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Alexander Paseau

Alexander Paseau

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College Wadham College

Area of Specialisation Epistemology Logic Metaphysics Philosophy of Mathematics Philosophy of Religion

Membership Postholders

Professor of Mathematical Philosophy

Stuart Hampshire Fellow and Tutor in Philosophy, Wadham College

alexander.paseau@philosophy.ox.ac.uk

I read Mathematics (BA 1996) followed by a year of Philosophy (Part II) at Trinity College, Cambridge. After taking the BPhil in Philosophy at Oxford (1999), I returned to Cambridge for my PhD, supervised by Alex Oliver. I spent 2001 as a visiting graduate student at Princeton, working with Paul Benacerraf and David Lewis. After three years of a Research Fellowship at Jesus College, Cambridge, I came to Oxford in 2005, where I am now a professor and a fellow of Wadham College. I am currently the Editor-in-chief of the Journal for the Philosophy of Mathematics and was an Associate Editor of Mind from 2015 to 2018. I have held Research Fellowships from the Mind Association and the Leverhulme Trust, as well as visiting appointments at the Sydney Centre for the Foundations of Science, King’s College London, the Institut d’histoire et de philosophie des sciences et des techniques in Paris, and the Academy of Athens.

CV (PDF)

Books

8. What is Mathematics About?, Oxford University Press, in preparation.

7. The Blackwell Companion to the Philosophy of Mathematics, editor, Wiley-Blackwell, 2027.

6. Propositional Logic, MIT Press, 2027.

5. The Euclidean Programme, with Wesley Wrigley, Cambridge University Press, 2024.

4. Indispensability, with Alan Baker, Cambridge University Press, 2023.

3. One True Logic, with Owen Griffiths, Oxford University Press, 2022.

2. Philosophy of Mathematics, editor, 5 volumes, Routledge Major Works, 2017.

1. Mathematical Knowledge, co-edited with Mary Leng and Michael Potter, Oxford University Press, 2007.

Journal articles (42) and book chapters (11)

53. 'Is Historical Mathematics Largely True?', with Fabian Pregel, in A.C. Paseau (ed.), The Blackwell Companion to the Philosophy of Mathematics, Wiley-Blackwell, forthcoming.

52. ‘Problems for Plenitudinous Platonism’, Philosophia Mathematica, forthcoming.

51. ‘From Structuralism-Within-Set-Theory to Structuralism-Within-a-Theory-of-Structure’, in L. Incurvati & G. Venturi (eds), The Oxford Handbook of the Philosophy of Set Theory, Oxford University Press, forthcoming.

50. ‘Formal Validity: Model-Theoretic and Proof-Theoretic Conceptions’, with Owen Griffiths, in E. Brendel & M. Carrara & F. Ferrari & O. Hjortland & G. Sagi & G. Sher & F. Steinberger (eds), Oxford Handbook of Philosophy of Logic, Oxford University Press, forthcoming.

49. `Indispensabilism's Unfinished Business’, Australasian Journal of Philosophy, forthcoming

48. ‘Necessary-Law Arguments’, Faith and Philosophy 42 (2026), pp. 1–19.

47. `What are the Formulas of a Logic?’, Erkenntnis 91 (2026), pp. 1371–1386.

46. 'Inferentialism and Uniformity', with Owen Griffiths, Journal of Philosophical Logic 54 (2025), pp. 1305–22.

45. ‘Deductive Theories and Non-Deductive Knowledge’, in F. Sterpetti & E. Ippoliti (eds), The Heuristic View (Springer 2025), pp. 97–113 .

44. 'Lakatos and the Euclidean Programme', with Wesley Wrigley, in R. Frigg, J. Alexander, L. Hudetz, M. Rédei, L. Ross & J. Worrall (eds), The Continuing Influence of Imre Lakatos's Philosophy: a Celebration of the Centenary of his Birth (Springer 2025), pp. 47–67.

43. `Is There a Countable Omega-Universal Logic?’, with Felix Weitkämper, Review of Symbolic Logic' 18 (2025), pp. 963–70.

42. ‘Trumping Naturalism Revisited’, in S. Arbeiter & J. Kennedy (eds), The Philosophy of Penelope Maddy (Springer 2024), pp. 267–90.

