Philosophy of Mathematics (ii) — Frege and Abstractionism

Forthcoming. ‘What would be a reasonable assessment of Frege’s achievement in Grundlagen and Grundgesetze if the contradiction had never come to light?’. In Proceedings of the 4th International Gottlob Frege Conference, edited by Dieter Schott. Springer International Publishing.

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]