# 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. 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

**EDITED COLLECTIONS**

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

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

**JOURNAL ARTICLES (29) & BOOK CHAPTERS (3)**

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

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

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 Society*101 (2001), pp. 369-78.

**REVIEWS & SYMPOSIA**

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 *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.

**ENCYCLOPEDIA ENTRIES**

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). [plato.stanford.edu/entries/naturalism-mathematics]

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

**ARTICLES & REVIEWS FOR A GENERAL MATHEMATICAL AUDIENCE**

6. Review of *Philosophy of Mathematics* by Øystein Linnebo, *The Mathematical Gazette*, forthcoming.

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.

**ARTICLE FOR A GENERAL AUDIENCE**

‘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**

Pre-university or first-year undergraduate students interested in logic may enjoy reading this.