .

And given the notion of satisﬁability (at a world in a model), it is possible to deﬁne a number of increasingly general and increasingly powerful notions of validity: validity at a world in a frame, validity in a frame, validity in a class of frames, and validity in the class of all frames.

Definition B.2.4. A well-formed formula ∈ ℒ∗ is valid at a world, w, in a frame, F∗,

denoted F∗, w ⊨ , if is satisﬁed at w in every model, M∗, based on F∗.

Definition B.2.5. A well-formed formula ∈ ℒ∗ is valid in a frame, F∗, denoted F∗ ⊨ ,

if is valid at every world w ∈ F∗.

Definition B.2.6. A well-formed formula ∈ ℒ∗ is valid in a class of frames, F , denoted F ⊨ , if is valid on every frame F ∈ F .

Definition B.2.7. A well-formed formula ∈ ℒ∗ is valid if is valid in the class of all frames. Modal Logic Crash Course 248

Intuitively, each might be understood as correspondingly stronger notions of logical truth. When a formula is a logical truth, it is necessarily true; it cannot be false; its denial is unsatisﬁable.

The language ℒK is closed under a number of inference rules and contains a number of axiom schemata. In addition to TC, it is closed under the following inference rules:

Rule Name Rule Schema RN If ⊢ , then ⊢ □ RM If ⊢ → , then ⊢ □ → □ RR If ⊢ ( ∧ ) → , then ⊢ □( ∧ ) → □ RE If ⊢ ↔ , then ⊢ □ ↔ □

And it contains all instances of the following axiom schemata:

Axiom Name Axiom Schema E ◇ ↔ ¬□¬ N □⊤ M □( ∧ ) → (□ ∧ □ ) C (□ ∧ □ ) → □( ∧ ) R □( ∧ ) ↔ (□ ∧ □ ) K □( → ) → (□ → □ )

By design, the language ℒK is a normal modal logic.

Definition B.2.8. The standard modal logic, ℒ∗, is normal if, and only if, ℒ∗ contains all instances of the axiom schema K and is closed under the inference rule RN.

ℒK is a normal modal logic because it satisﬁes all the conditions of the deﬁnition: it is a standard modal logic (i.e., it contains all propositional tautologies and is closed under TC),

it contains all instances of axiom schema K, and it is closed under RN. In point of fact, ℒK is the smallest normal modal logic, otherwise known as the system K. It is possible to validate additional axiom schemata. This is achieved by imposing certain constraints on the class of Kripkean frames. More speciﬁcally, the behavior of the accessibility relation is constrained. Here is a very small sample of famous axiom schemata alongside their constraints: B.3. Neighborhood Structures 249

Constraint Axiom Name Axiom Schema Constraint on Frames Name D □ → ◇ Serial ∃w¨(wℜw¨) T □ → Reﬂexive wℜw 4 □ → □□ Transitive (wℜw¨&w¨ℜw¨¨) ⇒ wℜw¨¨ B → □◇ Symmetric wℜw¨ ⇒ w¨ℜw 5 ◇ → □◇ Euclidean (wℜw¨&wℜw¨¨) ⇒ w¨ℜw¨¨

Above I use ‘∃’ to metalinguistically abbreviate ‘there exists a. . . such that. . . ’ and ‘⇒’ to metalinguistically abbreviate ‘if. . . , then. . . ’. For example, the logic KD is deﬁned by imposing the seriality constraint on the class of Kripkean frames, meaning that every world in the domain has access to at least one world in the domain (possibly itself, but not necessarily). In addition to everything constitutive of K, the language fragment KD contains all instances of the axiom schema D; or, the class of all Kripkean frames satisfying the seriality constraint contains all instances of axiom schema D. And so on for the other constraints.

B.3 Neighborhood Structures

I now want to deﬁne a diﬀerent formal language. As will become clear, this language is

weaker than ℒK in the sense that lacks some of the axiom schemata valid in the class of all

K frames. Let ℒE be an extension of ℒ augmented with a single modal operator.

ℒE ∶= Atom | ( → ) | □

In a word, ℒE has the same primitive grammar as ℒK .

