The Intentions of Intentionality and Other New Models for Modalities by Jaakko Hintikka Review By: Tyler Burge Source: Synthese, Vol

Total Page:16

File Type:pdf, Size:1020Kb

The Intentions of Intentionality and Other New Models for Modalities by Jaakko Hintikka Review By: Tyler Burge Source: Synthese, Vol Review Reviewed Work(s): The Intentions of Intentionality and Other New Models for Modalities by Jaakko Hintikka Review by: Tyler Burge Source: Synthese, Vol. 42, No. 2, Philosophical Logic (Oct., 1979), pp. 315-334 Published by: Springer Stable URL: http://www.jstor.org/stable/20115484 Accessed: 16-05-2018 19:58 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms Springer is collaborating with JSTOR to digitize, preserve and extend access to Synthese This content downloaded from 131.179.58.33 on Wed, 16 May 2018 19:58:08 UTC All use subject to http://about.jstor.org/terms CRITICAL NOTICE Jaakko Hintikka, The Intentions of Intentionality and Other New Models for Modalities, Synthese Library 90, D. Reidel Publishing Company, Dordrecht, 1975. xviii + 262 pp. This book consists of an introduction and eleven essays written by Professor Hintikka approximately between 1970 and 1975. All but one of the essays is published in some form elsewhere. But more than most such collections, this one has a measure of unity and continuity. All the essays involve applications of Hintikka's semantical approach to epistemic notions. And although the book contains few major alterations in Hintikka's previously published views, reading the essays from first to last provides a good overall picture of his philosophical stance in this area. Read this way, the book does have limitations. Several of the articles largely elaborate on viewpoints more fully stated in earlier work (especially in 'Semantics for Pro positional Attitudes,' 'Existential Presuppositions and Uniqueness Pr?supposions,' and 'On the Logic of Perception'- all collected in Hintikks's earlier Models for the Modalities). There is also an un usually large amount of repetition in matters great and small. Nonethe less, the volume conveys a broad, coherent, and important viewpoint that has been applied to an admirably large number of interesting issues. The method of this review will be to give the reader some notion of the contents of the book and then turn to a critical consideration of a few of its primary ideas. Chapter 1, 'Problems and Proposals,' argues that all constructions containing the expression 'knows,' or cognates, are reducible to the 'knows that' construction. The treatment of the 'knows how' construction is (to this reviewer) unintuitive; and the essay seems hurried - though perhaps this may be attributed to its purpose as a brief survey. 'The Semantics of Modal Notions and the Indeterminacy of Ontology,' reprinted from Synthese 1970, maintains that cross-identification over possible worlds is not to be stipulated or taken for granted. Hintikka further agrees with Quine in holding that, at least with the 'logical' modalities, quantification into modal con Synthese 42 (1979) 315-334. 0039-7857/79/0422-0315 $02.00. Copyright ? 1979 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston, U.S.A. 315 This content downloaded from 131.179.58.33 on Wed, 16 May 2018 19:58:08 UTC All use subject to http://about.jstor.org/terms 316 TYLER B?RGE texts is strictly speaking inadmissable. He holds that no object (possibly excepting abstract objects like numbers) can be reasonably traced through all possible worlds. Use of modal logic is claimed to depend on assumptions about the kinds of worlds that are contex tually admissible for consideration. Quantified epistemic logic is sup posed to be better off since in this domain quantification depends on tracing an object only through all worlds compatible with what the subject believes. Here, as with the rejection of stipulation in cross identification, one feels that the issue could stand more clarification. A deeper consideration of what is at issue seems necessary to understanding how one could adjudicate between Hintikka's complex view and more common views among modal logicians. Both view points can enlist at least some of our pretheoretical intuitions. Chap ter 3, 'Objects of Knowledge and Belief: Acquaintance and Public Figures' discusses two methods of cross-identification based on con textual reference and description respectively. It is a compact and highly suggestive essay. Hintikka argues in 'Information, Causality and the Logic of Perception' that possible worlds analysis of the informational elements in perception is compatible with etiological conditions in the explication of perceptual statements. Chapter 5, 'Carnap's Heritage in Logical Semantics,' reprinted from Synthese 1973, contains an historical interpretation of the relation between possible worlds semantics and the tradition running from Frege through Carnap. 