Woensdag 21 april 2004
Vanaf half 11 is er koffie en chocola in de
||Giuseppina Ronzitti (Genova)
|| On the philosophy of intuitionistic mathematics
||11:00 - 12:00
||CK N4 (N3045)
The intuitionistic view of mathematics is a very intriguing subject for
philosophers as it defies the validity of mathematical ideas, methods and
notions which are otherwise considered completely certain or at least are
widely taken for granted.
Two directions can be identified in the development of intuitionism as
philosophy of mathematics, one emphasizes logical analysis and the other
focuses on notions of idealistic derivation.
My claim in this talk is that intuitionism, in both characterizations,
constitutionally eludes its main philosophical thesis, that mathematics along
intuitionistic lines is possible.
While this is an example of a philosophical thesis which cannot be justified by
philiosophical arguments (the philosophical thesis is justified if actually
intuitionistic mathematical theories are being developed), philosophy could
still contribute to it by critically analyzing basic mathematical concepts and
methdos of intuitionistic mathematics also in relation to the classical ones.
This does not coincide with reducing philosophy to logical analysis or with
offering highly intractable subjectivist conceptions as explanations.