41. ‘Ways of Being and Logicality’, with Owen Griffiths, The Journal of Philosophy 120 (2023), pp. 94–116.

40. ‘Non-deductive justification in mathematics’, in B. Sriraman (ed), Handbook of the History and Philosophy of Mathematical Practice, (Springer 2023). [Pre-publication draft]

39. ‘Logos, Logic and Maximal Infinity’, Religious Studies 58 (2022), pp. 420–35.

38. ‘Non-metric propositional similarity’, Erkenntnis 87 (2022), pp. 2307-2328.

37. ‘Arithmetic, Enumerative Induction and Size Bias’ Synthese 199 (2021), pp. 9161–9184.

36. ‘Propositional Logics of Truth by Logical Form’, with Owen Griffiths, in G. Sagi & J. Woods (eds), The Semantic Conception of Logic: Essays on Consequence, Invariance, and Meaning (Cambridge University Press 2021), pp. 160–185.

35. ‘Propositionalism’, The Journal of Philosophy 118 (2021), pp. 430–449.

34. ‘Is English Consequence Compact?’, with Owen Griffiths, Thought 10 (2021), pp. 188–98.

33. ‘Capturing Consequence’, Review of Symbolic Logic 12 (2019), pp. 271-95.

32. ‘A Measure of Inferential-Role Preservation’, Synthese 196 (2019), pp. 2621-42.

31. ‘Philosophy of the Matrix’, Philosophia Mathematica 25 (2017), pp. 246-67.

30. ‘Isomorphism Invariance and Overgeneration’ (with Owen Griffiths'), Bulletin of Symbolic Logic 22 (2016), pp. 482-503.

29. ‘What’s the Point of Complete Rigour?’, Mind 125 (2016), pp. 177-207.

28. ‘Fairness and Aggregation’ (with Ben Saunders'), Utilitas 27 (2015), pp. 460-9.

27. ‘Did Frege commit a cardinal sin?’, Analysis 75 (2015), pp. 379-86.

26. ‘Six Similarity Theories of Properties’, in G. Rodriguez-Pereyra & G. Guigon (eds), Nominalism about Properties (Routledge 2015), pp. 95-120.

25. ‘Knowledge of Mathematics without Proof’ (2014), The British Journal for the Philosophy of Science 66, pp. 775-99.

24. ‘The Overgeneration Argument(s) : a Succinct Refutation’, Analysis 74 (2014), pp. 40-7.

23. ‘An Exact Measure of Paradox’, Analysis 73 (2013), pp. 17-26.

22. ‘Against the Judgment-Dependence of Mathematics and Logic’, Erkenntnis 76 (2012), pp. 23-40.

21. ‘Resemblance Theories of Properties’, Philosophical Studies 157 (2012), pp. 361-82.

20. ‘Proving Induction’, Australasian Journal of Logic 10 (2011), pp. 1-17.

19. ‘Mathematical Instrumentalism, Gödel’s Theorem and Inductive Evidence’, Studies in the History and Philosophy of Science 42 (2011), pp. 140-9.

18. ‘A Puzzle about Naturalism’, Metaphilosophy 41 (2010), pp. 642-8.

17. ‘Pure Second-Order Logic with Second-Order Identity’, Notre Dame Journal of Formal Logic 51 (2010), pp. 351-60.

16. ‘Proofs of the Compactness Theorem’, History and Philosophy of Logic 31 (2010), pp. 73-98. [A corrigendum appeared in History and Philosophy of Logic 32 (2011), p. 407.]

15. ‘The Definitions of Ultimate Ontological Basis and the Fundamental Layer’, Philosophical Quarterly 60 (2010), pp. 169-75.

14. ‘Reducing Arithmetic to Set Theory’, in Ø. Linnebo & O. Bueno (eds), New Waves in Philosophy of Mathematics (Palgrave Macmillan 2009), pp. 35-55.

13. ‘How to type: reply to Halbach’, Analysis 69 (2009), pp. 280-6.

12. ‘Justifying Induction Mathematically: Strategies and Functions’, Logique et Analyse 203 (2008), pp. 263-9.

11. ‘Motivating Reductionism about Sets’, Australasian Journal of Philosophy 86 (2008), pp. 295- 307.

