Aristotle on the Transcendentals

MICHAEL J. LOUX

n this paper, I want to examine two claims found in Aristotle's Metaphysics : (A) the claim that notions like being and unity do not constitute genera and (B) the claim that such notions are not univocally predicable of all things. I want, in particular, to consider the view (expressed by Porphyry, William of Ockham, and J. L. Ackrill) that (A) entails (B). I shall argue that the alleged entailment cannot hold since while (A) is true, (B) is false.

I

The claim that neither being nor unity can function generically is discussed in a number of places. The most detailed discussion of the thesis is found in Metabhysics B 3, 998 b 22-27, where Aristotle says :1

But it is not possible that either being (Tb 6v) or unity (ib guv)should be a single genus of things, for the differentiae of any genus must each of them have being and be one (xai elvoctxat clvai) but it is not possible for the genus taken apart from its species (any more than for the species of the genus) to be predicated of the differentiae, so that if unity or being is a genus, no differentia will either have being or be one (ours 8v

Aristotle is fairly explicit about the leading premise of this argument. The premise is (1) Genera are not predicable of their differentiae. For Aristotle, a genus is a kind or sort whose members belong to a variety of less general kinds or species. (1) Tells us that a genus is not predicable of the characteristics by which its species are distinguished. Provisionally, we can take Aristotle to be referring to true predication in (1), to be saying that propositions of the form 'D is a G' (where 'G' and 'D' range over genera and their differentiae, respectively) are never true. Aristotle's use of (1) to derive (A) is straightforward. He asks us to assume that being and unity are genera. Qua genera, they must have

225 differentiae; and, by (1), they cannot be predicable of these differen- tiae. Aristotle claims, however, that being and unity are predicable of every notion that could serve to differentiate them into species. Thus, we have a contradiction, and the assumption falls. But why is it that being and unity are predicable of all possible candidates as differentiae? Aristotle's response, I take it, is that being and unity are universally predicable notions. For Aristotle, 'being' and 'one' are terms that hold true of every item in every category; they are what the Medievals called transcendental terms and what I shall call T-Words. Once we expose this point, it becomes clear that the argument in Metaphysics B 3 extends beyond being and unity. Aristotle deals with these notions because, in his account, they are the most important (or only) transcendentals; nevertheless, it is best to construe the pas- sage as incorporating, if only implicitly, a general argument against all transcendental genera. Viewed in this way, the argument focuses on the claim (2) Some transcendental (Call it 'T' ) is a genus. Structurally, the attack on (2) takes the form of a reductio. Thus, from (1) and (2), we can derive (3) T is not predicable of its differentiae; but since, by (2), T is a transcendental, it follows that (4) T is predicable of its differentiae, so that (5) (2) is false, or, more perspicuously, no transcendental is a genus. This argument hinges on (1) ; and when we confront it with examples, (1) seems true. Thus, 'Rationality is an animal' and 'Being three sided is a figure', are, in accordance with (1), both false. But while these examples confirm (1), they do not provide the sort of insight we are likely to demand. For a more detailed defense of (1), we must turn to Topics VI 6, 144 a 32-b 1, where Aristotle says : Again, see if the genus be predicated of the differentiae; for the general view is that the genus is predicated, not of the differentia, but of the objects of which the differentia is predicated. Animal (e.g.) is predicated of man or ox or other walking animals, not of the actual differentia itself which we predicate of the species For if animal is to be predicated of each of its differentiae, then animal would be predicated of the species several times over; for the differentiae are predicates of the species.

The claim here is that if we assume the negation of (1), an undesirable

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