The Problem of Something in Logic; Gricean Defense of Substitutional Interpretation of Particular Quantifier

Grice puts an end to the disputes between propositional logic and natural language by fully enclosing their respective fields. He employs logic to semantics and natural language to pragmatics. This article claims that with the substitutional interpretation of quantifier, we are in a better position to extend Grice’s idea to cover the predicate logic as well and resolve paradoxes of this field. Strictly speaking, by adding a fifth principle to Grice’s fourfold, this article is aimed to demonstrate how appropriateness of quantified statements in natural language is tied to their implicatures and how it has nothing to do with their truth values. That is, by distinguishing between semantical meaning of quantifier and pragmatical meaning, the author inclines to substitutional interpretation. Likewise, because of the fact that a quantifier is closely related to the proper name, we extend our claim about quantifiers to the field of proper names by drawing on the names that do not name.