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Epistemic Modality Epistemic Possibilities A Thesis submitted to the faculty of San Francisco State University In partial fulfillment of /\ -5 the requirements for -p r the Degree ^Oil- Master of Arts -K5IW In Philosophy by David Anthony King San Francisco, California May 2017 Copyright by David Anthony King 2017 CERTIFICATION OF APPROVAL I certify that I have read Epistemic Possibilities by David Anthony King, and that in my opinion this work meets the criteria for approving a thesis submitted in partial fulfillment of the requirement for the degree Master of Arts in Philosophy at San Francisco State University. Asta, Ph.D. Associate Professor David Landy, Ph.D. Associate Professor Epistemic Possibilities David Anthony King San Francisco, California 2017 In this essay, I examine the nature of epistemic possibility. I argue that we have strong philosophical motivations to leave possible worlds semantics out of epistemic space. I argue that Lloyd Humberstone's possibility semantics better explain the domain of possibility that epistemic possibility talk quantifies over, and show how modeling epistemic possibilities in possibility semantics can explain and predict interesting features of epistemic possibility talk. I certify that the Abstract is a correct representation of the content of this thesis. Chair, Thesis Committee Date TABLE OF CONTENTS Introduction............................................................................................................................1 Section 1: Worlds Contra Possibilities.................................................................................2 1.1 The Explananda..................................................................................................3 1.2 Possible Worlds Accounts of Epistemic Possibilities........................................4 1.3 Argument from the Unpalatability of Impossible Worlds.................................5 1.4 Argument from Parsimony ................................................................................6 1.5 Argument from Infertility...................................................................................6 1.6 In Summary........................................................................................................7 Section 2: Modelling Epistemic Possibilities in Possibility Semantics................................8 2.1 Possibility Semantics..........................................................................................8 2.2 Epistemic Possibilities in Possibility Semantics...............................................11 Section 3: Explaining the Epistemic Might with Possibility Semantics............................13 3.1 An Introduction to the Epistemic Might ..........................................................13 3.2 Epistemic Contradictions..................................................................................16 3.3 Semantics for the Epistemic Might............................................ 17 Conclusion...........................................................................................................................19 Reference............................................................................................................................ 20 1 Introduction Epistemic possibilities are known to have some unique features. Epistemic possibilities may be impossibilities according to all other forms of modality. While other modalities are defined by objective standards about what is and is not possible, what is epistemically possible is plausibly defined relative to an agent. Typical explanations of modality have a possibility as a possible world—a maximally specified way that a world can be. But epistemic possibilities, being relativized to an agent do not need to be ways that a world can be in any robust sense. They may well be ways that a world cannot be, according to all other forms of modality. Rather, they are ways that an agent is capable of believing the actual world to be. Where reasoning with other forms of modality tends to widen the sphere of an agent’s consideration, by allowing the agent to see what possible choices exist, reasoning according to epistemic modality is aimed at narrowing the agent’s sphere of consideration, in order to locate the contents of the actual world. When we quantify over a domain of epistemic possibilities, it is tempting to think we are quantifying over a domain of possible worlds that are not ruled out as candidates for the actual world. This is typically how epistemic possibility is cashed out. But what is epistemically possible for a given agent may not map onto a set of possible worlds. If the space of what is epistemically possible for an agent is given by what her ignorance permits, then, if she is ignorant of the right things, she may well have epistemic possibilities that are not physically, metaphysically, or even logically possible. Our options then seem to be to add impossible worlds' to the domain of quantification for epistemic possibility, or to reject that quantification over epistemic possibilities is quantification over a set of possible worlds. This essay takes the latter tack, and argues that possible worlds semantics are not adequate for explaining epistemic possibilities. I will argue that epistemic possibility talk is better explained by Lloyd Humberstone’spossibility semantics, wherein a possibility is not seen as an entity that is maximally determined. While Humberstone may not have had epistemic modality in mind when creating possibility semantics, I will argue that the considerations he levels in their favor are exactly the sort of considerations we need to have in mind when modeling epistemic possibility. In section 1 of the paper, I will explain what reasons we have for preferring 1 See Berto 2013 for a survey of impossible worlds 2 Humberstone’s possibilities to possible worlds. In section 2,1 will introduce the reader to the basics of the model theory of possibility semantics. I will then explain its philosophical motivations and offer some critiques of Humberstone’s program. I will then offer a definition of an epistemic possibility in terms of possibility semantics. In section 3,1 will argue that modelling the epistemic modal might in possibility semantics successfully explains and predicts some of the most interesting features of the epistemic might. Readers unfamiliar with the themes of this paper may find it useful to read section 3.1 before engaging with the rest of the paper. Section 1: Worlds Contra Possibilities In this section, I will offer some philosophical motivation for abandoning Possible World Semantics for epistemic space. I will argue that these philosophical motivations should instead point us to adopting Lloyd Humberstone’s possibility semantics for epistemic space. Possible worlds are typically cashed out as maximally specified ways that a world can be.2 Humberstone’s possibility semantics model possibilities as entities that are not maximally specified.31 will use the italicized possibilities or possibility whenever I am talking about possibilities as conceived by Humberstone. I will use the same word without italics when I do not wish to make any commitment to the kind of possibility in question being either a possibility or a possible world. I will offer further details on the model theory of possibility semantics in section 2 of the paper. I will proceed in this section by first explaining some of the features a theory of epistemic possibility needs to be able to explain and how accounts employing possible worlds seek to explain these features. I will then make my case that we have reason to think that possible worlds do not have much of an explanatory role to play in accounting for epistemic possibility. I will give three arguments against possible worlds in epistemic space. The argument from the unpalatability of impossible worlds will argue that the route possible worlds theorists need to take in accounting for epistemic possibilities that are impossibilities according to non-epistemic forms of modality involves committing themselves to the existence of entities that we have good philosophical motivation to be leery of. The argument from parsimony will make the case that we reduce the size of our ontology by opting for possibilities 2 See, for example, Cappelen and Dever 2016 3 Humberstone 1981 3 instead of impossible worlds. Lastly, the argument from infertility will make the case that while possible worlds play an explanatory role in accounting for what a possibility is in the root modalities, they do not actually play an explanatory role in accounting for what an epistemic possibility is. Removing possible worlds from epistemic space does not rob us of any explanatory power. 1.1 The Explananda Talk of a strictly epistemic sense of possibility in contemporary thinking on modality goes back at least to Kripke’s Naming and Necessity. The basic idea that Kripke hit upon was that sometimes we use possibility talk when we are not talking about what is metaphysically possible, but because we don’t know what is the case. So, for example, we might take a mathematical theorem ®, whose truth or falsity is not known. We might say that <E> could be true or false. If someone were researching O, and we asked them why they are bothering to do so, they might say something to the effect of “because it could be true, and if it is, then it is worth knowing.” The kind of possibility talk at work here is not telling us anything about what is necessary or possible in the metaphysical sense. If
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