Philosophy of Mathematics (i) — general issues

2025. ‘Reflections on Wittgenstein on the Normativity of Arithmetic’. In New Essays on Normative Realism, edited by Paul Boghossian and Christopher Peacocke. Oxford University Press. [.pdf]

2008. Contribution to Philosophy of Mathematics: 5 Questions, edited by Vincent Hendriks and Hannes Leitgeb. Automatic Press. [.pdf]

(with Shapiro, Stewart). 2006. ‘All Things Indefinitely Extensible’. In Absolute Generality, edited by Agustin Rayo and Gabriel Uzquiano. Oxford University Press. [.pdf]

1995. ‘Intuitionists are not (Turing) Machines’. Philosophia Mathematica, 3 (3): 86-102. [.pdf]

1994. ‘About “The Philosophical Significance of Gödel’s Theorem”: Some Issues’. In The Philosophy of Michael Dummett, edited by Brian McGuinness and Gianluigi Oliveri. Kluwer Academic Publishers. [.pdf]

(with Hale, Bob). 1994. ‘A Reductio ad Surdum? Field on the Contingency of Mathematical Objects’. Mind 103: 169-84. [.pdf]

(with Hale, Bob). 1992. ‘Nominalism and the Contingency of Abstract Objects’. Journal of Philosophy 89: 111-35. [.pdf]

1991. ‘Wittgenstein on Mathematical Proof’. Royal Institute of Philosophy Supplement 28: 79-99. [.pdf]

1988. ‘Why Numbers Can Believably Be: A Reply to Hartry Field’. Special number on Philosophy of Mathematics, Revue Internationale de Philosophie 42: 425-73. [.pdf]

(with Benacerraf, Paul). 1985. ‘Skolem and the Sceptic’. Supplement, Proceedings of the Aristotelian Society 59: 117-37. [.pdf]

1982. ‘Strict Finitism’. Synthese 51: 203-82. [.pdf]