Definition B.3.1. A neighborhood frame is an ordered tuple

FE = ⟨, ⟩ where each element is deﬁned as follows:

∙  = {w, w¨, w¨¨, …} is the nonempty domain of all possible worlds. ∙  ∶  ↦ P (P ()) is a neighborhood function mapping elements of  into a set of set of subsets of . In other words,  assigns a set of subsets of  (i.e., a neighborhood of worlds) to each world in .

A neighborhood structure is a neighborhood frame. A neighborhood frame consists of a domain and a neighborhood function. It is crucial to observe that the accessibility Modal Logic Crash Course 250

relation of the relational structure is replaced by a neighborhood function. Whereas accessibility relations map worlds to worlds, neighborhood functions map worlds to a set of sets of worlds (hereafter neighborhoods). Each subset belonging to P (P ()) is a potential neighborhood. The neighborhood function assigns to each world some set of neighborhoods. Importantly, there is no structure imposed upon neighborhoods; they might even be empty.

Definition B.3.2. A neighborhood model is an ordered tuple

ME = ⟨FE, ℑ⟩ where each element is deﬁned as follows:

∙ FE = ⟨, ⟩ is a neighborhood frame.

∙ ℑ ∶  × Atom ↦ {1, 0} is an interpretation function assigning truth-values into world

and atom pairs for all atoms, Atom, belonging to the language ℒE.

A neighborhood model is a neighborhood frame plus an interpretation function. The

interpretation function behaves normally, giving truth assignments to all atoms of the ℒE at all the worlds in the domain. The semantics for atomic and Boolean formulas remain the same. However the modal operators must be redeﬁned because the accessibility relation has been replaced by the neighborhood function. Fortunately, the resultant semantics is wonderfully simple. The truth conditions for modal operators are deﬁned by appeal to both neighborhoods and to the truth set of the proposition that the modal operators operate upon. Every world w ∈ M (w)  in a neighborhood model  is associated with the set of its neighborhoods,  . ME ME The truth set of in model ME is denoted ‖‖ and its false set is denoted −‖‖ .

Definition B.3.3. The truth set of a formula, , belonging to a formal language, ℒ∗, is M denoted ‖‖ ∗ and is deﬁned as follows:

M∗ ‖‖ = {w ∈  ð M∗, w ⊨ } where M∗ is a model in the language ℒ∗. In other words, the truth set of is the set of all worlds in M∗ at which is true.

Definition B.3.4. The false set of a formula, , belonging to a formal language, ℒ∗, is M denoted −‖‖ ∗ and is deﬁned as follows: B.3. Neighborhood Structures 251

M∗ M∗ M∗ −‖‖ =  − ‖‖ = ‖¬‖ = {w ∈  ð M∗, w ⊨ ¬}

M where ‖‖ ∗ is the truth set of . In other words, the false set of is the complement of

its truth set; or, it is the set of all worlds in M∗ at which is false.

Operator Definition M , w ⊨ □ ‖‖ ∈ (w) M , w ⊨ ◇ ‖‖ ∉ (w)

The formula □ is true at world w in model MK if, and only if, the truth set of is (w) w¨ M a neighborhood in  ; or, the set of all world in  at which is true belongs to (w). Consider the contrast between relational and neighborhood semantics. In relational semantics, to decide whether □ is true at world w, check whether the set of all worlds accessible from w is a subset of the truth set of . If it is, then □ is true; false otherwise. In neighborhood semantics, check whether the truth set of is a neighborhood of w. If it is, then □ is true; false otherwise. Whereas necessity is in terms of neighborhood membership, possibility is deﬁned in

terms of neighborhood nonmembership. The formula ◇ is true at world w in model MK if, and only if, the truth set of is not a neighborhood in (w); or, the set of all world w¨ in M (w)  at which is true does not belong to  . In relational semantics, to decide whether ◇ is true at world w, check whether the set of all worlds accessible from w intersects with the truth set of . If it does, then ◇ is true; false otherwise. In neighborhood semantics, check whether the truth set of is a neighborhood of w. If it isn’t, then ◇ is true; false otherwise. Satisifability and validity are defined as usual. Plainly, the formula satisfiable when it is true at a world in a model. The formula is valid at a world in a frame when it is satisfied at a world in every model. The formula is valid in a frame if it is valid at every world in the frame. The formula is valid in a class of frames if it is valid on every frame in the class. The formula is valid if it is valid in the class of all frames.

