The Position of Intuitionistic Logic on the Principles of Traditional Logic

Mohamed Ghazy Ashmawy Hassanein, Huda; El-Nuahy, Seham; Ali, Hussein

doi:10.21608/buhuth.2021.87019.1164

The Position of Intuitionistic Logic on the Principles of Traditional Logic

Document Type : Academic research papers

Authors

¹ Department of Philosophical Studies -faculty of arts- Ain- shams University

² Department of Philosophical Studies, Women's College, Ain Shams University.

³ Department of Philosophical Studies - Faculty of Arts - Ain Shams University

10.21608/buhuth.2021.87019.1164

Abstract

This paper deals with the position of intuitionistic logic on the principles of traditional logic. The importance of this logic is due to the fact that it is different from traditional logic, as it expresses the views and ideas of the intuitionism, which be appeared as a result of researching into the problem of the foundations of mathematics. That intuitionistic logic is characterized by the non-existence of the principle of the excluded middle being a theorem of the intuitionistic system .That is due to the different concept of mathematical truth in relation to mathematical Propositions, as the proponents of intuitionistic logic reject the idea that truth is the basis of logic and believe instead in the idea of proof. As a result of replacing the concept of proof with the concept of truth, the difference appeared clearly between traditional logic and intuitionistic logic, especially with regard to the concept of negation and double negation. Traditional negation uses a language that relies on the concepts of truth and false, while the used language in the intuitionistic negation relies on the concepts of probability and refutation. One of the main points of controversy between intuitionistic logic and traditional logic is the absence of the rule of double negation at the proponents of intuitionistic logic.

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