Abstract

The problem of alternative models which arises at the explication of theory of numbers within the set theory is under discussion in this paper. The conceptions of W. Quine, P. Benacerraf and N. White are discussed here in this connection. The new solution of the above problem is suggested which is a modification of Benacerraffs conception through accepting substitutional interpretation of quantifiers. The consequences of admitting the substitutional interpretation are discussed in the paper which relate to the problems of genuine progression, counting and contemporary version of Pythgoreism.