形式論理学の哲学的位置

Abstract

1 Criticism on logical formalism. Carnap asserts that the system of symbolic logic is not a theory, but a language, and signs remain uninterpreted in pure logic. Wittgenstein says that the propositions of formal logic tell nothing about objects. Does formal logic really say nothing about objects? A connector 'and' is a conjunction of two propositions, and at the same time it denotes a kind of ontological relation between two objects, that is, it says something about these objects. Syntax and semantics are two aspects of a formal language. A language without semantics is not language at all. 2 Dialectical logic and formal logic. Fogarasi's criticism of symbolic logic from the standpoint of dialectical logic is rather superficial. Klaus thinks that dialectical logic deals with the necessary relation of propositions, whereas formal logic deals with the propositions which have no necessary relation with each other. And so he sharply distinguishes the latter from the former. But his distinction is not correct. Formal logic deals with both necessary and unnecessary relations of propositions. Ordinary formal logic is two-valued, hence any two propositions of the same truth-value are equivalent even if there is no necessary relation between them. To avoid such non-necessary connection of propositions logic must be infinite many-valued, and the infinite many-valued logic is a discipline of formal logic. Authoritative distinctions between two logics have been propounded by Engels and Lenin. Engels says that dialectical logic is a deductive system but formal logic is not. This distinction, however, applies only to traditional logic. Today's formal logic is a deductive system. Lenin says that dialectical logic deals with the law of development. It is sure that formal logic does not contain any law of this kind. But this does not mean that formal logic can not deal with the law of development at all. We may invent a new formal logic which enables us to formalize propositions essentially containing temporal element or dynamical structure in themselves. Sequential propositional calculus could probably be regarded as one such logic. 3 Characteristics of modern logic. In the theory of logic we find two types of logic: ancient and modern logic. Euclidean Geometry and Newtonian Physics would be typical examples of the theories which were built up on the bases of these two types of logic respectively. Contemporary systems of formal logic, however, are by and large a kind of ancient logic which, as far as its formal structure is concerned, is supposed to cover only the timeless or static aspect of our objects. It is largely the task of future formal logic to formalize the modern kind of logic. The leading characteristics of modern logic would be as follows: (1) temporal and dynamic, (2) quantitative (Qualities are reduced to the difference of quantities.), (3) continuous (Continuousness of quantity frees us from Zeno's paradox.), and (4) directional (Vector analysis is a powerful method of dynamics).