  Leśniewski intended to a formulate the full logical system that would serve as the basis for the whole of science, and in particular for mathematics. This system consists of three parts (a) protothetic (a generalized propositional calculus); (b) ontology (a logic of terms); (c) mereology (a theory of parts and wholes). Protothetic is a calculus in which quantifiers bind propositional variables and variables referr to arbitrary functors constructible over the usual functors: that is, functors of propositional variables, functors of functors, etc. In general, if we start with the category of sentences alone, protothetical quantifiers bind variables of all further definable categories. The shortest axiom of protothetic (written in the Russell-like symbolism) is the formula