Logic

Does "if p=q, then nec(p=q)" hold, if "p" and "q" are intended to denote properties? I am told that it holds. But it doesn't seem to be quite right. It seems to depend on what it is for two properties to be identical. Am I confused?

Comments

If two properties P and Q are the very same property, then how could they have been different? One could, indeed, have discussions about what it is for P and Q to be the very same property. But, if true identities are always necessary, then that fact acts as a constraint on theories of property identity. For example, suppose someone suggested that properties are the same just in case they are (actually) true of the same things. Then it would be an objection to this view that there are properties that are true of the same thing but might not have been.

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