The language ℒE is a classical system. In addition to TC, it is closed under the following inference rules:

Rule Name Rule Schema RM If ⊢ → , then ⊢ □ → □ RE If ⊢ ↔ , then ⊢ □ ↔ □

And it contains all instances of the following axiom schemata: Modal Logic Crash Course 252

Axiom Name Axiom Schema E ◇ ↔ ¬□¬

By design, the language ℒE is a classical modal logic.

Definition B.3.5. The standard modal logic, ℒ∗, is classical if, and only if, ℒ∗ contains all instances of the axiom schema E and is closed under the inference rule RE.

ℒE is a classical modal logic because it satisﬁes all the conditions of the deﬁnition: it is a standard modal logic (i.e., it contains all propositional tautologies and is closed under TC),

it contains all instances of axiom schema E, and it is closed under RE. In point of fact, ℒE is the smallest classical modal logic, otherwise known as the system E. It should be observed that the system E lacks the inference rules RN and RM as well as the axiom schemata N, M, C, R, and K. Given some of the topics of the dissertation, it is worth reproducing the countermodels to the axiom schemata.2

Proposition B.3.1. The axiom schema N

□⊤

is not a theorem of ℒE.

M Proof. Let  = {w} and (w) = {ç}. If so, then trivially follows that ‖⊤‖ ∉ (w). Consequently, □⊤ is false at w.

Proposition B.3.2. The axiom schema M

□( ∧ ) → (□ ∧ □ )

is not a theorem of ℒE.

¨ M M ¨ Proof. Let  = {w, w } and (w) = {ç} and ‖‖ = {w} and ‖ ‖ = {w }. M The formula □( ∧ ) is true at w if, and only if, ‖ ∧ ‖ ∈ (w). However M M M ¨ M ‖ ∧ ‖ = ‖‖ ∩ ‖ ‖ = {w} ∩ {w } = {ç}. Since ‖ ∧ ‖ is equivalent to the intersection of the truth sets of and , which in this case is the empty set, and since M (w) = {ç}, it follows that ‖ ∧ ‖ ∈ (w). So, □( ∧ ) is true at w. M M An inspection of the model reveals that ‖‖ ∉ (w) and ‖ ‖ ∉ (w), in which case both □ and □ are false at w, and therefore (□ ∧ □ ) is false at w.

2 Compare with Chellas (1980: 213–217). B.3. Neighborhood Structures 253

Consequently, □( ∧ ) → (□ ∧ □ ) is false at w.

Proposition B.3.3. The axiom schema C

(□ ∧ □ ) → □( ∧ )

is not a theorem of ℒE.

¨ ¨ M M ¨ Proof. Let  = {w, w } and (w) = {{w}, {w }} and ‖‖ = {w} and ‖ ‖ = {w }. M M If so, then ‖‖ ∈ (w) and ‖ ‖ ∈ (w), in which case both □ and □ are true at wand therefore (□ ∧ □ ) is true at w. M The formula □( ∧ ) is true at w if, and only if, ‖ ∧ ‖ ∈ (w). However M M M ‖ ∧ ‖ = ‖‖ ∩ ‖ ‖ = {w} ∩ { } = {ç}. Since {ç} ∉ (w), it follows that M ‖ ∧ ‖ ∉ (w). So, □( ∧ ) is false at w. Consequently, (□ ∧ □ ) → □( ∧ ) is false at w.

Proposition B.3.4. The axiom schema R

□( ∧ ) ↔ (□ ∧ □ )

is not a theorem of ℒE.

Proof. Repeat the countermodels to the M and C schemata.

Proposition B.3.5. The axiom schema K

□( → ) → (□ → □ )

is not a theorem of ℒE.

