Philosophy of Mathematics (ii) — Frege and Abstractionism

Forthcoming. “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).

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]