skip to content

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.


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



He has recently worked on the following areas:

  • The Tractatus
  • The philosophy of set theory
  • Wittgenstein's later philosophy of mathematics

His research students have worked on the following topics:

  • 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



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 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

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

Sets: An Introduction, Oxford: Clarendon Press, 1990

Front cover illustration 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 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

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

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)


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

  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)


image icon link 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


image icon link 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


image icon link 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.

image icon link 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.

image icon link 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.

image icon link 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.

image icon link (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.

image icon link (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.

image icon link (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.

image icon link 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]

image icon link 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.

image icon link 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.

image icon link Philosophical issues in arithmetic. Routledge Encyclopedia of Philosophy

A survey article.

image icon link Different systems of set theory. Routledge Encyclopedia of Philosophy

A survey article.

image icon link (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]

image icon link 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]

image icon link 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.

image icon link 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.

image icon link 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.

image icon link Iterative set theory. The Philosophical Quarterly, 43 (1993), 178-93

Discusses 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
image icon link 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 

Links marked PRE are to my final pre-publication drafts, which will differ in pagination, and may differ in content, from the published versions. Links marked PUB are to journal websites and may not work from non-University web addresses.

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 Facebook LinkedIn PhilPapers


Contact Details

Postal address: Fitzwilliam College, Cambridge CB3 0DG
Email address: