HEYTING CONTRIBUTION TO THE CHANGE IN RESEARCH INTO THE FOUNDATIONS OF MATHEMATICS

After the 1930s, the research into the foundations of mathematics changed. None of its main directions (logicism, formalism and intuitionism) had any longer the pretension to be the only true mathematics. Usually, the determining factor in the change is considered to be Godel's work, while Heyting's role is neglected. In contrast, in this paper I first describe how Heyting directly suggested the abandonment of the big foundational questions and the putting forward of a new kind of foundational research consisting in the isolation of formal, intuitive, logical and platonistic elements within classical mathematics. Furthermore, I describe how Heyting indirectly influenced the abandonment of the old directions of foundational research by making out some lists of degrees of evidence that exist within intuitionism.