Philosophy of Mathematics (ii) — Frege and Abstractionism

2024. ‘Is There Basic A Priori Knowledge of Necessary Truth?’. Disputatio 15 (68): 1–38. [.pdf]

2019. ‘How did the Serpent of Inconsistency enter Frege’s paradise?’. In Essays on Frege’s Basic Laws of Arithmetic, edited by Philip Ebert and Marcus Rossberg. Oxford University Press. [.pdf]

2017. ‘What Was Frege’s Mistake?’. In Truth, Meaning, Justification, and Reality: Themes from Dummett, edited by Michael Frauchiger. De Gruyter. [.pdf]

2016. ‘An Entitlement to Hume’s Principle?’. In Abstractionism, edited by Philip Ebert and Marcus Rossberg. Oxford University Press. [.pdf]

2016. ‘Whence the Paradox? Axiom V and Indefinite Extensibility’. In Truth, Meaning, Justification, and Reality: Themes from Dummett, edited by Michael Frauchiger. De Gruyter. [.pdf]

2012. ‘Frege and Benacerraf’s problem’. In Analysis and Interpretation in the Exact Sciences: Essays in Honour of William Demopoulos, edited by Robert DiSalle, Mélanie Frappier, and Derek Brown. Springer Science+Business Media. [.pdf]

(with Hale, Bob). 2009. ‘The Metaontology of Abstraction’. In Metametaphysics, edited by David Chalmers. Oxford University Press. [.pdf]

(with Hale, Bob). 2009. ‘Focus restored: Comment on John Macfarlane’. Special number on Bad Company, Synthese 170 (3), 457-82. [.pdf]

2009. ‘The Metaphysics and Epistemology of Abstraction’. In Reduction-Abstraction-Analysis, edited by Alexander Hieke and Hannes Leitgeb. Ontos Verlag. [.pdf]

(with Hale, Bob). 2008. ‘Abstraction and Additional Nature’. Philosophia Mathematica 16 (2), 182-208. [.pdf]

(with Hale, Bob). 2005. ‘Logicism in the 21st Century’. In The Oxford Handbook in the Philosophy of Mathematics and Logic, edited by Stewart Shapiro. Oxford University Press. [.pdf]

(with Hale, Bob). 2003. ‘Responses to Commentators’. Philosophical Books 44 (3) 245-63. (contribution to book symposium on The Reason’s Proper Study) [.pdf]

(with Hale, Bob). 2002. ‘Benacerraf’s Dilemma Revisited’. European Journal of Philosophy 10 (1): 101-29. [.pdf]

2001. ‘Field and Fregean Platonism’. In The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, edited by Bob Hale and Crispin Wright. Oxford University Press. [.pdf]

2001. ‘On the Harmless Impredicativity of N= (Hume’s Principle)’. In The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, edited by Bob Hale and Crispin Wright. Oxford University Press. [.pdf]

2001. ‘Response to Dummett’. In The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, edited by Bob Hale and Crispin Wright. Oxford University Press. [.pdf]

2001. ‘On the Philosophical Significance of Frege’s Theorem’. In The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, edited by Bob Hale and Crispin Wright. Oxford University Press. [.pdf]

(with Hale, Bob). 2001. ‘To Bury Caesar…’. In The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, edited by Bob Hale and Crispin Wright. Oxford University Press. [.pdf]

2000. ‘Neo-Fregean Foundations for Real Analysis: Some Reflections on Frege’s Constraint’. Notre Dame Journal of Formal Logic 41: 317-34. [.pdf]

1999. ‘Is Hume’s Principle Analytic?’. Notre Dame Journal of Formal Logic 40 (1): 6-30. (comprising a festschrift for the late George Boolos) [.pdf]

1995. Critical study of Michael Dummett’s Frege: Philosophy of Mathematics. Philosophical Books 36: 89-102. [.pdf]

1983. ‘Recent work on Frege’. Inquiry 26: 363-81. (critical study of Gregory Currie’s Frege: An Introduction to his Philosophy, Hans Sluga’s Gottlob Frege, and Michael Dummett’s The Interpretation of Frege’s Philosophy) [.pdf]