論理学とはなにか (完)

Abstract

A partially ordered set is represented by a Hasse's diagram. A lattice, a kind of a partially ordered set is represented by it too. In this paper, (1) classical propositional logic, modal logic, many-valued logic, and quantification logic is represented by a Hasse's diagram as a complemented distributive lattice (a Boolean lattice), (2) intuitionistic logic is represented by it as a pseudo-complemented distributive lattice with a minimum, and (3) Minimal-Logik is represented by it as a pseudo-complemented distributive lattice without a minimum. The logic of classes, Plato's diairesis, Kant's analytic judgement, the theory of classification, Aristotle's syllogistic, Leibniz's logical calculus, analysis and synthesis in the Port-Royal logic, Lull's ars combinatoria, Leibniz's combinatory art, Plato's theory of "analogia", the theory of Polarity, the theory of I'Ching, Piaget's group are represented as a Boolean lattice or a truncated part of it. At last the mystical logic is discussed.