I am a philosopher based in Sydney, Australia. I was educated at Yale College in New Haven, Connecticut in the US before heading over to Oxford, where I completed BPhil and DPhil degrees in philosophy. I lived at Wolfson College. Currently, I am affiliated with the Sydney School in philosophy of mathematics and based at UNSW.
My current research is in reconciling empiricism in the philosophy of mathematics with the full scope and power of classical, non-constructive mathematics. I am attracted to the Aristotelian view that mathematicians study aspects of the natural world. The difference between mathematicians and other natural scientists is that the mathematicians abstract more from the natural world, focusing just on properties such as symmetry, continuity, shape, size, and so on. This approach allows for a naturalist epistemology and realism. There are no mysterious acausal Platonic forms with which the mathematician is required to interact. Nonetheless, mathematical truth is not a subjective matter, but clearly answerable to the mathematical facts. Mathematical facts are themselves dependent on (i) the natural world, and (ii) the range of logical possibilities. A critical problem with such an empiricist approach is the rich ontology of classical analysis and set theory. For example, it is doubtful whether space is actually a continuum with the structure attributed to the real numbers. Therefore, it looks like there may be a need to restrict the Aristotelian approach to our cognition of a certain ground level of basic, finitistic mathematics.
My original interest in the philosophy of mathematics was sparked by reading The Infinite by A.W. Moore, a book which gives a history of the metaphysical and mathematical concept of infinity.
Created on ... March 03, 2007
Papers
(All are sole authored unless otherwise indicated. Most papers are presented here differ slightly from the final published versions and may be in penultimate draft form.)
Philosophy and history of mathematics
'On the reality of the continuum' Philosophy 83 (2008), 117-27.
Review of Oppy's Philosophical Perspectives on Infinity Australasian J. of Philosophy 85 (2007), 679-82.
'Infinity and the domain principle'
'Aristotle and modern mathematical theories of the continuum' (Warning: some of the
Greek fonts may not display properly)
Philosophy of Action (esp. Anscombe)
'Interpreting Anscombe's `Intention' 32ff', Journal of Philosophical Research, 2009.
'Knowledge by Intention'(final version appeared in S.Hetherington, ed., Aspects of Knowing, Amsterdam: Elsevier, 2006)
Epistemology
Showing the Sceptic the Door: Wittgenstein's Way with
the Sceptic
'Responsibility and Knowledge' (with Stephen Hetherington)[status:
Wittgenstein on
Responding to Scepticism with Action
Philosophy of Mind and Language, Cognitive Science
'Evans's Anti-Cartesian Argument'
(final version in Ratio XCIV, June 2006)
'Singling Out Objects without Sortals'
(ICCS conference paper)
'A Puzzle Concerning First Person Reference'