## The three logical systems of Leśniewski

This guy was a student of Łukasiewicz, who famously established ternary (and then later, multivalued) logic as an alternative to the binary which prevailed since Aristotle's time. I didn't know about the three logical systems here, though, and they bear further study:

The distinctive and original contribution of Leśniewski consists in the construction of three interrelated logical systems, to which he gave the names, derived from the Greek, of protothetic, ontology, and mereology. The logical basis of the whole theory, and hence its name (prōtos, “first”), is provided by protothetic, which is the most comprehensive theory yet developed of the relations between propositions. The other two systems are based on a distinction the lack of which, Leśniewski claimed, was the source of Russell’s difficulties with the antinomies: that between a distributive and a collective class. In its distributive use, a class expression is identical with a general name; thus, to say that a person belongs to the class of Poles is to say that that person is a Pole. Hence, ontology (on, “being”) is the logic of names; and, combined with protothetic, it yields all of the theorems of syllogistic (traditional Aristotelian logic) and of logical algebra, as well as of the logic of sets and relations. Mereology (meros, “part”) is the logic of a whole conceived as though physically constituted by its parts—i.e., of the collective class, as the class of all automobiles in Chicago consists of the entire collection of them. Hence, mereology is a general theory of the relation between part and whole.

Posted in Mathy Stuff on Aug 08, 2017