Abstract

This paper examines two logical principles that combine modality with quantification and with identity: a weaker version of the converse Barcan formula, and the principle of the necessity, not of identity, but of distinctness. It is argued that there are conceptual assumptions that lie behind and help the independence of these principles, and a semantics with some conceptual interest that invalidates them. A qualified converse Barcan formula is discussed. It is shown that the necessity of distinctness is an independent principle, even in a theory that includes the qualified converse Barcan formula.