Alexander Paseau

Alexander Paseau
Membership Type:

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. Following a three-year Junior Research Fellowship at Jesus College, Cambridge, I was appointed to my present post at Oxford in 2005. I have held visiting appointments at the Sydney Centre for the Foundations of Science (2008), King’s College London (2014) and the Institut d'histoire et de philosophie des sciences et des techniques in Paris (2017). I held a Mind Association Research Fellowship in 2012 and have been an Associate Editor of Mind since 2015. 

Full CV (PDF)

Most available here: Phil Papers 


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

1. Mathematical Knowledge, co-edited with M. Leng & M. Potter (Oxford University Press, 2007).


32. 'Isomorphism Invariance and Overgeneration' (with Owen Griffiths), Bulletin of Symbolic Logic (forthcoming).

31. ‘Philosophy of the Matrix’, Philosophia Mathematica (forthcoming).

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

29. ‘A Measure of Inferential-Role Preservation’, Synthese (2015), vol. & pp. tbc. [Erratum]

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 Society101 (2001), pp. 369-78.




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

9. Review of The Laws of Belief by Wolfgang Spohn, Mind, forthcoming.

8. Review of Rigor and Structure by John Burgess, The British Journal for the Philosophy of Science, forthcoming.

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 byMarcus 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.


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

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).


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.


‘Mathematical Philosophy: What is a Number?’, Fuse 1 (Magazine of the National Association for Gifted Children), Summer 2009.

I am a mathematical philosopher. I have published on topics in philosophy of mathematics, philosophy of logic, mathematical logic, philosophical logic, formal epistemology and formal metaphysics. I co-edited the collection Mathematical Knowledge and edited the five-volume anthology Philosophy of Mathematics. I am currently working on three books: What is a Number?, an advanced introduction to the philosophy of mathematics; One True Logic, a research monograph on Logical Monism co-authored with Owen Griffiths; and a longer-term project on non-deductive reasoning in 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

Outside philosophy and logic, my interests include languages. Born to a Belgian father (my surname is pronounced ‘Pazo’) and Greek mother and educated in continental Europe and England, I’m a native speaker of English, French and Greek. I also speak Italian, some Spanish, and try to keep up my German, Latin and ancient Greek reading. I support Manchester United from the armchair, am a quizzing enthusiast, and enjoy playing chess with fellow patzers.

Recent lecture or seminar courses at Oxford include: Philosophy of Mathematics; Elements of Deductive Logic; Logical Consequence; and Gödel’s Incompleteness Theorems. 

Mathematics and Philosophy BA/MMatPhil at Oxford

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