¨ ¨¨ ¨ ¨¨ M M Proof. Let  = {w, w , w } and (w) = {{w}, {w, w , w }} and ‖‖ = {w} and ‖ ‖ = {w, w¨}. M The formula □( → ) is true at w if, and only if, ‖ → ‖ ∈ (w). However M M M M ¨ ¨¨ ¨ ¨ ¨¨ ‖ → ‖ = ‖¬ ∨ ‖ = ‖¬‖ ∪ ‖ ‖ = {w , w } ∪ {w, w } = {w, w , w }. Since {w, w¨, w¨¨} ∈ (w), it follows that □( → ) is true at w. M M An inspection of the model reveals that ‖‖ ∈ (w) but ‖ ‖ ∉ (w), in which case □ is true at w but □ is false at w, and therefore (□ → □ ) is false at w. Consequently, □( → ) → (□ → □ ) is false at w. Modal Logic Crash Course 254

B.4 From Neighborhood Structures to Relational Structures

The language ℒK is the smallest normal modal logic and the language ℒE is the smallest

classical modal logic. Though ℒE is weaker than ℒK , it is possible to deﬁne strengthened extensions of the former that build up to the latter.

Begin with ℒM , an extension of ℒE. Let MM = ⟨, , ⟩ be a neighborhood model

extending ME, where the following constraint imposed upon the neighborhood function:

Supplemented: If X ∩ Y ∈ (w), then X ∈ (w) and Y ∈ (w).

The language ℒM is monotonic in the sense that its neighborhood models MM are mono-

tonic. It follows from supplementation that ℒM additionally contains all instances of the axiom schema M and is closed under the inference rule RM.3

By design, ℒM is a monotonic modal logic.

Definition B.4.1. The standard modal logic, ℒ∗, is monotonic if, and only if, ℒ∗ contains all instances of the axiom schema E and is closed under the inference rule RM.

Definition B.4.2. The modal logic, ℒ∗, is monotonic if, and only if, ℒ∗ is classical and contains all instances of the axiom schema M.

ℒM is a monotonic modal logic because it satisﬁes all the conditions of the deﬁnition: it is a classical modal logic (i.e., it is a modal logic that contains all instances of axiom schema E and is closed under RE) and it contains all instances of the axiom schema M. In point of

fact, ℒM is the smallest monotonic modal logic, otherwise known as the system M.

Now deﬁne ℒR, an extension of ℒM . Let MR = ⟨, , ⟩ be a neighborhood model

extending MM , where the following constraint imposed upon the neighborhood function:

Closed Under Intersections: If X ∈ (w) and Y ∈ (w), then X ∩ Y ∈ (w).

In other words, the language ℒR is a quasiﬁlter in the sense that its neighborhood models

MR are monotonic and closed under intersections. It follows that ℒR additionally contains all instances of the axiom schema C and is closed under the inference rule RR.4

By design, ℒR is a monotonic modal logic.

Definition B.4.3. The standard modal logic, ℒ∗, is regular if, and only if, ℒ∗ contains all instances of the axiom schema E and is closed under the inference rule RR.

3 Interested readers may consult Chellas (1980: 215–216) for proofs. 4 Ibid. B.5. Counterpossible Relational Structures 255

Definition B.4.4. The standard modal logic, ℒ∗, is regular if, and only if, ℒ∗ contains all instances of the axiom schemata E and C and is closed under the inference rule RM.

Definition B.4.5. The standard modal logic, ℒ∗, is regular if, and only if, ℒ∗ is monotonic and contains all instances of the axiom schema C.

ℒR is a regular modal logic because it satisﬁes all the conditions of the deﬁnition: it is a monotonic modal logic and it contains all instances of the axiom schema M. In point of

fact, ℒR is the smallest regular modal logic, otherwise known as the system R.

Finally, it is possible to deﬁne ℒK as an extension of ℒR. Let MK = ⟨, , ⟩ be a

neighborhood model extending MR, where the following constraint imposed upon the neighborhood function:

Contains the Unit:  ∈ (w).

