Anne Newstead

Welcome to my academic homepage.

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 an ARC Post-doctoral Research Associate affiliated with the Sydney School in philosophy of mathematics and based at UNSW. My CV is here.

My current research since 2007 is a synthesis of my research interests in philosophy of mind (cognitive science) and philosophy of mathematics. I am interested in the cognitive basis underlying the acquisition of mathematical concepts, such as the concept of the real number line, of number, and of shape. This interest naturally falls into two parts:

*The cognitive science of mathematics: What are the modules in our brains that allow us to do mathematics? Is there a ‘number sense’? To what extent is visualization and imagery involved? Is this involvement permissible?

*The metaphysics of mathematics: What is the metaphysical basis underlying mathematical cognition? Are mathematical patterns to be found in nature? Can this explain the marvellous applicability of mathematics?

This research is part of an ARC Discovery Project, ‘Mathematics, the Science of Structure’. For details, see the webpage of the ‘Sydney School’ (link above).

Many of my past papers (or penultimate versions thereof) are posted below. Contact me for the latest versions.

I. MIND

'Evans's Anti-Cartesian Argument' , Ratio XCIV, June 2006.

'Interpreting Anscombe's `Intention' 32ff', Journal of Philosophical Research, December 2009.

'Knowledge by Intention' in S.Hetherington, ed., Aspects of Knowing, Amsterdam: Elsevier, 2006)
'Singling Out Objects without Sortals', International Conference on Cognitive Science conference paper.
'A Puzzle Concerning First Person Reference' (draft)
Wittgenstein's Way with the Sceptic (review article)

Review of ‘Thought, Reference, and Experience’, Australasian Journal of Philosophy 84, 154.

II. METAPHYSICS AND 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.

'What finite minds can know' (with James Franklin). (under consideration)
'Aristotle and modern mathematical theories of the continuum' (Warning: some of the Greek fonts may not display properly)

'Intertwining metaphysics and mathematics: the development of Georg Cantor's set theory, 1871-1887', Review of Contemporary Philosophy 2008

‘Infinity in Nature and Mathematics’, forthcoming (draft attached)

‘Indispensability without Platonism’, forthcoming (draft attached)

III. MIND & MATHEMATICS TOGETHER

* Development of the number sense (acquisition of the concept of cardinality and number)

‘Knowing the numbers’ (draft)

‘Size Matters’ (draft)

* Pattern cognition

For most of its history, the philosophy of mathematics has not relied on empirical data. With the naturalistic turn, that is no longer the case. There is a wealth of interesting data about pattern cognition. In fact there is a wealth of data in cognitive science that supports a broadly structuralist philosophy of mathematics. For example, work at CRiMSE (Macquarie University) has demonstrated a correlation between young children’s ability to replicate patterns and their subsequent mathematical achievement (see link on Sydney School website).

*Visualization in Mathematics

To what extent is it permissible to rely on visualization in obtaining mathematical concepts and knowledge? Do mathematicians in fact rely on visual imagery? Is such imagery an integral part of mathematical proof?