A Proposed Refinement in Devereux's Argument

I said yesterday that there were difficulties in Devereux's interpretation of Z 3. Before criticising that interpretation I want to clarify it, because I think Devereux misconstrues his own interpretation Aristotle's argument, by introducing an unnecessary premise.

Recall that what is at issue is the following passage:

Matter is that which in itself is neither a particular thing nor a quantity ... for there is something of which each of these is predicated, but whose being is different from the being of any of them; for while the other things are predicated of substance, this is predicated of the matter ... nor is it the negations of these, for these will belong [to it] incidentally.

Devereux argues that 'substance' and 'this' (in the above passage) must indicate one and the same thing, and that it is a concrete substance. If it isn't (Devereux says) then it isn't true that 'each of these' gets predicated of the ultimate substratum as (Devereux claims) Aristotle's argument requires. "Aristotle needs to say that it is the 'same thing' that both underlies the attributes and is predicated of the matter," Devereux writes, because otherwise we do not "get the desired conclusion that both the attributes and the substance of which these are predicated are predicable of one thing, the matter."

That is, Devereux thinks it is crucial for his interpretation that 'the other things' predicated of 'substance' are predicated also of the ultimate substratum. That is why he introduced a transitivity principle, which he said was only implicit in the argument: "If X is predicable of Y, then whatever is predicated of X is predicated of Y".

But to see that this principle is unnecessary, we should consider what Aristotle wishes to show in this passage of Z 3. What he wishes to show, as Devereux agrees, are two claims:

(i) Every existent besides the ultimate substratum is not a substance; and yet
(ii) The ultimate substratum is either nothing or akin to nothing, because it is not anything predicated in any of the categories.

In order for Aristotle to reach (i), he needs to show merely that every existent besides the ultimate substratum is predicable of something or other. Why? Because by the Hypokeimenon Criterion ("a substance is that of which other things are predicated but which is not predicated of anything else") anything predicated of anything else at all would not be a substance. Thus, if the 'other things' are predicated of something, S, this suffices to show that these are not substances, whether or not these 'other things' are by some transitivity principle also predicable of the substratum. (This almost looks like a Quantifier Shift mistake on Devereux's part, and that he is confusing 'everything besides the ultimate subtratum is predicated of something' with 'there is something of which everything besides the ultimate substratum is predicated'. Only the former is needed for the argument, not the latter.)

Again, to establish (ii), Aristotle needs to show that the ultimate substratum is not anything in any of the categories. Now if something F is predicated of the substratum, Aristotle gives us an argument for establishing that the substratum is not F: the 'being' (einai), he says, of the substratum is different from that which is predicated. However, if something is not predicated of the substratum, Aristotle needs no argument to show that it does not belong to the substratum, because that is already presupposed in its not being predicated of the substratum! E.g., if Socrates is wearing a red hat, and 'red' is therefore predicated of the hat, no argument is needed for showing that, nonetheless, Socrates is not red--because it's his hat, we said, which is red. Similarly, if the 'other things' (in the passage above) are predicated of something, S, which is not the ultimate substratum, then, no argument is needed for showing that these other things do not belong to the substratum. That will be the case, whether or not S is predicable of the substratum.

(This looks like the confusion of a necessary with a sufficient condition: It suffices, to show that the substratum is not some existent, to argue that: that existent is predicated of the substratum, and the substratum is different from anything predicated of it. But it is not necessary to argue in this way, because obviously there will be all kinds of things that won't be attributable to the substratum on other grounds.)

Thus, Devereux should restate his argument in the following simpler form:

1. Unless Aristotle is supposing that (what he calls) 'substance' and 'this' (in the above passage) is predicated of the ultimate substratum, then Aristotle fails to establish (i).
2. (What Aristotle calls) 'substance' and 'this' (in the above passage) is a concrete substance.
3. Thus, Aristotle is supposing that a concrete substance is predicated of the ultimate substratum.