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Faculty of Philosophy


Michael Potter is Professor of Logic in the Philosophy Faculty at Cambridge University and a Life Fellow of Fitzwilliam College. 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 (in particular Frege, Russell, Wittgenstein and Ramsey), the philosophy of mathematics, and philosophical logic. He has supervised research students on the following topics:

  • Fictionalism
  • Animal action and intentionality
  • HIlbert's programme and neo-Fregean logicism
  • The concept horse
  • Ramsey
  • Putnam's permutation argument
  • Predicative mathematics
  • Impredicativity in mathematics
  • Harmony
  • Prospects for neo-Kantian philosophy of mathematics
  • Theories of ontology
  • Modal ontological arguments for the existence of God


Michaelmas Term 2022

Truth (for Part IB, Paper 1)

Realism and its alternatives (for Part II, Paper 1)

The nature of logic (for Part II, Paper 8)

Wittgenstein, Blue Book (for Part II, Paper 9) 

Lent Term 2023

Wittgenstein's Tractatus (for Part II, Paper 9)

Set theory (for Part II, Paper 7)

Russell on denoting and the external world programme (for Part IB, Paper 2)

Easter Term 2020




    The Rise of Analytic Philosophy 1879-1930: From Frege to Ramsey, Routledge, 2019

    The Rise of Analytic Philosophy 1879-1930

    Reviewed in Phenomenological Reviews.

    Wittgenstein's Notes on Logic, Oxford University Press, 2009 (paperback edition 2011)

    Front cover illustration 

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

    Front cover illustration 

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

    Front cover illustration


    Mengentheorie, Heidelberg: Spektrum Akademischer Verlag, 1994

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

    Sets: An Introduction, Oxford: Clarendon Press, 1990 [Now almost wholly supplanted by Set Theory and its Philosophy (which was originally conceived as a second edition of it).]

    Front cover illustration

    Forthcoming book

    Wittgenstein's 1916 Transformation

    Edited Collections

    (Ed. with Peter Sullivan) Wittgenstein's Tractatus: History and interpretation Oxford University Press, 2013

    Front cover illustration

    (Ed. with Tom Ricketts) The Cambridge Companion to Frege, Cambridge University Press, 2010

    Front cover illustration

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

    Front cover illustration

    Published articles

    Some outstanding questions, in Maurice Pope, The Keys to Democracy (Exeter: Imprint Academic, 2023), pp. 189-93

    Foreword to new edition of Russell's Introduction to Mathematical Philosophy (Routledge, 2023)

    Foreword to new edition of Russell's Essay on the Foundations of Geometry (Routledge, 2023)

    How substantial are Tractarian objects really?, Disputatio (Spain), 10 (2021), 93-107

    Intuitive and regressive justifications for set theories, Philosophia Mathematica, 28 (2020), 385-94

    Nonsense among the philosophers. in James Williams and Anna Barton (eds), The Edinburgh Companion to Nonsense (Edinburgh University Press, 2019)

    Propositions in Wittgenstein and Ramsey. In G. M. Mraas et al. (eds) Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium (de Gruyter, 2019) ISBN 9783110654301

    (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) ISBN 9780199287505

    Narodzhennja analytychnoi filosofii. Filosofska Dumka, 2011, no. 3, pp. 47-68 An abridgement and translation into Ukrainian by Oleksiy Panych of "The birth of analytic philosophy".

    Introduction. In Michael Potter and Tom Ricketts (eds), The Cambridge Companion to Frege (CUP, 2010), pp. 1-31

    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.

    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.

    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.

    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.

    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 Peter 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]

    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), 79-86Tries 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), 307-13Argues, 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), 178-93Discusses the metaphysics of the iterative conception of set.

    Book reviews

    Elucidating the Tractatus: Wittgenstein's Early Philosophy of Logic and Language by Marie McGinn. Philosophical Quarterly60 (2010) 192-4

    Routledge Philosophy Guidebook to Wittgenstein and the Tractatus by Michael Morris. Notre Dame Philosophical Reviews (2009)

    Constructibility and Mathematical Existence by Charles Chihara. Philosophical Quarterly 41 (1991) 345-8

    The Philosophy of Set Theory by Mary Tiles. Philosophical Books 

    Selected talks

    • Wittgenstein's early philosophy of religion

      Conference on philosophy of religion
      LMH, Oxford
      14-16 September 2011

    • Our grasp of the classical continuum

      Prof Leitgeb's seminar series
      LMU, Munich
      30 June 2011

    • Wittgenstein's early philosophy of religion

      Conference on philosophy of religion
      28 June 2011

    • 'Sometimes I seemto see a difficulty': Frege's conception of self-subsistence

      Colloquium on Frege's Philosophy of Mathematics
      28-30 May 2011

    • Great Thinkers: Wittgenstein

      CLIO (Cambridge University History Society)
      Trinity Hall, Cambridge
      3 May 2011

    • Our grasp of the classical continuum

      Set theory and higher order logic
      Birkbeck College London
      30 March 2011

    • Privacy and acquaintance in Frege, Russell and Wittgenstein

      Centenary of "Knowledge by acquaintance and knowledge by description"
      University of Texas at Austin
      26 March 2011

    • Our grasp of the classical continuum

      Logic Seminar
      Cambridge University
      24 February 2011

    • Privacy and acquaintance in Frege, Russell and Wittgenstein

      Logic Seminar
      17 February 2011

    • Two kinds of ambiguity?

