
46A procedural solution to the unexpected hanging and sorites paradoxesMind 107 (428): 751762. 1998.The paradox of the Unexpected Hanging, related prediction paradoxes, and the Sorites paradoxes all involve reasoning about ordered collections of entities: days ordered by date in the case of the Unexpected Hanging; men ordered by the number of hairs on their heads the case of the bald man version of the Sorites. The reasoning then assigns each entity a value that depends on the previously assigned value of one of the neighboring entities. The final result is paradoxical because it conflicts wit…Read more

143Frege meets zermelo: A perspective on ineffability and reflection: A perspective on ineffability and reflectionReview of Symbolic Logic 1 (2): 241266. 2008._1. Philosophical background: iteration, ineffability, reflection._ There are at least two heuristic motivations for the axioms of standard set theory, by which we mean, as usual, firstorder Zermelo–Fraenkel set theory with the axiom of choice : the iterative conception and limitation of size. Each strand provides a rather hospitable environment for the hypothesis that the settheoretic universe is ineffable, which is our target in this paper, although the motivation is different in each case.

14Essay ReviewHistory and Philosophy of Logic 6 (1): 215221. 1985.D. GABBAY and F. GUENTHNER (eds.), Handbook of philosophical logic. Volume 1: Elements of classical logic. Dordrecht, Boston, and Lancaster: D. Reidel Publishing Company, 1983. xiv + 497 pp. Dfl225/$98.00

1Objectivity, explanation, and cognitive shortfallIn Crispin Wright & Annalisa Coliva (eds.), Mind, Meaning, and Knowledge: Themes From the Philosophy of Crispin Wright, Oxford University Press. 2012.

116Secondorder languages and mathematical practiceJournal of Symbolic Logic 50 (3): 714742. 1985.

D. GABBAY and F. GUENTHNER "Handbook of philosophical logic. Volume 1: Elements of classical logic"History and Philosophy of Logic 6 (2): 215. 1985.

263We hold these truths to be selfevident: But what do we mean by that?: We hold these truths to be selfevidentReview of Symbolic Logic 2 (1): 175207. 2009.At the beginning of Die Grundlagen der Arithmetik [1884], Frege observes that “it is in the nature of mathematics to prefer proof, where proof is possible”. This, of course, is true, but thinkers differ on why it is that mathematicians prefer proof. And what of propositions for which no proof is possible? What of axioms? This talk explores various notions of selfevidence, and the role they play in various foundational systems, notably those of Frege and Zermelo. I argue that both programs are u…Read more

339Mathematics and realityPhilosophy of Science 50 (4): 523548. 1983.The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and nonmathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) sur…Read more

13Vagueness and LogicIn Giuseppina Ronzitti (ed.), Vagueness: A Guide, Springer Verlag. pp. 5581. 2011.

42Review of Michael P. Lynch, Truth as One and Many (review)Notre Dame Philosophical Reviews 2009 (9). 2009.

11Arithmetic Sinn and EffectivenessDialectica 38 (1): 316. 1984.SummaryAccording to Dummett's understanding of Frege, the sense of a denoting expression is a procedure for determining its denotation. The purpose of this article is to pursue this suggestion and develop a semi‐formal interpretation of Fregean sense for the special case of a first‐order language of arithmetic. In particular, we define the sense of each arithmetic expression to be a hypothetical process to determine the denoted number or truth value. The sense‐process is “hypothetical” in that t…Read more

216The Objectivity of MathematicsSynthese 156 (2): 337381. 2007.The purpose of this paper is to apply Crispin Wright’s criteria and various axes of objectivity to mathematics. I test the criteria and the objectivity of mathematics against each other. Along the way, various issues concerning general logic and epistemology are encountered.

118Philosophy of Mathematics: Structure and OntologyOxford University Press. 1997.Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests re…Read more

160Truth, function and paradoxAnalysis 71 (1): 3844. 2011.Michael Lynch’s Truth as One and Many is a contribution to the large body of philosophical literature on the nature of truth. Within that genre, advocates of truthascorrespondence, advocates of truthascoherence, and the like, all hold that truth has a single underlying metaphysical nature, but they sharply disagree as to what this nature is. Lynch argues that many of these views make good sense of truth attributions for a limited stretch of discourse, but he adds that each of the contenders …Read more

116Introduction to special issue: Abstraction and NeoLogicismPhilosophia Mathematica 8 (2): 9799. 2000.

14The Lindenbaum construction and decidabilityNotre Dame Journal of Formal Logic 29 (2): 208213. 1988.

23Expressive completeness and decidabilityNotre Dame Journal of Formal Logic 31 (4): 576579. 1990.

2Simple truth, contradiction, and consistencyIn Graham Priest, J. C. Beall & Bradley ArmourGarb (eds.), The Law of NonContradiction, Oxford University Press. 2004.

249Epistemology of mathematics: What are the questions? What count as answers?Philosophical Quarterly 61 (242): 130150. 2011.A paper in this journal by Fraser MacBride, ‘Can Ante Rem Structuralism Solve the Access Problem?’, raises important issues concerning the epistemological goals and burdens of contemporary philosophy of mathematics, and perhaps philosophy of science and other disciplines as well. I use a response to MacBride's paper as a framework for developing a broadly holistic framework for these issues, and I attempt to steer a middle course between reductive foundationalism and extreme naturalistic quietis…Read more

36Review of T. Franzen, Godel's theorem: An incomplete guide to its use and abuse (review)Philosophia Mathematica 14 (2): 262264. 2006.This short book has two main purposes. The first is to explain Kurt Gödel's first and second incompleteness theorems in informal terms accessible to a layperson, or at least a nonlogician. The author claims that, to follow this part of the book, a reader need only be familiar with the mathematics taught in secondary school. I am not sure if this is sufficient. A grasp of the incompleteness theorems, even at the level of ‘the big picture’, might require some experience with the rigor of mathemat…Read more
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Areas of Specialization
Philosophy of Language 
Logic and Philosophy of Logic 
Philosophy of Mathematics 
Areas of Interest
Philosophy of Language 
Logic and Philosophy of Logic 
Philosophy of Mathematics 