In other words, the language ℒK is a ﬁlter in the sense that its neighborhood models MK

are regular and contain the unit. It follows that ℒK additionally contains all instances of the axiom schema N and is closed under the inference rule RN.5

It has already been shown that ℒK is a normal modal logic, but here are other ways to putting the same point:

Definition B.4.6. The standard modal logic, ℒ∗, is normal if, and only if, ℒ∗ is regular and contains all instances of the axiom schema N.

Definition B.4.7. The standard modal logic, ℒ∗, is normal if, and only if, ℒ∗ is regular and is closed under the inference rule RN.

ℒK is a normal modal logic because it satisﬁes all the conditions of the deﬁnition: it is a regular modal logic and it contains all instances of the axiom schema N.

B.5 Counterpossible Relational Structures

In this section, I consider what happens when counterpossible worlds (or: impossible worlds or nonnormal worlds) are included in otherwise crisp relational structures. What is an impossible world and how is it diﬀerent from a normal possible world? A normal world is a maximally consistent set of propositions (or: well-formed formulas of a language). In other words, it is a complete and consistent description of the world. A nonnormal world is also set of propositions (or: well-formed formulas of a language),

5 Ibid. Modal Logic Crash Course 256

but it need neither be consistent nor maximal. Impossible world semantics supplements possible worlds semantics by adding an additional class of worlds to the domain. Begin by deﬁning ℒ , an impossible worlds extension of ℒ . No additions are made K− K to the primitive grammar, but the frames and models contain additional features.

Definition B.5.1. An counterpossible relational frame, F , is the ordered triple K−

F = , , ℜ K− ⟨ + ⟩ where each element is deﬁned as follows:

∙  = {w, w¨, w¨¨, …} is the nonempty domain of all possible worlds.

¨ ¨¨ ∙ + = {w+, w+, w+, …} is the nonempty subdomain of all normal worlds.

+ ¨ ¨¨ ∙ − =  −  = {w−, w−, w−, …} is the nonempty subdomain of all nonnormal worlds. + (To be clear, − isn’t oﬃcially included in the frame because it is deﬁned from  −  .)

∙ ℜ ⊆  ×  is a binary accessibility relation that relates one moment to another. The notation wℜw¨ expresses that w¨ is accessible from w, which is true if (w, w¨) ∈ ℜ.

The domain, , contains both normal worlds and nonnormal worlds. There are two

subdomains, + and −, where + is the partition containing all the normal worlds

and − is the partition defined from  − + containing all the nonnormal worlds. The accessibility relation works as usual, relating one world to another with no constraints as to whether the worlds are normal or nonnormal. The inclusion of nonnormal worlds raises an interesting question for the definitions of validity and logical consequence: should they include nonnormal worlds? Answering in the affirmative results in a definition that appeals solely to normal worlds and answering in the negative results in a definition that appeals to both normal and nonnormal worlds. I’ll offer both, calling the former ‘validity’ and the latter ’countervalidity’.

Definition B.5.2. A well-formed formula ∈ ℒ∗ is valid at a world, w+, in a frame, F∗,

if is satisﬁed at w+ ∈ + in every model, M∗, based on F∗.

Definition B.5.3. A well-formed formula ∈ ℒ∗ is valid in a frame, F∗, if is valid at

every normal world w+ ∈ F∗.

Definition B.5.4. A well-formed formula ∈ ℒ∗ is valid in a class of frames, F , if is normally valid on every frame F ∈ F . B.5. Counterpossible Relational Structures 257

Definition B.5.5. A well-formed formula ∈ ℒ∗ is valid if is normally valid in the class of all frames.

The newly defined notion of validity approximates the notions of validity defined earlier. Counterpossible relational structures paired with this novation are not importantly different than normal relational structures. In particular, they share all the same theorems.

Definition B.5.6. A well-formed formula ∈ ℒ∗ is countervalid at a world, w, in a

frame, F∗, if is satisﬁed at w ∈  in every model, M∗, based on F∗.

Definition B.5.7. A well-formed formula ∈ ℒ∗ is countervalid in a frame, F∗, if is valid at every world w ∈ F∗.

Definition B.5.8. A well-formed formula ∈ ℒ∗ is countervalid in a class of frames, F , if is countervalid on every frame F ∈ F .

