Fri Jan 23, 2009
60 Evans Hall, 4:10–6 PM
Charles Chihara (UC Berkeley, Emeritus)
Two Nominalistic Views of Mathematics
I describe two approaches to the problem of devising a view of mathematics that will account for applications of mathematics within a nominalistic framework. The first, Hartry Field’s fictionalist view of mathematics, holds that the theorems of mathematics are, like sentences in works of fiction, not true. Applications of mathematics are explained in terms of a property that good mathematical systems are supposed to possess, namely that of being “conservative” over nominalistic theories. My own account of mathematics takes a very different approach which is devised to explain important features of pure mathematics and the history of the calculus that Field’s view does not explain.