'Quine on Quantifying In: A Dialogue,' the only essay not published elsewhere, discusses Quine's doubts about the coherence of quantification into contexts governed by intensional operators. Chapter 7, 'Answers to Questions' defends the view, with various qualifications, that answers to Wh-questions purport to pro vide the questioner with knowledge of some particular individual. 'Grammer and Logic: Some Borderline Problems' is a rather rambling treatment of conundrums, discussed within linguistics, which hinge on the de re - de dicto distinction. In Chapter 9, 'Knowledge, Belief, and Logical Consequence,' Hintikka confronts the important problem that the most straightforward reading of the semantics of epistemic logic implies that a person believes all logical consequences of what he believes. He sketches a definition of the syntactical complexity of a This content downloaded from 131.179.58.33 on Wed, 16 May 2018 19:58:08 UTC All use subject to http://about.jstor.org/terms HINTIKKA ON PROPOSITION AL ATTITUDES 317 quantified sentence and maintains that a person necessarily believes all a belief's logical consequences whose derivation does not rely on sentences of greater complexity. The last two essays are historically oriented. 'The Intentions of Intentionality' takes up Husserl's view of noema. It argues that possible worlds semantics in epistemic logic provides an explication of the notion of intentionality which is superior to Husserl's. In 'Concept as Vision: On the Problem of Representation in Modern Art and in Modern Philosophy' Hintikka develops diverting comparisons between Husserlian and cubist concerns with perspective-free conceptual representation, and be tween cubist rejection of naturalistic perspective and the variations on intended interpretations characteristic of model-theoretic seman tics. There can be no question of reviewing each essay here. What I want to do is to consider Hintikka's general approach to the logical form of propositional attitudes against the background of an alter native approach. The issue must be joined on a variety of fronts, most of which I will ignore. My aim is to outline a critical viewpoint which may stimulate further discussion. Hintikka's approach to the semantics of propositional attitudes is founded on an analogy with the analysis of necessity in modal logic. Modal logic treats 'it is necessary that 2 + 2 = 4' as having the form of the application of an operator 'it is necessary that' to a sentence '2 + 2 = 4.' Hintikka sees 'John believes that 2 + 2 = 4' as the ap plication of the two-place operator expression 'believes that' to the sentence '2 + 2 = 4' and the term 'John.' Semantically, modal logic explicates the truth of the necessity sentence in terms of the truth of '2 + 2 = 4' in all possible worlds. Hintikka explicates the truth of the belief sentence in terms of the truth of '2 + 2 = 4' in all possible worlds compatible with what John believes. I shall call this general orientation 'the possible worlds approach' or 'the operator approach.' Hintikka's orientation to the syntax and semantics of propositional attitudes contrasts with a more traditional line, first expounded within a modern semantical system by Frege. According to this older approach, one treats the relevant belief sentence as having the form of an application of the predicate 'believes' to two terms 'John' and This content downloaded from 131.179.58.33 on Wed, 16 May 2018 19:58:08 UTC All use subject to http://about.jstor.org/terms 318 TYLER B?RGE 'that 2 + 2 = 4'. The truth of the sentence is explicated in terms of John's standing in the relation of belief to the proposition that 2 + 2 = 4. My word 'proposition' here is something of a catch-all expression. There are a number of options for explicating it which are available within the traditional approach that I shall be calling 'Fregean'. Frege himself treated that-clauses as denoting abstract, language-independent thoughts, whose components were senses expressed (sometimes contextually) by linguistic expressions. Others have taken that-clauses to denote sentence types or tokens. There are various other possibilities: subjective psychological entities, and a variety of non-Fregean abstractions. I will not be distinguishing among these options in what follows. Needless to say, a genuine theory along 'Fregean' lines must do so. The traditional approach provides an immediate response to certain simple linguistic facts. For example, from our earlier mentioned belief sentence and the premise that the most frequently cited truth of arithmetic is that 2 + 2 = 4, we commonly deduce that John believes the most frequently cited truth of arithmetic. The Fregean view represents the deduction as a simple substitution of identity. But since the operator approach does not recognize a singular term, or noun phrase, in direct-object position within propositional attitude sentences, this simple representation is not available. More generally, it is undeniable that the sentential expression in propositional attitude sentences is dominated by a noun-phrase.
