Abstract: Geach defended the thesis of relative identity according to which, for any theory there is an extension, in whose language the meaning of the identity sign does not coincide with the meaning of the identity sign in the original language. The argument fails for formalized languages, since the interpretation of a first-order language demands that a domain be specified for the variables, and in doing this we specify the finest possible interpretation of the identity sign. Yet an analogous question for natural languages is whether for any expression of restricted generality (such as `every A’ or `some A’) there is a definite identity-relation associated with the range of generality. Geach's thesis fails for natural languages, too, and furthermore, it is dependent upon the failure of the thesis for formalized languages.

Keywords: domain restriction, Geach, identity, quantification, Quine, relative identity,