# Alexander Paseau

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 have been an Associate Editor of the journal *Mind* and 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, and the Institut d’histoire et de philosophie des sciences et des techniques in Paris.

** Books**

6. What is Mathematics About?, Oxford University Press (under contract). |

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. 1731 pp. + xlv. |

1. Mathematical Knowledge, co-edited with Mary Leng and Michael Potter, Oxford University Press, 2007. 188 pp. + x. |

** Journal articles (36) and book chapters (7) **

43. ‘Ways of Being and Logicality’, with Owen Griffiths, The Journal of Philosophy 119 (2022), forthcoming. |

42. ‘Trumping Naturalism Revisited’, in J. Kennedy (ed.), On the Philosophy of Penelope Maddy: Set-theoretic Foundations and Naturalistic Methodology, Springer, forthcoming. [Draft] |

41. ‘Model-Theoretic and Proof-Theoretic Validity’, 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. |

40. ‘Non-deductive justification in mathematics’, in B. Sriraman (ed), Handbook of the History and Philosophy of Mathematical Practice, Springer, forthcoming. |

39. |

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

37. ‘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. |

36. ‘Propositionalism’, |

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

34. ‘Non-metric propositional similarity’, Erkenntnis, (2020), published online first, vol. & pp. tbc |

33. ‘Capturing Consequence’, |

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), |

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?’, |

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’, |

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’, |

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’, |

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’, |

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’, |

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), |

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)’, |

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”, |

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**

12. |

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 |

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 |

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 |

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**

3. (with Rob Leek) ‘The Compactness Theorem’, in J-Y. Beziau (ed.), |

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?’, |

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 |

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 CUP monograph in the same series is also in the works: *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. Finally, *What Is Mathematics About?*, under contract with Oxford University Press, is both an advanced introduction to the philosophy of mathematics and 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

3:16 am interview:

**Research Supervision**

Three students have gained their DPhils under my supervision, and four are currently working with me:

7. Dominik Ehrenfels (secondary supervisor)

6. Nuno Filipe Mendes da Silva Maia

4. Fabian Pregel

3. Michael Bevan, DPhil 2023

2. Robert Schwartzkopff, DPhil 2015

1. James Studd, DPhil 2012

I am also currently supervising one MLitt student, and have previously supervised four BPhil theses and four fourth-year dissertations.

**Lectures and Seminars**

Recent lecture or seminar courses at Oxford include: Philosophy of Mathematics; Elements of Deductive Logic (EDL); Logical Consequence; Logic and Philosophy of Logic; and Gödel’s Incompleteness Theorems. My EDL notes may be found here.

**Mathematics and Philosophy BA/MMathPhil at Oxford**

More information here. 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. A note on my surname: it’s French and pronounced ‘Pazo’.