Definition B.5.9. A well-formed formula ∈ ℒ∗ is countervalid if is countervalid in the class of all frames.

Whereas standard validity appeals solely to normal worlds, countervalidity appeals to both normal and nonnormal worlds. Counterpossible relational structures paired with countervalidity are genuinely different from normal relational structures, where the latter is an extension of the former (because truth across all worlds entails truth in normal worlds). In particular, given countervalidity, it is possible to construct countermodels to formulas that are axiom schemata of normal logics. In this sense, counterpossible relational structures result logics weaker than the system K. In what follows, I assume that countervalidity is the default notion of validity for counterpossible relational structures. I offer three different types of models based upon counterpossible relational frames. The first, and simplest, way to handle the augmentation of relational structures with impossible worlds is to simply add a single interpretation function, as per usual. I’ll

designate this system K−1.

Definition B.5.10. An counterpossible relational model, M , is an ordered tuple 1 K−1

M = F , ℑ K−1 ⟨ K− ⟩ where each element is deﬁned as follows:

∙ F = , , ℜ is a counterpossible relational frame. K− ⟨ + ⟩ Modal Logic Crash Course 258

∙ ℑ ∶  × Atom ↦ {1, 0} is an interpretation function assigning truth-values into worlds and atom pairs for all atoms, Atom, belonging to the language.

The semantics using impossible relational models is exactly as it is for typical relational models, especially at normal worlds, including the clause that □ is true at a normal world just in case is true at all accessible worlds and ◇ is true at a normal world just in case is true at some accessible worlds. The main exception is that modal operators behave somewhat like atomic formulas at impossible worlds and are assigned truth-values directly:

∙ (w−, □) = 0

∙ (w−, ◇) = 1

Intuitively, nonnormal worlds in the system K−1 are worlds at which “everything is possible,

and nothing is necessary” (Priest 2008: 64). Perhaps the most remarkable feature of K−1 is that it is weaker than K, lacking the N axiom and the inference rule RN.

Proposition B.5.1. The axiom schema N

□⊤

is not a theorem of ℒ (given countervalidity). K−1

Proof. Let w− ∈ , where w− is a nonnormal world. Even though (w−, ⊤) = 1, it is the

case that (w−, □⊤) = 0. Consequently, □⊤ is false at w−.

The system K−1 always assigns truth-value false to necessity formulas and truth-value true to possibility formulas at nonnormal worlds. But what if anarchical behavior is desired? That is, what if it is desired that □ is sometimes true or that ◇ is sometimes false at nonnormal worlds? Luckily, it is none too diﬃcult to achieve this end with but a

small modiﬁcation to K−1. The second way to handle the augmentation of relational structures with impossible worlds is to supplement the model with a second interpretation function designed to

handle modal formulas at nonnormal worlds. I’ll designate this system K−2.

Definition B.5.11. An counterpossible relational model, M , is an ordered triple 2 K−2

M = F , ℑ, ℑ K−2 ⟨ K− −⟩ where each element is deﬁned as follows: B.5. Counterpossible Relational Structures 259

∙ FK− = ⟨, +, ℜ⟩ is a counterpossible relational frame.

∙ ℑ ∶  × Atom ↦ {1, 0} is an interpretation function assigning truth-values into worlds and atom pairs for all atoms, Atom, belonging to the language ℒ . K−2

∙ ℑ− ∶ − × ■Ψ ↦ {1, 0} is an interpretation function assigning truth-values into nonnormal worlds and modal formulas pairs for the subset, ■Ψ ⊂ Ψ, of some subset, Ψ ⊂ ℒ , K−2 of well-formed formulas belonging to the language ℒ . K−2

In e ect, M supplements M with a nonnormal interpretation function that treats ﬀ K−2 K−1 modal formulas at nonnormal worlds like fully-ﬂedged atoms. As such, modal formulas are true at nonnormal worlds if, and only if, ℑ− outputs 1 when inputted the relevant nonnormal world and modal formula pair.

