The law of identity is rather simple, so I feel like there can be absolutely nothing that can contradict it or suggest it to be false, it's like a tautological truth that doesn't say anything. But is this true? Is there any exception that proves or suggests that the law of identity not always apply, especially in an intellectual discipline or in the real world?
Regarding the Law of Identity, Leibniz formulation "A is A" (of a very old idea) encapsulates a basic idea that something is itself and seems trivial and incapable of being contradicted. It is a tautology of proposition rather than a tautology of inference. In that regard there are no exceptions.
I think the general purpose of it's formulation, however, is not to challenge the mind with a deepity, but prove an axiomatic basis when considering whether or not two things are equivalent. In many philosophical cases, it may be hard to determine whether two things fulfill the proposition "Everything is itself". For instance, consider the philosophical problem of Ship of Theseus. The question asks, is the ship itself if all of the parts are replaced over time? Let S be the ship. Then is it true "S=S" has more than one tenable answer (to paraphrase):
- The ship is the ship. (T)
- The ship isn't the ship. (F)
- No ship is ever the same ship twice. (implies F)
- There is no ship. (neither T nor F)
In essence, while the statement seems trivial, it raises question of what it means to be identical, and that is difficult even with physical objects. What about questions of identity regarding abstractions? Are you actually you?