I do not think there is a need for Schrödinger to ascertain the insufficiency of the principle of identity.godelian wrote: ↑Sat Jun 25, 2022 2:04 am I personally think that the intuitionist ontology is not particularly helpful. Computing devices can mechanically verify the correctness of a proof, and sometimes even discover proof. These machines do not have intuition.
Restrictions to the law of identity actually do appear in certain types of logic:
Wikipedia on "Schrodinger logics" wrote: Schrödinger logics are a kind of non-classical logic in which the law of identity is restricted. These logics are motivated by the consideration that in quantum mechanics, elementary particles may be indistinguishable, even in principle, on the basis of any measurement. This in turn suggests that such particles cannot be considered as self-identical objects in the way that such things are usually treated within formal logic and set theory.
Everything in the world can provide us with the opportunity to find ourselves facing the limit of indistinguishability.
Zeno's paradoxes themselves show that nothing is ever distinct from all the rest.
However, the questioning of the validity of the identity principle must also use this principle.
Rational thinking necessarily requires it.
Apart from this principle, no definite thought is possible.
But we can intuit its insufficiency, without however demonstrating it rationally.
How could we?
We sense it when we reach the limit of the understandable.
Certainly the computer can prove the validity of a law.
And it can even come up with new laws.
Simply because it processes data rationally. And the more data you process, the easier it is to grasp new relationships between them.
But always in any case in the context of the principle of identity.
The principle of identity seems unsurpassable.
But love knows it is.