Talk:Identity of indiscernibles

Hack to prove identity of indiscernibles
If you allow arbitrary predicates in the definition of indiscernibility, then identity of indiscernibles is easily proven. Given $$x$$ and $$y$$ such that $$\forall F(Fx\leftrightarrow Fy)$$, one can instantiate $$F$$ as $$\lambda z.x=z$$, and thus we have $$x=x\leftrightarrow x=y$$, which proves that $$x=y$$. I feel like Max Black missed something here, but I'm not sure what.

I think it's probably that if you require $$F$$ to have no free variables, this trick doesn't work, but I feel like "identity of things that are in the same orbit of an automorphism" is too obviously false. NoLongerBreathedIn (talk) 01:05, 16 September 2023 (UTC)