I'm making a distinction about what identity is bound to and how it is bound. The way our brain presents the world to us it seems as if the things themselves 'have' identities, but it is some function that is being computed in our brain that makes those things distinct from each other. It is the structure of the function that gives distinctness. This inverts the question of whether things 'have' distinct identities, into whether it is possible to find a function that can distinguish between any set of things. My point about failure was that all identities as we think of them are something like a hash function with finite length, there is always a chance of collision and it is important to know how they fail. For example, if you pick primary DNA sequence as the definition for identity, then your functional will fail for all identical twins. If you pick some metric on facial structure as measured by a 2d camera, then anything that can evoke the same pattern on the sensor of the camera will be indistinguishable, even a picture of your face. This is not because these things do not 'have' unique identities, it is because the function we choose was bad. Proving that there is no function that can distinguish between two things is exceedingly difficult.

A has no identity. B has no identity. C has no identity.

But perhaps {A, B, C} can have identity?