The knowing mathematician
The author diagnoses a ''new foundational crisis'' in mathematics, caused by external conditions of today mathematical working as well as by problems of the usual set-theoretic foundation, especially its reductionistic tendency. In analogy to two theories in modern physics, relativity and quantum mechanics, he claims that a ''similar dualistic view on the foundations of mathematics is both possible and desirable''. One essential element of such a view must be the inclusion of the (researching) human subject - the ''knowing mathematician''. The author refers to a formalization of such a view, published in \textit{S. Shapiro} (ed.), Intensional Mathematics, North-Holland Publ. Co. (1984). Besides the concept of ''knowability'', ''properties'', instead of extensionally defined sets, play an important role in this theory. The aim is the ''reintroduction of intensional epistemic notions into mathematical practice''.
scientific article; zbMATH DE number 3863153