Recommended publications
  • Two-Dimensionalism: Semantics and Metasemantics
    Two-Dimensionalism: Semantics and Metasemantics YEUNG, \y,ang -C-hun ...:' . '",~ ... ~ .. A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of Master of Philosophy In Philosophy The Chinese University of Hong Kong January 2010 Abstract of thesis entitled: Two-Dimensionalism: Semantics and Metasemantics Submitted by YEUNG, Wang Chun for the degree of Master of Philosophy at the Chinese University of Hong Kong in July 2009 This ,thesis investigates problems surrounding the lively debate about how Kripke's examples of necessary a posteriori truths and contingent a priori truths should be explained. Two-dimensionalism is a recent development that offers a non-reductive analysis of such truths. The semantic interpretation of two-dimensionalism, proposed by Jackson and Chalmers, has certain 'descriptive' elements, which can be articulated in terms of the following three claims: (a) names and natural kind terms are reference-fixed by some associated properties, (b) these properties are known a priori by every competent speaker, and (c) these properties reflect the cognitive significance of sentences containing such terms. In this thesis, I argue against two arguments directed at such 'descriptive' elements, namely, The Argument from Ignorance and Error ('AlE'), and The Argument from Variability ('AV'). I thereby suggest that reference-fixing properties belong to the semantics of names and natural kind terms, and not to their metasemantics. Chapter 1 is a survey of some central notions related to the debate between descriptivism and direct reference theory, e.g. sense, reference, and rigidity. Chapter 2 outlines the two-dimensional approach and introduces the va~ieties of interpretations 11 of the two-dimensional framework.
    [Show full text]
  • The Modal Logic of Potential Infinity, with an Application to Free Choice
    The Modal Logic of Potential Infinity, With an Application to Free Choice Sequences Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Ethan Brauer, B.A. ∼6 6 Graduate Program in Philosophy The Ohio State University 2020 Dissertation Committee: Professor Stewart Shapiro, Co-adviser Professor Neil Tennant, Co-adviser Professor Chris Miller Professor Chris Pincock c Ethan Brauer, 2020 Abstract This dissertation is a study of potential infinity in mathematics and its contrast with actual infinity. Roughly, an actual infinity is a completed infinite totality. By contrast, a collection is potentially infinite when it is possible to expand it beyond any finite limit, despite not being a completed, actual infinite totality. The concept of potential infinity thus involves a notion of possibility. On this basis, recent progress has been made in giving an account of potential infinity using the resources of modal logic. Part I of this dissertation studies what the right modal logic is for reasoning about potential infinity. I begin Part I by rehearsing an argument|which is due to Linnebo and which I partially endorse|that the right modal logic is S4.2. Under this assumption, Linnebo has shown that a natural translation of non-modal first-order logic into modal first- order logic is sound and faithful. I argue that for the philosophical purposes at stake, the modal logic in question should be free and extend Linnebo's result to this setting. I then identify a limitation to the argument for S4.2 being the right modal logic for potential infinity.
