HSE Publishing House

This monograph is devoted to the ontology of standard and deviant quantification. It compares the heuristic capabilities and ontological obligations of two paradigms of quantifier interpretation – second-order predicates or functions of choice, traced from their origins (G. Frege and C. S. Peirce) to their current state (abstract logic and IF logic). Its novelty lies in the fact that it provides a philosophical review of the recent years' findings concerning the expressive and deductive power of nonstandard quantification logics. The monograph provides an overview of tools for a logical analysis of language, and for the logical and ontological explication of classical philosophical difficulties caused by a predicative interpretation of existence.