How much did Aristotle understand about numerical sameness (identity)?

According to this lucid and entertaining recent article by Dr. F.A. Muller “Aristotle on Identity: Close Enough!” the answer is: a lot more than he’s usually given credit for.

This is relevant to William Lane Craig’s new strategy for trying to block any unitarian reading of the New Testament (on which the Father = God) as anachronistic, as discussed here. In discussion Craig seems to downplay Aristotle’s grasp of being numerically the same thing as, suggesting it only pops up in a single passage. But this is mistaken. Muller shows how a bunch of insights about identity pop up in several of Aristotle’s works. In part, Dr. Muller writes,

	Aristotle is not only the creator of Syllogistic Logic, and thereby one of the founding fathers of Logic, but also the first to acknowledge the concept of identity and think about it.
	Aristotle distinguished quantitative, achronic identity from diachronic, qualitative identity.
	Aristotle understood statements of numerical identity as expressing that two singular terms co-refer.
	Aristotle advanced, as the first on record, a number of conceptual truths about identity, among which Euclid’s common notion 1 of his The Elements, symmetry, transitivity . . .
	Aristotle held that identity statements imply the substitutivity of the terms in propositions; we propose to call Substitutivity: Aristotle’s Law of Identity.
	Aristotle was aware that his Law of Identity does not hold unrestrictedly: in sentences that contain epistemic propositional attitudes, it fails—this casts a long shadow forward to the discovery of the distinction between extensional and intensional propositions.
	Aristotle advanced co-extensiveness of predicates as a necessary condition for their identity.
	Leibniz’s Substitutivity Salve Veritate Principle is about concepts, not about objects, like Aristotle’s Law of Identity.

You can read and download the whole piece here; I highly recommend it. As a bonus it dunks on the overrated Leibniz.

Another much broader piece covering all Aristotle’s work in logic is this excellent SEP entry by Robin Smith.

It strikes me that Aristotle didn’t say more about identity because he neglected statements about single things, given his drive for general understanding. Even this argument, much discussed since John Stuart Mill, isn’t anywhere in Aristotle’s works.

1. Socrates is a man.
2. All men are mortal.
3. Therefore Socrates is mortal.

It’s a valid argument; never mind that since Jesus’ resurrection 2 has been false, making it unsound.

Back to Craig, I make the point in our forthcoming 4-views book that the concept same-thing-as seems to be a part of the cognitive equipment which is normal to human beings. Thus, that logicians had not yet integrated identity statements into their logical systems does nothing to show that ordinary people in New Testament times lacked this concept. In fact, as I explain towards the end of this episode, we can see people in the New Testament reasoning using the concept of same-thing-as.

And in the final episode in that series I’ll have more to say on this topic, in discussion with Craig.

This is one of Aristotle’s great strengths as a philosopher: starting with common sense, the sorts of things people usually think and say, and trying to organize it all into some coherent understanding. In this work he’s feeling out the contours of a commonly-used concept.