From certainty to fallibility in mathematics?
pp. 39-50
in: Evandro Agazzi, György Darvas (eds), Philosophy of mathematics today, Berlin, Springer, 1997Abstract
The title of this paper was borrowed from the heading of a chapter in Davis and Hersh's celebrated book The mathematical experience.1 Here, however, we have inserted a question-mark: is it really true, as some people maintain, that mathematics has lost its certainty? For the sake of simplicity, we refer to this conception as mathematical fallibilism which is a feature of the quasi-empiricism initiated by Lakatos and popularized by Davis and Hersh, Kline, Tymoczko and many others. In this paper we would like to make a critical survey of this viewpoint which constitutes an interesting trend in philosophy of mathematics today.