    [Show full text]
  • DRAFT: Final Version in Journal of Philosophical Logic Paul Hovda
    Tensed mereology DRAFT: final version in Journal of Philosophical Logic Paul Hovda There are at least three main approaches to thinking about the way parthood logically interacts with time. Roughly: the eternalist perdurantist approach, on which the primary parthood relation is eternal and two-placed, and objects that persist persist by having temporal parts; the parameterist approach, on which the primary parthood relation is eternal and logically three-placed (x is part of y at t) and objects may or may not have temporal parts; and the tensed approach, on which the primary parthood relation is two-placed but (in many cases) temporary, in the sense that it may be that x is part of y, though x was not part of y. (These characterizations are brief; too brief, in fact, as our discussion will eventually show.) Orthogonally, there are different approaches to questions like Peter van Inwa- gen's \Special Composition Question" (SCQ): under what conditions do some objects compose something?1 (Let us, for the moment, work with an undefined notion of \compose;" we will get more precise later.) One central divide is be- tween those who answer the SCQ with \Under any conditions!" and those who disagree. In general, we can distinguish \plenitudinous" conceptions of compo- sition, that accept this answer, from \sparse" conceptions, that do not. (van Inwagen uses the term \universalist" where we use \plenitudinous.") A question closely related to the SCQ is: under what conditions do some objects compose more than one thing? We may distinguish “flat” conceptions of composition, on which the answer is \Under no conditions!" from others.
    [Show full text]
  • Durham E-Theses
    Durham E-Theses The Metaphysics of Mental Representation DE-BLACQUIERE-CLARKSON, RICHARD How to cite: DE-BLACQUIERE-CLARKSON, RICHARD (2011) The Metaphysics of Mental Representation, Durham theses, Durham University. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/833/ Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in Durham E-Theses • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full Durham E-Theses policy for further details. Academic Support Oce, Durham University, University Oce, Old Elvet, Durham DH1 3HP e-mail: [email protected] Tel: +44 0191 334 6107 http://etheses.dur.ac.uk Abstract The representational theory of mind (RTM) explains the phenomenon of intentionality in terms of the existence and nature of mental representations. Despite the typical characterisation of mental representations in terms of their semantics, RTM is best understood as a metaphysical – more specifically formal ontological – theory whose primary defining feature is stipulating the existence of a class of mental particulars called representations. In this regard it is false, since mental representations do not exist. My argument is primarily methodological. Using an extended analysis of mereology and its variants as paradigmatic examples of a formal ontological theory, I argue for a ‘synthetic’ approach to ontology which seeks to form a sound descriptive characterisation of the relevant phenomena from empirical data, to which philosophical analysis is applied to produce a rigorous theory.
    [Show full text]
  • You and I Some Puzzles About ‘Mutual Recognition’
    You and I Some puzzles about ‘mutual recognition’ Michael Thompson University of Pittsburgh Slide 0 Predicating “ξ has a bruised nose” in speech NOMINALLY: “Hannah has a bruised nose” DEMONSTRATIVELY: “This girl has a bruised nose” FIRST PERSONALLY: “I have a bruised nose” Slide 1 Where these are made true by the same bruised nose, the first might be said by anyone, the second by anyone present, and the third by the injured party herself, Hannah. In particular, if Hannah is given to her own senses – in a mirror, for example – she herself might employ any of these three forms of predication. The inner basis of outward speech Outward Speech Hannah said “Hannah has a bruised nose” Hannah said “This girl has bruised nose” Hannah said “I have a bruised nose” Belief Knowlege Hannah believed she had a bruised nose Hannah knew that she had a bruised nose Hannah believed she had a bruised nose Hannah knew that she had a bruised nose Hannah believed she had a bruised nose Hannah knew that she had a bruised nose Slide 2 When Hannah does employ one of these sentences, she is not just saying words, but saying something,orclaiming something; she is perhaps also expressing a belief; and perhaps also manifesting knowledge and imparting knowledge to her hearers. co But whatever she says, it’s the same bruised nose that’s in question: her own, not Martha’s or Solomon’s. There is, as we might say, just one fact in question, one content available, and it pertains to her. We might thus represent the more intellectual states of affairs as follows.
