ABSTRACT
Platonic and Aristotelian logics were generated out of natural language. The classical logician claimed to discover in language the conceptual relations necessary for formal relations or the grammatical regularities allowing syllogistic manipulations. Classical logic, even when algebraicized by logicians such as Boole, retained a linguistic analysis of sentence structure which would always resist mathematical thought. In order to find a logic in which mathematical and scientific truth can be expressed, it is necessary to be critical not only of the formal relations insisted upon by logicians and grammarians, but also of language itself. The seemingly irreducible distance between the notation of arithmetic and notation of logic is closed. Logic offers the only approximation of understanding: a thought from which personal differences are erased, a thought which exists apart from any individual and which is graspable by all. Logic makes possible the only kind of communication possible, a communication in which what is to be said is fixed beforehand.
