On the Logical Information of Analytic Sentence

Abstract

In this paper I shall define the concept logical information distinguished from a customary concept (semantic) information, which is called "factual information" in the paper. In accordance with the contemporary theory of semantic information, if i is an analytic sentence, then i conveys no information. It means that
inf (i) = -log m (i) = 0
where i is an analytic sentence and inf is the measure of information. According to our intuition, however, it seems that most analytic sentences convey much more information than "A is A", which is a trivial analytic sentence or tautology. I shall give only one example here.
1. Man is man. (S1)
2. Man is a rational animal. (S2)
Let us suppose that the both sentences Si and S2 are analytic. Then S2 has the same intention, and hence conveys the same amounts of factual information, as S1, whereas S2 has the more complicated intensional structure, and hence conveys much larger amounts of logical information, than S1.