Operator Definition M , w ⊨ □ ℑ (w , □) = 1 K−2 − − − M , w ⊨ ◇ ℑ (w , ◇) = 1 K−2 − − −

In all other semantical respects, M agrees with M , including the behavior of well- K−2 K−1 formed formulas at normal worlds. Interestingly, M is weaker than M in that, in addition to lacking the N axiom and K−2 K−1 rule RN, it also lacks the E, M, C, R, and K axiom schemata as well as the inference rules RE, RM, and RR. This is a result of the fact that modal formulas behave anarchically at nonnormal worlds in M . K−2

Proposition B.5.2. The axiom schema E

◇ ↔ ¬□¬ is not a theorem of ℒ (given countervalidity). K−2

Proof. The proof proceeds in two steps, one for each direction of the biconditional.

Left-to-Right. Let w− ∈ , where w− is a nonnormal world such that −(w−, ◇) = 1 and −(w−, □¬) = 1. It follows that −(w−, ¬□¬) = 0. Consequently, ◇ → ¬□¬ is false at w−.

Right-to-Left. Let w− ∈ , where w− is a nonnormal world such that −(w−, □¬) = 0 but −(w−, ◇) = 0. It follows that −(w−, ¬□¬) = 1. Consequently, ¬□¬ → ◇ is false at w−.

Consequently, ◇ ↔ ¬□¬ is false at w− in both directions. Modal Logic Crash Course 260

Proposition B.5.3. The axiom schema M

□( ∧ ) → (□ ∧ □ )

is not a theorem of ℒ (given countervalidity). K−2

Proof. Let w− ∈ , where w− is a nonnormal world such that −(w−, □( ∧ )) = 1 and

−(w−, □) = 1 but −(w−, □ ) = 0. Consequently, □( ∧ ) → (□ ∧ □ ) is false at

w−.

Proposition B.5.4. The axiom schema C

(□ ∧ □ ) → □( ∧ )

is not a theorem of ℒ (given countervalidity). K−2

Proof. Let w− ∈ , where w− is a nonnormal world such that −(w−, □) = 1 and

−(w−, □ ) = 1 but −(w−, □( ∧ )) = 0. Consequently, (□ ∧ □ ) → □( ∧ ) is

false at w−.

Proposition B.5.5. The axiom schema R

□( ∧ ) ↔ (□ ∧ □ )

is not a theorem of ℒ (given countervalidity). K−2

Proof. Repeat the countermodels to the M and C schemata.

Proposition B.5.6. The axiom schema K

□( → ) → (□ → □ )

is not a theorem of ℒ (given countervalidity). K−2

Proof. See countermodel to axiom schema M.

The system K−2 treats modal formulas anarchically at nonnormal worlds, but Boolean connective behave as normally. But what if it is desired that all formulas, modal and nonmodal, behave anarchically at nonnormal worlds? Luckily, this, too, can be achieved with a small modiﬁcation to K−2. The third, and ﬁnal, way to handle impossible worlds in relational structures is to B.5. Counterpossible Relational Structures 261

tweak the nonnormal interpretation function introduced by K−2 to operate on both modal

and nonmodal well-formed formulas. I’ll designate this system K−3.

Definition B.5.12. An counterpossible relational model, M , is an ordered triple 3 K−3

M = F , ℑ, ℑ K−3 ⟨ K− −⟩ where each element is deﬁned as follows:

∙ FK− = ⟨, +, ℜ⟩ is a counterpossible relational frame. ∙ ℑ ∶  × Atom ↦ {1, 0} is an interpretation function assigning truth-values into worlds and atom pairs for all atoms, Atom, belonging to the language ℒ . K−3

∙ ℑ− ∶ −×Ψ ↦ {1, 0} is an interpretation function assigning truth-values into nonnormal worlds and formulas pairs for the subset, Ψ ⊂ ℒ , of well-formed formulas belonging K−3 to the language ℒ . K−3

M is weaker than M . In addition to lacking the N, E, M, C, R, and K axiom K−3 K−2 schemata as well as the inference rules RN, RE, RM, and RR, the system lacks all the introduction and elimination rules associated with all the Boolean connectives.