The Paradox of Definition in the Deductive Theory
The article investigates the philosophical difficulties associated with the definition of terms in a deductive theory. Trying to replace in some context some expression of its definition leads to loss of some information or, conversely, to the emergence of new information. The concept of identity definiendum and definiens in natural languages leads to logical paradoxes and semantic difficulties. As a solution to the paradox of definition two approaches, which use the concept of semantic information, are requested: the theory of semantic information of Y. Bar-Hillel and R. Carnap and the theory of surface information and depth information of J. Hintikka. The article explains the effectiveness of the solution to the paradox for the first-order languages and the impossibility of such solution for natural languages. Coping with the paradox of analysis is only possible in the case of creating a new artificial language. In these decisions the principle of interchangeability of identical expressions work with certain limitations, and criteria of definability and reducibility of terms become relevant.