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 Philip Ebert and Marcus Rossberg (eds.), Essays on Frege’s Basic Laws of Arithmetic, Oxford University Press, 411-436 [.pdf]

2017. “What Was Frege’s Mistake?” in Michael Frauchiger (ed.). Truth, Meaning, Justification, and Reality: Themes from Dummett, De Gruyter, 63-80. [.pdf]

2016. “An Entitlement to Hume’s Principle?” in Philip Ebert and Marcus Rossberg, eds, Abstractionism (Oxford University Press), pp. pp. 154-78. [.pdf]

2016. “Whence the Paradox? Axiom V and Indefinite Extensibility” in Michael Frauchiger ed, Truth, Meaning, Justification, and Reality: Themes from Dummett, The Lauener Library of Analytical philosophy vol. 4 (De Gruyter). [.pdf]

2012. “Frege and Benacerraf’s problem” in Robert DiSalle, Mélanie Frappier, and Derek Brown, eds., Analysis and Interpretation in the Exact Sciences: Essays in Honour of William Demopoulos, Springer, Dordrecht Heidelberg London New York, pp. 117-33. [.pdf]

2009 (with Bob Hale). “The Metaontology of Abstraction” in David Chalmers et al, Eds., Metametaphysics, Oxford University Press, 178-212. [.pdf]

2009 (with Bob Hale). ‘Focus restored: Comment on John Macfarlane’s “Double Vision”’ in Synthese 170 (3), 457-82, special number on Bad Company, edited by Øystein Linnebo. [.pdf]

2009. “The Metaphysics and Epistemology of Abstraction” in Alexander Hieke and Hannes Leitgeb, eds., Reduction-Abstraction-Analysis 195-216 (Publications of the Austrian Ludwig Wittgenstein Society: New Series, vol. 11) (Heusenstamm bei Frankfurt, Ontos Verlag). [.pdf]

2008 (with Bob Hale). “Abstraction and Additional Nature”, in Philosophia Mathematica 16 (2), 182-2008. [.pdf]

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

2003 (with Bob Hale). ‘Responses to Commentators’—book symposium on The Reason’s Proper Study, Philosophical Books Vol. 44, No. 3, 245-63. [.pdf]

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

2001 (with Bob Hale). “To Bury Caesar…” in Bob Hale and Crispin Wright The Reason’s Proper Study (Oxford, the Clarendon Press) 335-96. [.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?” in the Notre Dame Journal of Formal Logic, (40, 1) comprising a festschrift for the late George Boolos, 6-30. [.pdf]

1998. “Response to Dummett”, in M. Schirn, ed., Philosophy of Mathematics Today (Oxford), ch. 15, 389-405.

1998. “On the (Harmless) Impredicativity of Hume’s Principle”, in M. Schirn, ed., Philosophy of Mathematics Today (Oxford), ch. 13, 339-68.

1997. “On the Philosophical Significance of Frege’s Theorem”, in R. Heck, ed., Language, Thought and Logic: Essays in Honour of Michael Dummett (Oxford), 201-44.

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

1990. “Field and Fregean Platonism” in Physicalism in Mathematics, edited by Andrew Irvine, Kluwer Academic Publishers, 73-93. (Reprinted in French translation in M. Marion and A, Voizard, eds., Frege: Logique et Philosophie, Montreal: Harmattan 1998).

1983. “Recent work on Frege”, critical study of Gregory Currie, Frege: An Introduction to his Philosophy, Harvester 1982; Hans Sluga, Gottlob Frege, Routledge 1980; Michael Dummett, The Interpretation of Frege’s Philosophy, Duckworth 1981), Inquiry 26, 363-81. [.pdf]