The intuitionism and the problem with non-constructive proofs

Abstract

This article aims to evaluate the intuitionist problem with non-constructive mathematicals proofs. For this constructivist position the principle of the excluded middle, of classical logic, shouldn't operate on mathematical demonsrations. Non-constructive proofs aren't accepted, and the constructive proofs are the only with positive character. After a brief introduction about intuitionism and its creator, the article will address the relationship between the principle of the excluded middle and the mathematicals demonstrations, so to talk about the problem of non-constructive proofs and the consequences for not to accepting them. Taking the mathematics only as a mental construction project, the intuitionism break with the dominant platonic realism and establishing a fruitful debate on the foundations of mathematics.