10. ‘Fitch’s Argument and Typing Knowledge’, Notre Dame Journal of Formal Logic 49 (2008), pp. 153-76.

9. ‘Scientific Platonism’, in M. Leng, A. Paseau & M. Potter (eds), Mathematical Knowledge (Oxford University Press 2007), pp. 123-49.

8. ‘Boolos on the Justification of Set Theory’, Philosophia Mathematica 15 (2007), pp. 30-53.

7. ‘Genuine Modal Realism and Completeness’, Mind 115 (2006), pp. 721-9.

6. ‘The Subtraction Argument(s)’, Dialectica 60 (2006), pp. 145-156.

5. ‘Naturalism in Mathematics and the Authority of Philosophy’, The British Journal for the Philosophy of Science 56 (2005), pp. 399-418.

4. ‘On an Application of Categoricity’, Proceedings of the Aristotelian Society 105 (2005), pp. 411- 415.

3. ‘The Open-Endedness of the Set Concept and the Semantics of Set Theory”, Synthese 135 (2003), pp. 379-99.

2. ‘Why the Subtraction Argument Does Not Add Up’, Analysis 62 (2002), pp. 74-6.

1. ‘Should the Logic of Set Theory Be Intuitionistic?’, Proceedings of the Aristotelian Society 101 (2001), pp. 369-78.

Reviews and symposia

14. Review of Once Upon a Prime by Sarah Hart, The Mathematical Gazette 108 (2024), pp. 572–4.

13. ‘What is Logical Consequence?’, Essay Review of Logical Consequence by Gila Sher, Philosophia Mathematica 32 (2024), pp. 385–400.

12. Review (with Michael Bevan) of Mathematics and Morality by Justin Clarke-Doane, Philosophia Mathematica 28 (2020), pp. 442–6.

11. Review of Naturalizing Logico-Mathematical Knowledge, S. Bangu (ed.), Notre Dame Philosophical Reviews (16 May 2018).

10. Review of Truth, Objects, Infinity: New Perspectives on the Philosophy of Paul Benacerraf, F. Pataut (ed.), Notre Dame Philosophical Reviews (4 July 2017).

9. Review of The Laws of Belief by Wolfgang Spohn, Mind 126 (2017), pp. 273-8.

8. Review of Rigor and Structure by John Burgess, The British Journal for the Philosophy of Science, 67 (2016), pp. 1185-7.

7. Review of Philosophical Devices by David Papineau, Philosophia Mathematica 22 (2014), pp. 121-3.

6. Review of Platonism, Naturalism and Mathematical Knowledge by James Robert Brown, Philosophia Mathematica 20 (2012), pp. 359-64.

5. ‘Practitioners First’, Book Symposium on Mathematics and Reality by Mary Leng, Metascience 21 (2012), pp. 282-8.

4. Review of Logical Pluralism by JC Beall and Greg Restall, Mind 116 (2007), pp. 391-6.

3. ‘What the Foundationalist Filter Kept Out’, Essay Review of Towards a Philosophy of Real Mathematics by David Corfield, Studies in History and Philosophy of Science 36 (2005), pp. 191-201.

2. Review of The Search for Certainty by Marcus Giaquinto, Philosophical Books 46 (2005), pp. 382- 4.

1. Review of Resemblance Nominalism by Gonzalo Rodriguez-Pereyra, European Journal of Philosophy 13 (2005), pp. 146-50.

Encyclopedia entries

4. (with Fabian Pregel) ‘Deductivism in the Philosophy of Mathematics’, in E. Zalta (ed.), Stanford Encyclopedia of Philosophy (2023–present).

3. (with Rob Leek) ‘The Compactness Theorem’, in J-Y. Beziau (ed.), Encyclopedia of Logic/Internet Encyclopedia of Philosophy (2022 - present).

2. ‘Naturalism in the Philosophy of Mathematics’, in E. Zalta (ed.), Stanford Encyclopedia of Philosophy (2008 - present).

1. ‘Naturalised Philosophy of Mathematics’, Routledge Encyclopedia of Philosophy (2008).

Articles and reviews for a general academic audience

8. ‘Dissemination Corner: One True Logic’, with Owen Griffiths, The Reasoner 16 (2022), pp. 3-4.