    [Show full text]
  • Frege: “On Sense and Denotation”
    Frege: “On Sense and Denotation” TERMIOLOGY • ‘On Sense and Nominatum’ is a quirky translation of ‘ Über Sinn und Bedeutung’. ‘On Sense and Denotation’ is the usual translation. • ‘Sameness’ is misleading in stating the initial puzzle. As Frege’s n.1 makes clear, the puzzle is about identity . THE PUZZLE What is identity? Is it a relation? If it is a relation, what are the relata? Frege considers two possibilities: 1. A relation between objects. 2. A relation between names (signs). (1) leads to a puzzle; (2) is the alternative Frege once preferred, but now rejects. The puzzle is this: if identity is a relation between objects, it must be a relation between a thing and itself . But everything is identical to itself, and so it is trivial to assert that a thing is identical to itself. Hence, every statement of identity should be analytic and knowable a priori . The “cognitive significance” of ‘ a = b ’ would thus turn out to be the same as that of ‘a = a’. In both cases one is asserting, of a single object, that it is identical to itself. Yet, it seems intuitively clear that these statements have different cognitive significance: “… sentences of the form a = b often contain very valuable extensions of our knowledge and cannot always be justified in an a priori manner” (p. 217). METALIGUISTIC SOLUTIO REJECTED In his Begriffschrift (1879), Frege proposed a metalinguistic solution: identity is a relation between signs. ‘ a = b’ thus asserts a relation between the signs ‘ a’ and ‘ b’. Presumably, the relation asserted would be being co-referential .
    [Show full text]
  • Probabilistic Semantics for Modal Logic
    Probabilistic Semantics for Modal Logic By Tamar Ariela Lando A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Philosophy in the Graduate Division of the University of California, Berkeley Committee in Charge: Paolo Mancosu (Co-Chair) Barry Stroud (Co-Chair) Christos Papadimitriou Spring, 2012 Abstract Probabilistic Semantics for Modal Logic by Tamar Ariela Lando Doctor of Philosophy in Philosophy University of California, Berkeley Professor Paolo Mancosu & Professor Barry Stroud, Co-Chairs We develop a probabilistic semantics for modal logic, which was introduced in recent years by Dana Scott. This semantics is intimately related to an older, topological semantics for modal logic developed by Tarski in the 1940’s. Instead of interpreting modal languages in topological spaces, as Tarski did, we interpret them in the Lebesgue measure algebra, or algebra of measurable subsets of the real interval, [0, 1], modulo sets of measure zero. In the probabilistic semantics, each formula is assigned to some element of the algebra, and acquires a corresponding probability (or measure) value. A formula is satisfed in a model over the algebra if it is assigned to the top element in the algebra—or, equivalently, has probability 1. The dissertation focuses on questions of completeness. We show that the propo- sitional modal logic, S4, is sound and complete for the probabilistic semantics (formally, S4 is sound and complete for the Lebesgue measure algebra). We then show that we can extend this semantics to more complex, multi-modal languages. In particular, we prove that the dynamic topological logic, S4C, is sound and com- plete for the probabilistic semantics (formally, S4C is sound and complete for the Lebesgue measure algebra with O-operators).
