Information Semantics and Antinomies

Abstract

Among logicians and linguists there are long standing widespread opinions about the foundations of semantics which, like any other scientific opinion, should be scrutinized in the light of recent advances. According to one of the opinions in question, to keep a sharp distinction between a language and its metalanguages is necessary under the penalty of contradictions. The second opinion is that there is a substantive difference between the semantical antinomies and the set theoretical antinomies. To exemplify, the liar’s antinomy is considered semantical (it supposedly confuses a language with its metalanguage) but Russell’s antinomy is viewed as set theoretical (as it allegedly deals with the concept of a set). The third opinion to be critically examined holds that there is a sharp cleavage between syntax and semantics of a language. According to this view, syntax should determine all well formed sentences independently of any semantics. Only after that does semantics assign values to the well formed sentences and to their parts. Finally, among logicians, there is a suspicion that a natural language is doomed to trouble, inconsistencies, unresolvable ambiguities. Montague and others have done a great deal to allay some such fears but further defence of natural language and its own logic is needed.