7. ‘Why are there no infinite left-sided decimal expansions?’, The Mathematical Gazette 105 (2021), pp. 78-86.

6. Review of Philosophy of Mathematics by Øystein Linnebo, The Mathematical Gazette 102 (2018), pp. 379-81.

5. ‘Letter Games: A Metamathematical Taster’, The Mathematical Gazette 100 (2016), pp. 442-9.

4. Review of Why is there Philosophy of Mathematics at all? by Ian Hacking, The Mathematical Gazette 100 (2016), pp. 381-2.

3. Review of L.E.J. Brouwer: Topologist, Intuitionist, Philosopher by Dirk van Dalen, The Mathematical Gazette 98 (2014), pp. 552-4.

2. ‘The stop after k girls or N children policy’, The Mathematical Gazette 98 (2014), pp. 402-13.

1. ‘Family Planning’, The Mathematical Gazette 95 (2011), pp. 213-7.

Popular articles

Various venues incl. Fuse (Magazine of the National Association for Gifted Children), Oxford Philosophy Faculty newsletter, Varsity (Cambridge University student newspaper), OUP blog and Philosophy Now.

I have published on topics in philosophy of mathematics, logic, epistemology, metaphysics, as well as in ethics and philosophy of religion. I edited the five-volume anthology Philosophy of Mathematics (Routledge 2017) and co-edited the collection Mathematical Knowledge (Oxford University Press 2007). In 2022, Owen Griffiths and I published One True Logic (Oxford University Press), a research monograph arguing that there is only one correct foundational logic and that its nature is highly infinitary. In 2023, Indispensability came out with Cambridge University Press. In this short monograph, Alan Baker and I assess the Indispensability Argument in its various guises, from Quine and Putnam to the present day. A longer monograph appeared in the same series in 2024: The Euclidean Programme (co-authored with Wesley Wrigley). A historical and conceptual study, it charts the rise and fall of Euclidean foundationalism in the philosophy of mathematics.

I recently completed the mathematical textbook Propositional Logic, which will be published by MIT Press in 2027. It covers classical propositional logic and introduces modal, intuitionistic and infinitary propositional logic. I am also the editor of The Blackwell Companion to the Philosophy of Mathematics, to be published in 2027. Each of its 31 chapters offers an up-to-date critical survey of the state of the art in a particular subfield of the philosophy of mathematics. My next book project is What is Mathematics About?, under contract with Oxford University Press. This monograph will be a defence of a form of structuralism as the correct metaphysics of mathematics.

Specific interests include:

Indispensability arguments
Rigour in mathematics
Naturalism
Inductive reasoning
Philosophy of set theory
Logical consequence
Logical constants
Formalisation
The metaphysics of properties
Modal logic and metaphysics
The a priori
Second-order logic
God and logic
Euclidean foundationalism
Foundations of Probability Theory

3:16 am interview:

https://316am.site123.me/articles/along-with-the-eggs-are-there-sets-of-eggs-in-the-fridge-too-and-other-key-questions?c=end-times-archive

Research Supervision

Six students have gained their DPhils under my supervision and one is currently working with me.

7. Tibo Rushbrooke

6. Dominik Ehrenfels (secondary supervisor) DPhil 2025

5. Nuno Filipe Mendes da Silva Maia, DPhil 2023

4. Fabian Pregel, DPhil 2023

3. Michael Bevan, DPhil 2023

2. Robert Schwartzkopff, DPhil 2015

1. James Studd, DPhil 2012

I have also supervised two visiting DPhil students, an MLitt student, five BPhil theses and one MPhil thesis in Philosophical Theology, and five fourth-year dissertations.

Lectures and Seminars

Lecture or seminar courses taught at Oxford include: Philosophy of Mathematics; Probability and Philosophy; Topics in Mathematical Logic; Elements of Deductive Logic (EDL); Logical Consequence; Logic and Philosophy of Logic; and Gödel’s Incompleteness Theorems.

Mathematics and Philosophy BA/MMathPhil at Oxford

More information her e. Students new to logic may enjoy reading this popular article (English original, Italian translation).

I have lived in Greece, Spain, France and the US as well as England. I hold British and Greek citizenship. My interests outside philosophy and mathematics include languages, Hellenism, urban walks, quizzes and chess.

My surname is French and pronounced ‘Pazo’.