Honest toil or sheer magic?

Weir, A.J. (2006) Honest toil or sheer magic? Dialectica, 61(1), pp. 89-115. (doi: 10.1111/j.1746-8361.2006.01076.x)

Abstract

In this article I discuss the 'procedural postulationist' view of mathematics advanced by Kit Fine in a recent paper. I argue that he has not shown that this view provides an avenue to knowledge of mathematical truths, at least if such truths are objective truths. In particular, more needs to be said about the criteria which constrain which types of entities can be postulated. I also argue that his reliance on second-order quantification means that his background logic is not free of ontological commitment and that his doctrine of 'creative expansion' only makes sense from a radically anti-realist perspective.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Weir, Professor Alan
• Authors: Weir, A.J.
• Subjects: B Philosophy. Psychology. Religion > B Philosophy (General); Q Science > QA Mathematics
• College/School: College of Arts & Humanities > School of Humanities > Philosophy
• Journal Name: Dialectica
• ISSN: 0012-2017