Principle of Identity

First off, what is it?

It can’t be reduplication or a generalization of saying an apple is an apple. This makes it a mechanical act which hits no term. You might as well say an apple is an apple is an apple is an apple is….

We need something stronger than “is”, since the principle is uninteresting as a matter of fact (oh look, that apple is still an apple! Let’s check again in twenty minutes, ‘kay?) It only becomes interesting for reasoning as indicating necessity, e.g.

The same thing must be itself. 

(Where “same” has the same scope as in the principle of contradiction, sc. when it refers to the same time, in the same part, in the same respect, etc.)

So taken, we avoid mechanical repetition of predicates and get a principle that does real work, like in this the last sentence of this argument from St. Thomas:

[W]hen I say, “What the soul understands is immaterial,” this is to be understood that it is immaterial as it is in the intellect, not as it is in itself. Likewise if I say, “If God knew anything, it will be,” the consequent must be understood as it is subject to the divine knowledge, i.e. as it is in the present time when it is happening (presentalitas). And thus it is necessary, as also is the antecedent: “For everything that is, while it is, must be necessarily be,” as the Philosopher says in Peri Herm. i.

ST. 1. 14. 13 ad. 2

Whenever a thing is, when it is, must be. That is, the same thing must be itself. To say that is not a vacuous repetition, but an interesting statement about what it is to be at all. It turns out that same is contrary to contingency. There is a whole theology in that.

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