From the Foundations of Protothetic

Abstract

My system of the foundations of mathematics ... consists of three deductive theories, whose union forms one of the possible bases of the whole structure of mathematics. The theories in question are the following: (1) What I call Protothetic, which is the result of a certain peculiar enlargement of the wellknown theory which goes by the name of the ‘propositional calculus’, or ‘theory of deduction’. (2) What I call Ontology, which forms a type of modernized ‘traditional logic’ and which most closely resembles in its content and power Schröder’s ‘logic of classes’, regarded as including the theory of’individuals’. (3) What I call Mereology, whose first outline was published by me in a work of 1916 entitled [Foundations of a general set theory I. ¹]