    [Show full text]
  • Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics
    axioms Article Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics Lorenz Demey 1,2 1 Center for Logic and Philosophy of Science, KU Leuven, 3000 Leuven, Belgium; [email protected] 2 KU Leuven Institute for Artificial Intelligence, KU Leuven, 3000 Leuven, Belgium Abstract: Aristotelian diagrams, such as the square of opposition, are well-known in the context of normal modal logics (i.e., systems of modal logic which can be given a relational semantics in terms of Kripke models). This paper studies Aristotelian diagrams for non-normal systems of modal logic (based on neighborhood semantics, a topologically inspired generalization of relational semantics). In particular, we investigate the phenomenon of logic-sensitivity of Aristotelian diagrams. We distin- guish between four different types of logic-sensitivity, viz. with respect to (i) Aristotelian families, (ii) logical equivalence of formulas, (iii) contingency of formulas, and (iv) Boolean subfamilies of a given Aristotelian family. We provide concrete examples of Aristotelian diagrams that illustrate these four types of logic-sensitivity in the realm of normal modal logic. Next, we discuss more subtle examples of Aristotelian diagrams, which are not sensitive with respect to normal modal logics, but which nevertheless turn out to be highly logic-sensitive once we turn to non-normal systems of modal logic. Keywords: Aristotelian diagram; non-normal modal logic; square of opposition; logical geometry; neighborhood semantics; bitstring semantics MSC: 03B45; 03A05 Citation: Demey, L. Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics. Axioms 2021, 10, 128. https://doi.org/ 1. Introduction 10.3390/axioms10030128 Aristotelian diagrams, such as the so-called square of opposition, visualize a number Academic Editor: Radko Mesiar of formulas from some logical system, as well as certain logical relations holding between them.
    [Show full text]
  • Frege's Theory of Sense
    Frege’s theory of sense Jeff Speaks August 25, 2011 1. Three arguments that there must be more to meaning than reference ............................1 1.1. Frege’s puzzle about identity sentences 1.2. Understanding and knowledge of reference 1.3. Opaque contexts 2. The theoretical roles of senses .........................................................................................4 2.1. Frege’s criterion for distinctness of sense 2.2. Sense determines reference, but not the reverse 2.3. Indirect reference 2.4. Sense, force, and the theory of speech acts 3. What are senses? .............................................................................................................6 We have now seen how a theory of reference — a theory that assigns to each expression of the language a reference, which is what it contributes to determining the truth or falsity of sentences in which it occurs — might look for a fragment of English. (The fragment of English includes proper names, n-place predicates, and quantifiers.) We now turn to Frege’s reasons for thinking that a theory of reference must be supplemented with a theory of sense. 1. THREE ARGUMENTS THAT THERE MUST BE MORE TO MEANING THAN REFERENCE 1.1. Frege’s puzzle about identity sentences As Frege says at the outset of “On sense and reference,” identity “gives rise to challenging questions which are not altogether easy to answer.” The puzzle raised by identity sentences is that, if, even though “the morning star” and “the evening star” have the same reference — the planet Venus — the sentences [1] The morning star is the morning star. [2] The morning star is the evening star. seem quite different. They seem, as Frege says, to differ in “cognitive value.” [1] is trivial and a priori; whereas [2] seems a posteriori, and could express a valuable extension of knowledge — it, unlike [1], seems to express an astronomical discovery which took substantial empirical work to make.
    [Show full text]
  • Lexical Meaning and Propositional Representation
    CORE Metadata, citation and similar papers at core.ac.uk Provided by University of East Anglia digital repository LEXICAL MEANING AND PROPOSITIONAL REPRESENTATION AN INVESTIGATION INTO THE PROBLEM OF THE UNITY OF THE PROPOSITION Simon Summers Thesis Submitted for the Degree of PhD in Philosophy University of East Anglia School of Philosophy (PHI) October 2012 Word Count: 66, 585 © This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with the author and that any use of the information derived there from must be in accordance with current UK Copyright Law. In addition, any quotation or extract must include full attribution. 1 Abstract In this thesis, I offer a novel account of how best to reorient our semantic and conceptual inquiries into lexical meaning and propositional representation. I achieve this by means of a partly historical investigation into the problem of the unity of the proposition; this is the problem of distinguishing a proposition - the bearer of truth, the complex object or content of a belief or other propositional attitude, and the meaning of a true/false statement - from an „aggregate‟ of its constituent parts. In chapter 1, I assess Bertrand Russell‟s first attempt at a solution, and give a detailed account of why his proposed analysis of a proposition and the sentence expressing it generates a viciously regressive analysis. In chapter 2, I assess Frege‟s approach to the problem, and show that he offers a fundamental insight by way of his approach to analysis which draws an absolute distinction between functions and their argument, and treats concepts as functions to truth-values.
