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
considered. The aim is to emphasize that in asserting that ‘two’ objects
of a certain domain (generally, a non empty set) are the same object,
one becomes committed to the axioms of set theory, since the structures where
these concepts are expressed are generally taken as set theoretical constructs.
Some of the consequences of these points to the philosophical discussion
on identity and indiscernibility in quantum theory are then investigated.
