I'm following three threads, now: (i) the status of primary substances in the Categories; (ii) the nature of the investigation in Met. Z; and (iii) how Met. Z contributes to the 'first philosophy' of Lambda. Here is something on that second thread.
Recall that I took a hint from Aquinas in De Ente et Essentia and began to think of Z as asking not, as is commonly supposed, 'What is substance?', but rather, 'What makes something such that it can be sorted?'--it being presumed that substance does that. I said that, according to Aquinas, Aristotle regarded this investigation as suggested by the doctrine of the categories. I gave Aquinas' argument for this, based on the fact of the categories, and I gave an alternative argument, based on the priority of substance among the categories. I said that I saw no evidence that Aquinas' argument was in Z1, but that I did see evidence that the other argument was in Z1.
I want to take that back. I now believe that both arguments are put forward at the opening of Z1. To see that they are requires that we parse the opening of the chapter appropriately. Here is the relevant passage, parsed as I think it should be:
(A) There are several senses in which a thing may be said to 'be', as we pointed out previously in our book on the various senses of words;' for in one sense the 'being' meant is 'what a thing is' or a 'this', and in another sense it means a quality or quantity or one of the other things that are predicated as these are.
(B) While 'being' has all these senses, obviously that which 'is' primarily is the 'what', which indicates the substance of the thing.
(i) For when we say of what quality a thing is, we say that it is good or bad, not that it is three cubits long or that it is a man; but when we say what it is, we do not say 'white' or 'hot' or 'three cubits long', but 'a man' or 'a 'god'.I take (i) and (ii) to provide reasons for the inference from (A) and (B).
(ii) And all other things are said to be because they are, some of them, quantities of that which is in this primary sense, others qualities of it, others affections of it, and others some other determination of it. (And so one might even raise the question whether the words 'to walk', 'to be healthy', 'to sit' imply that each of these things is existent, and similarly in any other case of this sort; for none of them is either self-subsistent or capable of being separated from substance, but rather, if anything, it is that which walks or sits or is healthy that is an existent thing. Now these are seen to be more real because there is something definite which underlies them (i.e. the substance or individual), which is implied in such a predicate; for we never use the word 'good' or 'sitting' without implying this. Clearly then it is in virtue of this category that each of the others also is. Therefore that which is primarily, i.e. not in a qualified sense but without qualification, must be substance.)
But--and this is crucial--I understand (B) to be, not the assertion of the priority of substance (which has been said many times earlier in the treatise), but rather the added idea that this category which is prior indicates 'what' a thing is and that this is called 'substance'. That is, substance is that which makes something such that it is identifiable as a 'what' and can be sorted.
Argument (i) in support of this does seem to be Aquinas' argument. Commentators puzzle over why Aristotle starts talking about the category of quantity here. "Aristotle's object being to distinguish quality from substance, not from the other categories," Ross comments, "'three cubits long' is irrelevant and was suspected by Bonitz. It was, however, read by Alexander, and apparently by Asclepius, and Aristotle is not incapable of such irrelevancies..." Better, I should think, to conclude that Ross is not correct about Aristotle's object. Suppose his object is to make a point about sorting. Suppose he wants to make the subtle and complex observation that, to say anything at all (white, three cubits) presupposes a fundamental act of sorting, viz. into one of the categories; and yet it's not as if all of the categories are on a par, since that which we explicitly recognize as telling us 'what' a thing is gets priority. (Odd, because all the categories tell us what a thing is.)--This, then, would be an argument like that which Aquinas puts forward.--And in this connection the mention of a quantity would hardly be an 'irrelevancy'.
Argument (ii) is the argument that I proposed.
Note, by the way, that if by 'substance' we mean that which makes something such that it can be sorted, then 'substance' would have to indicate some part or aspect of a thing (and so we would want to talk about the substance of a thing) because, clearly, we do not count everything about an individual as relevant to sorting it.