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220The Frontloading ArgumentPhilosophical Studies 175 (10): 2583-2608. 2018.Maybe the most important argument in David Chalmers’s monumental book Constructing the World is the one he calls the ‘Frontloading Argument’, which is used in Chapter 4 to argue for the book’s central thesis, A Priori Scrutability. And, at first blush, the Frontloading Argument looks very strong. I argue here, however, that it is incapable of securing the conclusion it is meant to establish.
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216The Logical Strength of Compositional PrinciplesNotre Dame Journal of Formal Logic 59 (1): 1-33. 2018.This paper investigates a set of issues connected with the so-called conservativeness argument against deflationism. Although I do not defend that argument, I think the discussion of it has raised some interesting questions about whether what I call “compositional principles,” such as “a conjunction is true iff its conjuncts are true,” have substantial content or are in some sense logically trivial. The paper presents a series of results that purport to show that the compositional principles for…Read more
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179Communication and Knowledge: Rejoinder to Byrne and ThauMind 105 (417). 1996.A reply to Byrne and Thau's criticisms of "The Sense of Communiction".
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174Die Grundlagen der Arithmetik, 82-3In Matthias Schirn (ed.), The Philosophy of mathematics today, Clarendon Press. 1998.A close look at Frege's proof in "Foundations of Arithmetic" that every number has a successor. The examination reveals a surprising gap in the proof, one that Frege would later fill in "Basic Laws of Arithmetic".
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157Meaning and truth-conditions: A reply to KempPhilosophical Quarterly 52 (206). 2002.In his 'Meaning and Truth-Conditions', Gary Kemp offers a reconstruction of Frege's infamous 'regress argument' which purports to rely only upon the premises that the meaning of a sentence is its truth-condition and that each sentence expresses a unique proposition. If cogent, the argument would show that only someone who accepts a form of semantic holism can use the notion of truth to explain that of meaning. I respond that Kemp relies heavily upon what he himself styles 'a literal, rather wood…Read more
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154The development of arithmetic in Frege's Grundgesetze der ArithmetikJournal of Symbolic Logic 58 (2): 579-601. 1993.Frege's development of the theory of arithmetic in his Grundgesetze der Arithmetik has long been ignored, since the formal theory of the Grundgesetze is inconsistent. His derivations of the axioms of arithmetic from what is known as Hume's Principle do not, however, depend upon that axiom of the system--Axiom V--which is responsible for the inconsistency. On the contrary, Frege's proofs constitute a derivation of axioms for arithmetic from Hume's Principle, in (axiomatic) second-order logic. Mor…Read more
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133Semantic Accounts of VaguenessIn J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox, Clarendon Press. 2004.Written as a comment on Crispin Wright's "Vagueness: A Fifth Column Approach", this paper defends a form of supervaluationism against Wright's criticisms. Along the way, however, it takes up the question what is really wrong with Epistemicism, how the appeal of the Sorities ought properly to be understood, and why Contextualist accounts of vagueness won't do.
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127The Finite and the Infinite in Frege's Grundgesetze der ArithmetikIn Matthias Schirn (ed.), The Philosophy of mathematics today, Clarendon Press. 1998.Discusses Frege's formal definitions and characterizations of infinite and finite sets. Speculates that Frege might have discovered the "oddity" in Dedekind's famous proof that all infinite sets are Dedekind infinite and, in doing so, stumbled across an axiom of countable choice.
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123Syntactic reductionismPhilosophia Mathematica 8 (2): 124-149. 2000.Syntactic Reductionism, as understood here, is the view that the ‘logical forms’ of sentences in which reference to abstract objects appears to be made are misleading so that, on analysis, we can see that no expressions which even purport to refer to abstract objects are present in such sentences. After exploring the motivation for such a view, and arguing that no previous argument against it succeeds, sentences involving generalized quantifiers, such as ‘most’, are examined. It is then argued, …Read more
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115Reply to Hintikka and Sandu: Frege and Second-Order LogicJournal of Philosophy 90 (8): 416-424. 1993.Hintikka and Sandu had argued that 'Frege's failure to grasp the idea of the standard interpretation of higher-order logic turns his entire foundational project into a hopeless daydream' and that he is 'inextricably committed to a non-standard interpretation' of higher-order logic. We disagree.
