Is Numerical Identity Really All It's Cracked Up To Be?

[olivershetler]

I believe that labels are not ontologically innocent. That is, if we label an object, it takes on a position in an abstract space which is different from that of another numerically identical object. For example, if x=y, then x and y are not absolutely identical, though they are numerically identical. This is because there are such things as locational or referential properties. That is, if something is about x, then x has the relational referential property of being the object of something. Therefor, absolute identity is not possible to state, for when one states an identity relation, one must instantiate the object twice. Thus, we can see that numerical identity is almost absolute identity but not quite. Another way to think about this is that there is no way to state a true equivalence relation because, to state a relation is to specify a different between two objects. Thus, identity is a distinguisher as well as an equivalence relation.

[Philos]

That is, if we label an object, it takes on a position in an abstract space which is different from that of another numerically identical object. For example, if x=y, then x and y are not absolutely identical, though they are numerically identical. This is because there are such things as locational or referential properties. That is, if something is about x, then x has the relational referential property of being the object of something. Therefor, absolute identity is not possible to state, for when one states an identity relation, one must instantiate the object twice. Thus, we can see that numerical identity is almost absolute identity but not quite. Another way to think about this is that there is no way to state a true equivalence relation because, to state a relation is to specify a different between two objects. Thus, identity is a distinguisher as well as an equivalence relation.

I think you misunderstand the concept of numerical identity. If you label an object "x", then obviously there is no 'other' object that is identical to that object that you did not label "x."