Universals and mathematical linguistics

Universals (from Latin “universalis” - general) - general concepts - are a subject matter of logicians since the ancient times. The question of universals represents the eternal issues. The nature of universals was thoroughly studied the philosophers of the Middle Ages. In IX-XIV centuries the scholastics continued the discussion about the essence of universals: do they really exist or are they certain names? The supporters of realism claimed that universals really existed and preceded the emergence of singular objects. Nominalists (from the Latin word ‘nomen’ - name) defended the contrary view point. In the article we emphasize the linguistic aspect. Mathematical linguistics develops methods of learning natural and formal languages. Linguistics, logic and mathematics are closely connected. Besides, there exists psycholinguistics as well. In our paper we consider current difficult sections: logic and linguistics of non-formalized and even non-formalizable concepts, the topic closely adjacent with the one discussed in the book by T.K. Kerimov of the same name. These sections broaden the opportunities of studying complex systems of logic and linguistics. As it was noted by the authors of “Mathematical linguistics” (R.G. Piotrovsky, K.B. Bektaev, A.A. Piotrovskaya) mathematics and a natural language represent semantic systems of information transfer. Moreover, there occurred a verbal analysis of mathematical problems solution. Language universal, a feature common for all the languages, is a kind of generalization of the language concept. The existential assertion of universals gives the opportunity to formulate a more grounded theory and practice of linguistics. The language universal determination is based both on extrapolation and empirical matter.