СЕМАНТИЧЕСКИЕ АНТИНОМИИ

Antinomies, Semantic

Semantic antinomies arise in propositions whose object is expressions of a certain language. A representative of one of the main types of semantic antinomies is the liar antinomy, which is credited to Eubulides of Miletus (4th century B.C.). It can be formulated as follows: [The sentence in square brackets on this page is false.] If this proposition is true, then from its content it follows that it is false. But if it is false, then again it follows from its content that it is true. Thus, in violation of the logical law of contradiction, this proposition proves to be both true and false.

Another example of semantic antinomies is the antinomy of Grelling, based on the concept of the "heterological predicate." A predicate, i.e., a word expressing a certain property, is called heterological if it does not possess this property (for example, the word "tetrasyllable" is not tetrasyllable). An antinomy arises when applying this definition to the predicate "heterological": if it is heterological, according to the definition it does not possess the property it expresses, i.e., it is not heterological; if it is not heterological, then again, according to the definition, it must possess the property it expresses, i.e., it is heterological.

Antinomies of this kind arise in cases when the language in which the antinomy is constructed contains names for its own expressions and also predicates such as "true," "false," "heterological," etc. There are different methods for excluding semantic antinomies: one of them is to differentiate between a metalanguage and an object-language and to define corresponding predicates strictly in a metalanguage.