Absolute identity seems at first sight to be presupposed in the branch of formal logic called identity theory. Classical identity theory may be obtained by adjoining a single schema to ordinary quantification theory.

I defend a slightly modified version of geach's rule r, I.E., That although both a and b are g, It is possible for a to be the same f as b and a different h than b, Provided that the question whether a and b are the same g is undecidable. Answering those who object to relative identity I claim that they tacitly adhere to a false fregean view, I.E., That one cannot use a singular term to denote an entity (...) x if it is not true that for every y, X=y or not x=y. I show, However, That such terms are, And must be, Used by every empirically oriented language with finite or infinite predicative arsenal, And hence relative identity is more handy than absolute identity. Finally I give a version of leibniz's law for relative identity. (shrink)