| (With Peter Sullivan) Introduction. In Peter Sullivan and Michael Potter (eds), Wittgenstein's Tractatus: History and interpretation (Oxford University Press, 2013) |
| Wittgenstein's pre-Tractatus manuscripts: A re-assessment. In Peter Sullivan and Michael Potter (eds), Wittgenstein's Tractatus: History and interpretation (Oxford University Press, 2013) |
 | Frege, Russell and Wittgenstein. In Gillian Russell and Delia Graff Fara (eds), Routledge Companion to the Philosophy of Language (Routledge, 2012) ISBN 9780415993104 |
| Set theory, Philosophy of. Routledge Encyclopaedia of Philosophy, online edition, April 2011 |
| Wittgenstein's philosophy of mathematics. In Oskari Kuusela and Marie McGinn (eds), The Oxford Handbook of Wittgenstein (Oxford University Press, 2011) |
| Narodzhennja analytychnoi filosofii. Filosofska Dumka, 2011, no. 3, pp. 47-68 "The birth of analytic philosophy", abridged and translated into Ukrainian by Oleksiy Panych.
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| Introduction. In Michael Potter and Tom Ricketts (eds), The Cambridge Companion to Frege (CUP, 2010), 1-31
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| Abstractionist class theory: Is there any such thing? In Jonathan Lear and Alex Oliver (eds), The Force of Argument: Essays in Honor of Timothy Smiley (Routledge, 2009), pp. 186-204 A discussion of the philosophical prospects for basing a neo-Fregean theory of classes on a principle that attempts to articulate the limitation-of-size conception.
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| The logic of the Tractatus. In Dov M. Gabbay and John Woods (eds), Handbook of the History of Logic, vol. 5 (North-Holland, 2009), pp. 255-304 Describes some of the main features of the logic and metaphysics of Wittgenstein's Tractatus.
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| | The birth of analytic philosophy. In Dermot Moran (ed), The Routledge Companion to Twentieth Century Philosophy (Routledge, 2008), pp. 60-92 Tries to identify some strands in the birth of analytic philosophy and to identify in consequence some of its distinctive features.
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| | What is the problem of mathematical knowledge? In Mary Leng, Alexander Paseau and Michael Potter (eds), Mathematical Knowledge (OUP, 2007), 16-32 Suggests that the recent emphasis on Benacerraf's access problem locates the peculiarity of mathematical knowledge in the wrong place. Instead we should focus on the sense in which mathematical concepts are or might be "armchair concepts" - concepts about which non-trivial knowledge is obtainable a priori.
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| | Ramsey's transcendental argument. In Hallvard Lillehammer and D. H. Mellor (eds), Ramsey's Legacy (OUP, 2005), 71-82 Explores the historical and philosophical background to a curious argument of Ramsey's that in the Tractatus the possibility of the infinite proves its actuality.
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 | (With Peter Sullivan) What is wrong with abstraction? Philosophia Mathematica, 13 (2005) 187-93 We correct a misunderstanding by Hale and Wright of an objection we raised in 'Hale on Caesar' to their abstractionist programme for rehabilitating logicism in the foundations of mathematics.
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| | (With Timothy Smiley) Recarving content: Hale's final proposal. Proceedings of the Aristotelian Society, 102 (2002) 351-4 A follow-up, showing why Bob Hale's revision of his notion of weak sense is still inadequate.
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| | (With Timothy Smiley) Abstraction by recarving. Proceedings of the Aristotelian Society, 101 (2001), 327-38 Explains why Bob Hale's proposed notion of weak sense cannot explain the analyticity of Hume's principle as he claims. Argues that no other notion of the sort Hale wants could do the job either.
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| | Was Gödel a Gödelian platonist? Philosophia Mathematica, 9 (2001) 331-46 Gödel's appeal to mathematical intuition to ground our grasp of the axioms of set theory is notorious. I extract from his writings an account of this form of intuition which distinguishes it from the metaphorical platonism of which Gödel is sometimes accused and brings out the similarities between Gödel's views and Dummett's. [Reviews: Zbl 1007.01017, MR 2002g:01014]
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| | Intuition and reflection in arithmetic. Arist. Soc. Supp. Vol., 73 (1999) 63-73 Classifies accounts of arithmetic into four sorts according to the resources they appeal to in constructing its subject matter.
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| | Classical arithmetic as part of intuitionistic arithmetic. Grazer Philosophische Studien, 55 (1998) 127-41 Argues that classical arithmetic can be viewed as a proper part of intuitionistic arithmetic. Suggests that this largely neutralizes Dummett's argument for intuitionism in the case of arithmetic.
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| | Philosophical issues in arithmetic. Routledge Encyclopedia of Philosophy A survey article.
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| | Different systems of set theory. Routledge Encyclopedia of Philosophy A survey article.
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| | (With P. M. Sullivan) Hale on Caesar. Philosophia Mathematica, 5 (1997), 135--52 Presents a battery of difficulties for the notion that arithmetic can be based on Hume's principle. [Reviews: Zbl 0938.01016, MR 98h:03009]
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| | Taming the infinite. British Journal of Philosophy of Science, 47 (1996), 609-19 A critique of Shaughan Lavine's attempt in Understanding the Infinite to reduce talk about the infinite to finitely comprehensible terms. [Review: MR 97m:03012]
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| | Critical notice of `Parts of classes' by David Lewis. The Philosophical Quarterly, 43 (1993), 362-366 Argues that Lewis is not as ontologically innocent as he pretends.
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| | The metalinguistic perspective in mathematics. Acta Analytica, 11 (1993), 79-86 Tries to find a common source for several well-known paradoxes in mathematics - Skolem's paradox, the permutation argument, and Russell's paradox.
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| | Infinite coincidences and inaccessible truths. In Philosophy of Mathematics, Proceedings of the 15th International Wittgenstein Symposium, Vol. 1 (Vienna: Hölder-Pichler-Tempsky, 1993), 307-13 Argues, contra Dummett, that the platonist need not be any more committed than the intuitionist to the notion that there are arithmetical truths in principle inaccessible to any finite intelligence.
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| Iterative set theory. The Philosophical Quarterly, 43 (1993), 178-93 Discusses the metaphysics of the iterative conception of set.
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