      Principa Centenary Symposium
      Trinity College Cambridge
      27 November 2010

    • The role of classes in Principia

      One Hundred Years of Principia Mathematica
      Trinity College Dublin
      12 July 2010, 11am - 12pm

      The axiom of reducibility in Principia can be thought of as a class existence axiom. Yet class terms are incomplete symbols which disappear on analysis. I shall discuss the interaction between these two features of the system and relate them to later critcisims of Principia by Wittgenstein and Ramsey.

    • Why ZF is not a foundation for mathematics (but nor is ZU)

      Paris VII
      22 June 2010

    • More on replacement

      Logic Seminar
      Cambridge University
      18 February 2010

    • More on replacement

      22 October 2009

    • Wittgenstein on solipsism

      Department Seminar
      Sheffield University
      16 October 2009

    • Why study philosophy?

      UUM, Sintok, Malaysia
      30 July 2009

    • Classes as ideal elements and limitation of size

      The Imaginary, the Ideal and the Infinite in Mathematics
      Pont-a-Mousson, France
      26th June 2009

    • Wittgenstein 1916

      Conference on the Tractatus
      Clermont Ferrand
      8 June 2009

    • Wittgenstein and the club but not the poker

      Moral Sciences Club
      Cambridge University
      October 2008

    • Where does arithmetic fit into transcendental philosophy?

      Transcendental Philosophy and Naturalism
      Stewart House, University of London
      25 April 2008

    • More thoughts on replacement

      Philosophy of Mathematics Seminar
      Oxford University
      29 October 2007

    • Wittgenstein in conflict: How the Tractatuswas born

      Alumni Weekend
      Cambridge University
      22 September 2007

    • Frege's influence on Wittgenstein

      Stapledon Philosophy Colloquium
      Liverpool University
      30 April 2007

    • Set Theory without Replacment

      Reinhardt Memorial Lecture
      University of Colorado at Boulder
      22 March 2007, 3.15-5pm

    • How much set theory does topology need?

      General Topology Seminar
      Oxford University
      7 March 2007, 4pm - 6pm

    • Wittgenstein in conflict: How the Tractatus was born

      Undergraduate Philosophy Society
      Reading University
      20 February 2007

    • How abstract is topology?
      Conference in honour of Peter Colliins
      Mathematical Institute, Oxford
      10 August 2006

    • How does a set depend on its members?

      Colloquium on Set Theory
      20 May 2006

    • Wittgenstein's debt to Frege

      Workshop on Wittgenstein's Tractatus
      Cambridge University
      29 April 2006

    • Wittgenstein's later philosophy of mathematics: Is there any such thing?

      Conference on Wittgenstein's Philosophy of Mathematics
      University of Kent at Canterbury
      28 January 2006, 2pm - 4pm

    • The genesis of the Notes on Logic

      Logic Seminar
      Cambridge University
      19 January 2006

    • Negative facts in the Notes on Logic

      Conference on The Tractatus and its History
      Stirling University
      10 September 2005

    • The genesis of the Notes on Logic

      Workshop on Wittgenstein's Tractatus
      Stirling University
      4 June 2005

    • What is wrong with abstractionism?

      Neo-Fregean Logicism Seminar
      St Andrews University
      25th November 2004, 11am - 1pm

    • Ramsey's transcendental argument for the axiom of infinity

      Notre Dame University
      22nd September 2004, 3pm

    • Tatsache, Sachverhalt and Sachlage

      Workshop on Wittgenstein's Tractatus
      Stirling University
      3rd April 2004

    • Is the Tractatus really nonsense?

      Philosophy Departmental Seminar
      Trinity College Dublin
      30th January 2004

    • Ramsey's transcendental arguments for infinity

      Ramsey Centenary Conference
      Newnham College, Cambridge
      30th June 2003

    • Logic and analyticity

      Oxford University Philosophical Society
      14th February 2002

    • Mathematics as tautological

      Philosophy Department Seminar
      20th October 2000

    • Hilbertian formalism

      Moral Sciences Club
      26th January 1999

    • Intuition and reflection in arithmetic

      Joint Session
      July 1998

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    Contact Details

    Postal address: Fitzwilliam College, Cambridge CB3 0DG
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