•  138
    Frege on definitions
    Philosophy Compass 3 (5): 992-1012. 2008.
    This article treats three aspects of Frege's discussions of definitions. First, I survey Frege's main criticisms of definitions in mathematics. Second, I consider Frege's apparent change of mind on the legitimacy of contextual definitions and its significance for recent neo-Fregean logicism. In the remainder of the article I discuss a critical question about the definitions on which Frege's proofs of the laws of arithmetic depend: do the logical structures of the definientia reflect the understa…Read more
  •  127
    On the conceptual foundations of anti-realism
    Synthese 115 (1): 33-70. 1998.
    The central premise of Michael Dummett's global argument for anti-realism is the thesis that a speaker's grasp of the meaning of a declarative, indexical-free sentence must be manifested in her uses of that sentence. This enigmatic thesis has been the subject of a great deal of discussion, and something of a consensus has emerged about its content and justification. The received view is that the manifestation thesis expresses a behaviorist and reductive theory of meaning, essentially in agreemen…Read more
  •  88
    Teaching & learning guide for: Frege on definitions
    Philosophy Compass 4 (5): 885-888. 2009.
    Three clusters of philosophically significant issues arise from Frege’s discussions of definitions. First, Frege criticizes the definitions of mathematicians of his day, especially those of Weierstrass and Hilbert. Second, central to Frege’s philosophical discussion and technical execution of logicism is the so‐called Hume’s Principle, considered in The Foundations of Arithmetic . Some varieties of neo‐Fregean logicism are based on taking this principle as a contextual definition of the operator…Read more
  •  79
    This collection of previously unpublished essays presents a new approach to the history of analytic philosophy--one that does not assume at the outset a general characterization of the distinguishing elements of the analytic tradition. Drawing together a venerable group of contributors, including John Rawls and Hilary Putnam, this volume explores the historical contexts in which analytic philosophers have worked, revealing multiple discontinuities and misunderstandings as well as a complex inter…Read more
  •  77
    Undecidability in anti-realism
    Philosophia Mathematica 6 (3): 324-333. 1998.
    In this paper I attempt to clarify a relatively little-studied aspect of Michael Dummett's argument for intuitionism: its use of the notion of ‘undecidable’ sentence. I give a new analysis of this concept in epistemic terms, with which I resolve some puzzles and questions about how it works in the anti-realist critique of classical logic.
  •  71
    Review: The anti-realist's past (review)
    History and Theory 47 (2): 270-278. 2008.
  •  57
    Review of Danielle Macbeth, Frege's Logic (review)
    Notre Dame Philosophical Reviews 2005 (11). 2005.
  •  54
    Reading Cavell (edited book)
    with Alice Crary
    Routledge. 2005.
    Alongside Richard Rorty, Hilary Putnam and Jacques Derrida, Stanley Cavell is arguably one of the best-known philosophers in the world. In this state-of-the-art collection, Alice Crary explores the work of this original and interesting figure who has already been the subject of a number of books, conferences and Phd theses. A philosopher whose work encompasses a broad range of interests, such as Wittgenstein, scepticism in philosophy, the philosophy of art and film, Shakespeare, and philosophy o…Read more
  •  40
    In What Way Does Logic Involve Necessity?
    Philosophical Topics 42 (2): 289-337. 2014.
    In this paper I advance an account of the necessity of logic in Wittgenstein’s Tractatus. I reject both the “metaphysical” reading of Peter Hacker, who takes Tractarian logical necessity to consist in the mode of truth of tautologies, and the “resolute” account of Cora Diamond, who argues that all Tractarian talk of necessity is to be thrown away. I urge an alternative conception based on remarks 3.342 and 6.124. Necessity consists in what is not arbitrary, and contingency in what is up to our a…Read more
  •  35
    Reason’s Nearest Kin
    Philosophical Review 111 (3): 442-447. 2002.
    This book is a study of the philosophy of arithmetic in one of the most significant periods of its history—from Frege to Carnap—prefaced by an account of Kant. Potter aims at a philosophical history, a story told from an explicit interpretative perspective. These theories of arithmetic are seen as attempts to account for its “source of content” and “source of concepts.” Potter never explains these terms; I take the former to be the thing that, when we have knowledge of it or insight into it, pro…Read more
  •  32
    Frege’s Philosophy of Mathematics (review)
    Philosophical Review 106 (2): 275. 1997.
    The days when Frege was more footnoted than read are now long gone; still, until very recently he has been read rather selectively. No doubt many had an inkling that there’s more to Frege than the sense/reference distinction; but few, one suspects, thought that his philosophy of mathematics was as fertile and intriguing as the present collection demonstrates. Perhaps, as Paul Benacerraf’s essay in this collection suggests, logical positivism should be held partly responsible for the neglect of t…Read more
  •  27
    Wittgenstein's Early Philosophy
    Philosophical Quarterly 65 (259): 304-307. 2015.
  •  14
    Reason’s Nearest Kin (review)
    Philosophical Review 111 (3): 442-447. 2002.
    This book is a study of the philosophy of arithmetic in one of the most significant periods of its history—from Frege to Carnap—prefaced by an account of Kant. Potter aims at a philosophical history, a story told from an explicit interpretative perspective. These theories of arithmetic are seen as attempts to account for its “source of content” and “source of concepts.” Potter never explains these terms; I take the former to be the thing that, when we have knowledge of it or insight into it, pro…Read more
  •  5
    What is the Great Debt to Frege?
    Disputatio 10 (18). 2021.
    In this paper I examine two substantial interpretations of Wittgenstein’s criticisms of Frege’s conception of logic. One is based on Frege’s rejection of psychologism and alleges that this rejection engenders a tension that is resolved in the Tractatus. The other is based on the claim that there are patterns of inference involving what are now known as propositional attitude ascriptions that Frege’s conception of logic is not equipped to handle. I show that neither of these interpretations prese…Read more
  •  4
    Philosophers since Aristotle have traditionally held that impossibilities make up the nature of logic. Sanford Shieh investigates an important but underexplored break with this tradition: Frege and Russell questioned whether there really are such things as possibilities or necessities, and sought the foundations of logic elsewhere.
  • What is Non-Realism About Arithmetic?
    Poznan Studies in the Philosophy of the Sciences and the Humanities 90 (1): 317-341. 2006.
  • Reading Cavell
    with Alice Crary, Russell B. Goodman, and William Rothman
    Journal of Aesthetics and Art Criticism 65 (2): 229-233. 2007.
  • Michael Dummett, "Frege: Philosophy of Mathematics" (review)
    Journal of the History of Philosophy 31 (2): 303. 1993.
  • Could Kant Have Been a Logicist?
    In Valerio Hrsg V. Rohden, Ricardo Terra & Guido Almeida (eds.), Recht Und Frieden in der Philosophie Kants, . pp. 1--203. 2008.
  • The most puzzling and intriguing aspect of intuitionism as a philosophy of mathematics is its claim that classical deductive reasoning in mathematics is illegitimate. The two most well-known proponents of this position are L. E. J. Brouwer and Michael Dummett. Both of their criticisms of the use of classical logic in mathematics have, by and large, been taken to depend on the thesis that the principle of bivalence does not apply to mathematical statements; and the difference between these critic…Read more