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Does it make a difference to logic if the law of identity is never true instead of being sometimes true? It seems like when we don't consider the law of identity is not an axiomatic truth, we assume it is never true and therefore logic cannot exist, but is it possible to make a logic based on the fact that the law of identity is sometimes true?

Example, the law of identity applies for most things, but not all things.

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  • I don't know what you mean by the law of identity not being true in some cases. Perhaps you can elaborate on that? If I show you a picture and a mirror or duplicate picture of the same object how are they different? Can I say one is more beautiful than it exact duplicate? If you keep the context identical as well then what you say about one picture must also apply to the duplicate picture. By duplicate I mean 100 percent the same as in the size, color, shape, etc. If I don't know the trut of a proposition I can rely on the law of identity to show the values must be the same. They can't differ
    – Logikal
    Jun 7 at 5:57
  • Again, if an element is selected with criteria, and cannot violate those known criteria, but is able to change in any other way, you can still have all the upside of the law of identity, without having the law of identity. It would not matter whether those other changes are optional or mandatory. Logic still works. You just don't get to pick 'Soctrates' without knowing what type of thing you intend to use him as (e.g. a person, or a collection of atoms.). It removes the artificial illusion of a form of simplicity that was never thee. Jun 7 at 19:27
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When we don't consider something an axiom, this means that we don't require it to always be true. This still allows it to be sometimes true. This is different from and weaker than forcing it to always be false, i.e. having an anti-identity axiom.

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  • Does that mean we can still prove things using the law of identity?
    – Sayaman
    Jun 7 at 13:51
  • No. If it is no longer a law, we can't use it to prove things.
    – lemontree
    Jun 7 at 14:09

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