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

## Lectures

### 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

None

## Publications

### Books

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

Reviewed in *Phenomenological Reviews.*

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

*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)

*Mengentheorie*, Heidelberg: Spektrum Akademischer Verlag, 1994

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).]*

### Forthcoming book

*Wittgenstein's 1916 Transformation*

### Edited Collections

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

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

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

### Published articles

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 https://doi.org/10.17863/CAM.57333

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), 79-86*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.*

### Book reviews

*Elucidating the Tractatus: Wittgenstein's Early Philosophy of Logic and Language* by Marie McGinn. *Philosophical Quarterly*60 (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

Krakow

28 June 2011 - 'Sometimes I
*seem*to see a difficulty': Frege's conception of self-subsistenceColloquium on Frege's Philosophy of Mathematics

Bucharest

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

Cambridge

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 - 12pmThe 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
Nancy

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
*Tractatus*was bornAlumni 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

Neuchatel

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

Oxford

14th February 2002 - Mathematics as tautological
Philosophy Department Seminar

Sheffield

20th October 2000 - Hilbertian formalism
Moral Sciences Club

Cambridge

26th January 1999 - Intuition and reflection in arithmetic
Joint Session

Nottingham

July 1998

### Contact Details

Postal address: Fitzwilliam College, Cambridge CB3 0DG

Email address: michael.potter@phil.cam.ac.uk