Identity Theory, Indiscernibility, and Philosophical Claims

The standard ways classical logic and mathematics deal with the concept of indiscernibility (indistinguishability), with special emphasis to the concept of indiscernibility in a structure are taken into account. It is emphasized that in asserting that ‘two ’ objects of a certain domain (generally, a non empty set) are the same object, one is committed to the axioms of set theory, since the structures to be considered are set theoretical constructs. Some of the consequences of these points to the philosophical discussion on identity and indiscernibility are also investigated.