Faculty of Philosophy: Michael Potter

Michael Potter

Michael Potter is a Reader in the Philosophy of Mathematics at Cambridge and has been a Fellow of Fitzwilliam College since 1989. He was previously at Oxford, where he took a D.Phil. in pure mathematics and was a Fellow of Balliol College. He spent periods of research leave in the Department of Logic and Metaphysics at St Andrews and the Department of Philosophy at Harvard. In 2004 and 2005 he was on research leave from Cambridge as a Senior Research Fellow at Stirling University funded by the AHRC.

His research interests lie mainly in the history of analytic philosophy (Wittgenstein, Russell and Frege), the philosophy of mathematics, and philosophical logic.

He is also Director of Studies in Philosophy at Fitzwilliam College.

Lectures

Michaelmas Term 2008

Lent and Easter Terms 2009

On sabbatical leave

Research

He is currently working in the following areas:

The Tractatus
The philosophy of set theory
Wittgenstein's later philosophy of mathematics
Constructive philosophies of arithmetic

His current and recent research students have worked on the following topics:

Modal ontological arguments for the existence of God
Theories of ontology
Intuitionism
Prospects for neo-Kantian philosophy of mathematics
Impredicativity in mathematics
The analyticity of logic

Publications

Books

Wittgenstein's Notes on Logic, Oxford University Press, 2009 (online edition January 2009)

(Ed. with Mary Leng and Alexander Paseau) Mathematical Knowledge, Oxford University Press, 2007

Set Theory and its Philosophy: A Critical Introduction, Oxford University Press, 2004

Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap, Oxford University Press, 2000 (paperback edition 2002, online edition May 2007)

An account of attempts from Kant onwards to solve the problem of reconciling the necessity of arithmetic with its applicability. Argues that this can be done only if we appeal in some way or other to the notion that we are unitary selves with an ability to reflect on our own grasp of language. Discusses the relationship between this problem and the corresponding problem for logic.

Mengentheorie, Heidelberg: Spektrum Akademischer Verlag, 1994

This is a German translation (by Achim Wittmüss) of the following.

Sets: An Introduction, Oxford: Clarendon Press, 1990

A presentation of set theory intended for beginning graduate students. Innovative principally because of its use of a simplified and significantly weaker version of Dana Scott's very intuitive axiom system for set theory. Now almost wholly supplanted by Set Theory and its Philosophy (which was originally conceived as a second edition of it).

Forthcoming articles

Wittgenstein's philosophy of mathematics. In Marie McGinn (ed), The Oxford Handbook to Wittgenstein (Oxford University Press, forthcoming)
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, to appear in 2009) Set theory, Philosophical issues in. To appear shortly in Routledge Encyclopaedia of Philosophy, online edition

Selected published articles

The logic of the Tractatus. In Dov M. Gabbay and John Woods (eds), Handbook of the History of Logic, vol. 5 (North-Holland, 2009), 255-304
Explains some features of the account of logic in the Tractatus.
The birth of analytic philosophy. In Dermot Moran (ed), The Routledge Companion to Twentieth Century Philosophy (Routledge, 2008), 60-92
Tries to identify some strands in the birth of analytic philosophy and to identify in consequence some of its distinctive features.
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 problem locates the peculiarity of mathematical knowledge in the wrong place.
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.
(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.
(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.
(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.
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]
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.
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.
Philosophical issues in arithmetic. Routledge Encyclopedia of Philosophy
A survey article.
Different systems of set theory. Routledge Encyclopedia of Philosophy
A survey article.
(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.

Zbl 0938.01016

MR 98h:03009

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]
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.
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.
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.
Iterative set theory. The Philosophical Quarterly, 43 (1993), 178-93
Discusses the metaphysics of the iterative conception of set.

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Contact Details

Postal address: Fitzwilliam College, Cambridge CB3 0DG
Email address: mdp10@cam.ac.uk

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