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106Finitude and Hume’s PrincipleJournal of Philosophical Logic 26 (6): 589-617. 1997.The paper formulates and proves a strengthening of ‘Frege’s Theorem’, which states that axioms for second-order arithmetic are derivable in second-order logic from Hume’s Principle, which itself says that the number of Fs is the same as the number ofGs just in case the Fs and Gs are equinumerous. The improvement consists in restricting this claim to finite concepts, so that nothing is claimed about the circumstances under which infinite concepts have the same number. ‘Finite Hume’s Principle’ al…Read more
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94Sense as Mode of RepresentationIn Modes of Representation: Content, Communication, and Frege, Oxford University Press. pp. 200-258. 2024.There are two main models for explaining Frege's notion of sense, both of which have their roots in the work of Sir Michael Dummett. One, nowadays most familiar from the work of David Chalmers, is broadly internalist and descriptivist in character. The other, most familiar from the work of Gareth Evans, is externalist and anti-descriptivist. I first consider the former project, arguing that Dummett anticipated Chalmers's version of the view, and that no version of this view is going to be defens…Read more
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85Frege's theoremClarendon Press. 2011.The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues.
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79Grundgesetze der arithmetic I §10Philosophia Mathematica 7 (3): 258-292. 1999.In section 10 of Grundgesetze, Frege confronts an indeterm inacy left by his stipulations regarding his ‘smooth breathing’, from which names of valueranges are formed. Though there has been much discussion of his arguments, it remains unclear what this indeterminacy is; why it bothers Frege; and how he proposes to respond to it. The present paper attempts to answer these questions by reading section 10 as preparatory for the (fallacious) proof, given in section 31, that every expression of Frege…Read more
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77Grundgesetze der Arithmetik I §§29‒32Notre Dame Journal of Formal Logic 38 (3): 437-474. 1997.Frege's intention in section 31 of Grundgesetze is to show that every well-formed expression in his formal system denotes. But it has been obscure why he wants to do this and how he intends to do it. It is argued here that, in large part, Frege's purpose is to show that the smooth breathing, from which names of value-ranges are formed, denotes; that his proof that his other primitive expressions denote is sound and anticipates Tarski's theory of truth; and that the proof that the smooth breathin…Read more
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64Self-Reference: The Meta-Mathematics of the Liar ParadoxIn TBA. forthcoming.Central to the liar paradox is the phenomenon of 'self-reference'. The paradox typically begins with a sentence like: (L): (L) is not true Historically, doubts about the intelligibility of self-reference have been quite common. In some sense, though, these doubts were answered by Kurt Gödel's famous 'diagonal lemma'. This paper surveys some of the methods by which self-reference can be achieved, focusing first on purely syntactic methods before turning attention to the 'arithmetized' methods…Read more
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57Critical Notice of Michael Dummett, Frege: Philosophy of Mathematics (review)Philosophical Quarterly 43 223-33. 1993.
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54It has been known for some time that context-dependence poses a problem for disquotationalism, but the problem has largely been regarded as one of detail: one that will be solved by the right sort of cleverness. I argue here that the problem is one of principle and that extant solutions, which are based upon the notion of translation, cannot succeed.
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54Perhaps the most important argument against deflationism is the so-called Success Argument: The success of certain behavioral strategies depends upon the truth of a person's beliefs. If so, then the notion of truth appears to play an important role in psychological explanation, contradicting the central thesis of deflationism. I argue here that this type of argument poses a particularly difficult problem for disquotationalism, but that the important case concerns the role that the falsity of a p…Read more
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52Reading Frege's GrundgesetzeOxford University Press UK. 2012.Gottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would finally establish his logicist philosophy of arithmetic. But because of the disaster of Russell's Paradox, which undermined Frege's proofs, the more mathematical parts of the book have rarely been read. Richard G.
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16Modes of Representation: Content, Communication, and FregeOxford University Press. 2024.Modes of Presentation analyses a collection of problems, known as 'Frege's puzzle', resulting from how thinkers and speakers have a limited perspective on reference in thought and language. Heck argues that these puzzles have much to teach us both about the foundations of cognition and the nature of linguistic communication.
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Die Grundlagen der Arithmetik, §§82–3In Matthias Schirn (ed.), The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993, Clarendon Press. pp. 407-428. 1998.
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Ch. 28. The function is unsaturatedIn Michael Beaney (ed.), The Oxford Handbook of The History of Analytic Philosophy, Oxford University Press. 2013.
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