Aristotle vs. Boole: A case of the Universe of Discourse

Abstract

K arel Šebela Faculty of Arts Palacky University Olomouc Křížkovského 12 771 80 Olomouc karel.sebela@upol.cz abstract I will present a case study comparing Aristotelian and modern predicate logic. The traditional square of opposition embodied certain relations between propositions. When rewritten into the language of modern logic, the relations embodied in the traditional square mostly disappear. As a matter of fact, some conservative versions of predicate logic, namely sortal logic, preserve relations in the square. I will argue that the explanation of the fact is that modern logic accepts the socalled principle of wholistic reference. The principle was stated initially by Boole with respect to his concept of a so-called universe of discourse. According to the principle, each and every proposition refers to the universe of discourse as such. The difference between Aristotelian and modern logic will thus be portrayed as a difference in the concept of what are we talking about in the universal propositions.*