1. The Identity of Indiscernibles: If two things have all their properties in common, they are identical.
2. The Indiscernibility of Identicals: If two things are identical, they have all their properties in common.
THESIS: there is no application of these principles that is not implicitly epistemic, and self-refuting.
I used to think that both of these principles were acceptable. Or that perhaps (1) was acceptable, but not (2). But upon further thought, both are problematic if "have all their properties in common" is read as "are indiscernible." Having all properties in common with something is not equivalent to being indiscernible from it. Indiscernibility is an epistemic notion. As an epistemic notion, it is incomplete until the perspective of the discerner has been specified. (It makes a difference whether we're talking about things being indiscernible to God, or to me; and it might make a difference what else I know about the entity in question.) Thus Descartes's use of (1), which turns not on shared properties but on indiscernibility from his perspective, is not legitimate.
For uses that do not on indiscernibility from a perspective, (1) seems fine. But it also seems like a principle that will never be used, as no two things have all their properties in common--unless what we really mean to say is that what seem, from some perspective, to be two things, have all their properties in common. But if that's the case, they only seem to have some properties in common: there are sufficient differences for them to seem to be two things in the first place. There won't be any such "two things" ("two things" should be put in scarequotes).
Non-epistemically motivated uses of (2) are equally impossible to apply. We're never going to encounter TWO THINGS that have all their properties in common. We might encounter what seem to be two things but are actually one, which have all their properties in common except seeming to be two things. This is an epistemic interpretation of (2), and it refutes itself. In seeming to be two things, the "two things" do not have all their properties in common. They have sufficient difference to seem to be two.
The purely metaphysical version of (2) might also be false in quantum physics: if, in quantum physics, the same thing can be in different places at once, (2) is false for whatever sort of thing has that ability.
To do the work philosophers want to put them to, both (1) and (2) need to include epistemic notions. But they can't. The purely metaphysical versions are not much use.