Çelişkilere Dönüş: Łukasiewicz İtirazı

Abstract

The Principle of Non-Contradiction is found and christened as “the firmest principle” by Aristotle. Since then, almost no objection has been raised against this principle and its firmness, until Łukasiewicz. By reflecting on the possibility of the emergence of new systems of logic with reference to the developments in non-Eucledian geometry, Łukasiewicz stated that the reconsideration of the principles of logic may lead to new systems. With the guidance of this idea, in his revolutionary work “On the Principle of Contradiction in Aristotle” Łukasiewicz approaches Aristotle’s account on the Principle of Non-Contradiction and analyzes it thoroughly. Starting with the identification and the comparison of three distinct definitions of the Principle of Non-Contradiction in Metaphysics, the Polish logician criticizes Aristotle’s arguments regarding the unprovability and the firmness of the principle. Even though Aristotle defended that the principle cannot be proved by direct proof but can be proved by indirect ones, i.e. elenchus, Łukasiewicz realizes that Aristotle’s aforementioned distinction is actually built on sand, since the Stagirate had stated in Prior Analytics that these two types of proof can be used interchangeably. This statement means that there is no err in using direct proofs instead of elenchtic ones and thus it appears that if the principle can be proved by elenchus, it can be proved by direct proof as well. In other words, Aristotle runs into a contradiction by trying to prove the principle that cannot be proved. Having found that there lies a contradiction in the very foundations of the Principle of Non-Contradiction regarding its unprovability, he continues with scrutinizing Aristotle’s elenchtic proofs in Metaphysics. With the discovery of fallacies appealed by Aristotle in those proofs, Łukasiewicz is ready for raising his objection to the firmness of the Principle of Non-Contradiction. Starting with stating how contradictions were defined before and by Aristotle, how the Stagirate formulated the Principle of Non-Contradiction, our study aims to examine Łukasiewicz’s objection and summarize his arguments against the Principle of Non-Contradiction.