Cooperative Intuitionism

Intuitionism

Intuitionism and Formalism

The subject for which I am asking your attention deals with the foundations of mathematics. To understand the development of the opposing theories existing in this field one must first gain a clear understanding of the concept “science”; for it is as a part of science that mathematics originally took its place in human thought. By science we mean the systematic cataloguing by means of laws of n...

Anti-intuitionism and paraconsistency

This paper aims to help to elucidate some questions on the duality between the intuitionistic and the paraconsistent paradigms of thought, proposing some new classes of anti-intuitionistic propositional logics and investigating their relationships with the original intuitionistic logics. It is shown here that anti-intuitionistic logics are paraconsistent, and in particular we develop a first an...

Intuitionism - Counting its Blessings

A brief survey of the impact of intuitionistic logic and mathematics on modern practice is presented. The main influence is via the so-called “BHK interpretation” (or “proof interpretation”). By somewhat relaxing the conditions on the notion of proof the familiar notions of ‘realizability’, ‘Curry-Howard isomorphism’ etc. are motivated. Also some attention is paid to the characteristic process ...

Mass Problems and Intuitionism

Let Pw be the lattice of Muchnik degrees of nonempty Π1 subsets of 2. The lattice Pw has been studied extensively in previous publications. In this note we prove that the lattice Pw is not Brouwerian.