مجلة المقدمة للدراسات الانسانية و الاجتماعية

From Truth To Proof: Intuitionistic Logic And The Limits Of Classical Reasoning

Auteurs : Bouzidi Naim .

Résumé

This paper examines the fundamental divide between classical and intuitionistic logic, emphasizing their distinct epistemological foundations. Classical logic assumes that mathematical truths exist independently of proof, preserving truth across inferences. In contrast, intuitionistic logic, rooted in Brouwer’s constructivism, maintains that a proposition is valid only if it can be constructively proven. The paper explores Brouwer’s ontological justification, where mathematics is viewed as a mental construct, rejecting truth beyond provability. It then discusses Heyting and Kolmogorov’s epistemic interpretation, redefining logical connectives in terms of problem-solving. The rejection of the law of the excluded middle in intuitionistic logic underscores its focus on proof availability rather than abstract truth. Ultimately, this study argues that classical and intuitionistic logic serve different roles, reinforcing logical pluralism. Their coexistence is not contradictory but reflects different approaches to mathematical reasoning, emphasizing either truth or constructive proof.

Mots clés

Mathematical Truth ; Constructive Proof ; Intuitionistic Logic ; Brouwer-Heyting-Kolmogorov