    [Show full text]
  • Boxes and Diamonds: an Open Introduction to Modal Logic
    Boxes and Diamonds An Open Introduction to Modal Logic F19 Boxes and Diamonds The Open Logic Project Instigator Richard Zach, University of Calgary Editorial Board Aldo Antonelli,y University of California, Davis Andrew Arana, Université de Lorraine Jeremy Avigad, Carnegie Mellon University Tim Button, University College London Walter Dean, University of Warwick Gillian Russell, Dianoia Institute of Philosophy Nicole Wyatt, University of Calgary Audrey Yap, University of Victoria Contributors Samara Burns, Columbia University Dana Hägg, University of Calgary Zesen Qian, Carnegie Mellon University Boxes and Diamonds An Open Introduction to Modal Logic Remixed by Richard Zach Fall 2019 The Open Logic Project would like to acknowledge the gener- ous support of the Taylor Institute of Teaching and Learning of the University of Calgary, and the Alberta Open Educational Re- sources (ABOER) Initiative, which is made possible through an investment from the Alberta government. Cover illustrations by Matthew Leadbeater, used under a Cre- ative Commons Attribution-NonCommercial 4.0 International Li- cense. Typeset in Baskervald X and Nimbus Sans by LATEX. This version of Boxes and Diamonds is revision ed40131 (2021-07- 11), with content generated from Open Logic Text revision a36bf42 (2021-09-21). Free download at: https://bd.openlogicproject.org/ Boxes and Diamonds by Richard Zach is licensed under a Creative Commons At- tribution 4.0 International License. It is based on The Open Logic Text by the Open Logic Project, used under a Cre- ative Commons Attribution 4.0 Interna- tional License. Contents Preface xi Introduction xii I Normal Modal Logics1 1 Syntax and Semantics2 1.1 Introduction....................
    [Show full text]
  • Accepting a Logic, Accepting a Theory
    1 To appear in Romina Padró and Yale Weiss (eds.), Saul Kripke on Modal Logic. New York: Springer. Accepting a Logic, Accepting a Theory Timothy Williamson Abstract: This chapter responds to Saul Kripke’s critique of the idea of adopting an alternative logic. It defends an anti-exceptionalist view of logic, on which coming to accept a new logic is a special case of coming to accept a new scientific theory. The approach is illustrated in detail by debates on quantified modal logic. A distinction between folk logic and scientific logic is modelled on the distinction between folk physics and scientific physics. The importance of not confusing logic with metalogic in applying this distinction is emphasized. Defeasible inferential dispositions are shown to play a major role in theory acceptance in logic and mathematics as well as in natural and social science. Like beliefs, such dispositions are malleable in response to evidence, though not simply at will. Consideration is given to the Quinean objection that accepting an alternative logic involves changing the subject rather than denying the doctrine. The objection is shown to depend on neglect of the social dimension of meaning determination, akin to the descriptivism about proper names and natural kind terms criticized by Kripke and Putnam. Normal standards of interpretation indicate that disputes between classical and non-classical logicians are genuine disagreements. Keywords: Modal logic, intuitionistic logic, alternative logics, Kripke, Quine, Dummett, Putnam Author affiliation: Oxford University, U.K. Email: [email protected] 2 1. Introduction I first encountered Saul Kripke in my first term as an undergraduate at Oxford University, studying mathematics and philosophy, when he gave the 1973 John Locke Lectures (later published as Kripke 2013).
    [Show full text]