Universal, not Universal

In an effort to start my blog by jumping right into a hot topic everybody is talking about, I’ve decided to write about two conflicting twenty year old solutions to a logical difficulty in a 2400 year old book.

The problem is this: in Aristotle’s Metaphysics vii, Aristotle says things that lead one to the logical conclusion that substance is a universal, then turns around and claims in vii.13 that substance is not a universal.

Daniel Graham (1987) and Frank Lewis (1991) offer different solutions to this problem, which I think are interesting in a couple of regards.

Graham’s identification of the problem is part of his thesis that the ontological framework of the early work of Aristotle in the Organon is “incommensurable” with the ontology of the later works (he calls the two “systems” S1 and S2 respectively).

Here’s how Graham sees the problem. After arguing that species is essence which is form which is substance, and despite the fact that his conception of form and essence require that those be universals, Aristotle argues in vii.13 that universals cannot be substance (Graham 1987: 252). He applies the substance criteria to the concept of the universal, and determines that the universal is ruled out as potential candidate for substance (Graham 1987: 253). Aristotle recognizes this difficulty at 1039a14-23 (Graham 1987: 254).

Graham argues that at this juncture in Aristotle’s argument it would make sense for the philosopher to jettison the requirement that substance cannot be a universal, but instead Aristotle argues the opposite (Graham 1987: 255). Graham’s diagnosis of the source of the contradiction of substance as universal and not universal is that the requirement that substance not be universal is an out of place holdover from S1­, which has no grounding in the S2 ontology (Graham 1987: 261). Graham takes this as support for his Two Systems Hypothesis.

Lewis seems to express broad agreement with Graham on the nature of the consistency problems of Metaphysics vii, but views the problem as resolvable internally, using the conceptual resources of the Metaphysics itself.

The problem as Lewis sees it is the following (310-11):

For primary substance, Aristotle is committed to the thesis that for any x, if x is a substance then x is not a universal, or, formally:

(x)(Substance (x) → ~Universal (x))

But Aristotle is also committed to:

(x)(Form (x) →Species (x))
(x)(Species(x) → Universal (x))

And therefore he must hold that (x)(Form (x) →Universal (x)) by transitivity and modus ponens.

But given that Aristotle also holds that (x)(Substance (x) → Form (x)), he must hold that (x)(Substance (x) → Universal (x)).

So we have a contradiction. A logical consequence of his views on form, species and universals requires that substance be a universal, but his explicit view is that substance cannot be universal.

Graham contends that this contradiction is irresolvable, and that Aristotle’s problem is generated by carrying over the “non-universal” criterion for primary substance from the S1 ontology to the S2 ontology, and that the solution would be to discard this assumption. Lewis’s solution to this contradiction, by contrast, is one that offers Aristotle a way out by modification of the way substance is predicated. Instead of being a one-place predicate, whereby some x is a substance simpliciter, in Lewis’s view the terms “substance” and “universal” come to stand for two-place, relations in the Metaphysics ontology. Substance is “substance-of” and universal is “universal-to”. Something can be universally predicated of another only if it is not the substance-of that very same thing.

Formally this is expressible as

(x)(Universal-to(x, y) → ~Substance-of (x, y))

Thus a form can be universal-to a particular bit of matter, so that, Universal-to(F, m); in this case the form would not be the substance of the matter, but would instead be the substance of a compound particular, c so that Substance-of (F, c). In this way, Aristotle can avoid the contradiction by saying the non-universal requirement is simply modified as relations of forms to different entities. Since the compound is not identical to the matter, the form Man could be the substance of Socrates, and predicated of (universal to) Socrates’ matter.

The solution is appealing, since it would allow us to avoid attributing what would appear to be an egregious and obvious contradiction to Aristotle, but it does have the consequence of eliminating the prospect of being able to fully reconcile the ontological framework of the early metaphysics of the Categories with the later ontology of the Metaphysics. In the earlier work, Aristotle allowed as primary substances only those entities that become hylomorphic compounds in the later work; it is particular men or horses that have primary claim to substance-hood, but in the later work, those entities have something which is more primary predicated of them as the “substance-of” them. So it seems that even Lewis’ solution is at least potentially supportive of Graham’s hypothesis.

One curious aspect of this solution, however, is that if the substance-of relation is to be considered as a distinct metaphysical relation, then if F is the substance-of something, then it is the substance-of something of which F is itself already a component. I have difficulty making sense of this. Normally we think of relations as between two distinct things (with the exception of the identity relation) so I’m unclear how this relation should be conceived.