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2494Self-reference and the languages of arithmeticPhilosophia Mathematica 15 (1): 1-29. 2007.I here investigate the sense in which diagonalization allows one to construct sentences that are self-referential. Truly self-referential sentences cannot be constructed in the standard language of arithmetic: There is a simple theory of truth that is intuitively inconsistent but is consistent with Peano arithmetic, as standardly formulated. True self-reference is possible only if we expand the language to include function-symbols for all primitive recursive functions. This language is therefore…Read more
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3610Nonconceptual content and the "space of reasons"Philosophical Review 109 (4): 483-523. 2000.In Mind and World, John McDowell argues against the view that perceptual representation is non-conceptual. The central worry is that this view cannot offer any reasonable account of how perception bears rationally upon belief. I argue that this worry, though sensible, can be met, if we are clear that perceptual representation is, though non-conceptual, still in some sense 'assertoric': Perception, like belief, represents things as being thus and so.
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2334Frege on Identity and Identity-Statements: A Reply to Thau and CaplanCanadian Journal of Philosophy 33 (1): 83-102. 2003.The paper argues, as against Thau and Caplan, that the traditional interpretation that Frege abandoned his earlier views about identity and identity--statements is correct
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1564Predicative Frege Arithmetic and ‘Everyday’ MathematicsPhilosophia Mathematica 22 (3): 279-307. 2014.The primary purpose of this note is to demonstrate that predicative Frege arithmetic naturally interprets certain weak but non-trivial arithmetical theories. It will take almost as long to explain what this means and why it matters as it will to prove the results
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162Frege'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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941Use and MeaningIn R. E. Auxier & L. E. Hahn (eds.), The Philosophy of Michael Dummett, Open Court. pp. 531--57. 2007.Many philosophers have been attracted to the idea that meaning is, in some way or other, determined by use—chief among them, perhaps, Michael Dummett. But John McDowell has argued that Dummett, and anyone else who would seek to draw serious philosophical conclusions from this claim, must face a dilemma: Either the use of a sentence is characterized in terms of what it can be used to say, in which case profound philosophical consequences can hardly follow, or it will be impossible to make out the…Read more
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1399Reason and LanguageIn Cynthia Macdonald & Graham MacDonald (eds.), McDowell and His Critics, Wiley-blackwell. pp. 22--45. 2008.John McDowell has often emphasized the fact that the use of langauge is a rational enterprise. In this paper, I explore the sense in which this is so, arguing that our use of language depends upon our consciously knowing what our words mean. I call this a 'cognitive conception of semantic competence'. The paper also contains a close analysis of the phenomenon of implicature and some suggestions about how it should and should not be understood.
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129Grundgesetze 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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