At 998b22 of his Metaphysics, Aristotle argues that being cannot be a genus. Thomas Aquinas gives his version of the argument in Summa Contra Gentiles, Book I, ch. 25, para. 6. I find the presentation of the doctor angelicus clearer than that of the philosophus. After quoting Thomas' argument, I will offer a rigorous reconstruction and explanation of it. The argument issues in an important conclusion, one highly relevant to my running battle with the partisans of the 'thin' conception of being.
The Anton C. Pegis translation reads as follows:
Now, that being cannot be a genus is proved by the Philosopher in the following way. If being were a genus we would have to find a difference to contract it to a species. But no difference shares in the genus in such a way that the genus is included in the notion of the difference, for thus the genus would be included twice in the definition of the species. Rather, the difference is outside what is understood in the nature of the genus. But there can be nothing that is outside that which is understood by being, if being is included in the concept of the things of which it is predicated. Thus, being cannot be contracted by any difference. Being is, therefore, not a genus. (127)
Quod autem ens non possit esse genus, probatur per Philosophum in hunc modum: Si ens esset genus, oporteret differentiam aliquam inveniri, per quam traheretur ad speciem; nulla autem differentia participat genus, ita scilicet quod genus sit in ratione differentiae; quia sic genus poneretur bis in diffinitione speciei. Sed oportet differentiam esse praeter id quod intellegitur in ratione generis. Nihil autem potest esse quod sit praeter id quod intelligitur per ens, si ens sit de intellectu eorum de quibus praedicatur; et sic per nullam differentiam contrahi potest. Relinquitur ergo quod ens non sit genus.
I think it best to reconstruct the argument as a reductio ad absurdum. In such a style of proof one attempts to derive a contradiction (a logical absurdity) from an assumption together with premises that are believed by the producer and the consumers of the argument to be incontrovertible. The emergence of a contradiction shows that the assumption is false.
1. Being is a genus. (Assumption for reductio)
2. A genus is 'contracted' or specified to a species thereof by a specific difference. To employ the classical example, the genus animal is contracted to the species man by the difference rational. Every man is an animal but not conversely. What distinguishes man from the other animals is rationality.
Therefore (from 1 and 2)
3. If being were a genus, then being would have various species, and a given species S of being would be distinguished from the other species of being T, U, V, etc. by a specific difference that all and only the members of S would possess.
4. No genus is included in the specific differences that differentiate the species of the genus in question. For example, animal is not included in the difference rational. By sheer analysis of the concept rational one cannot extract the concept animal. For there is nothing in the concept rational to demand that anything that is rational also be an animal. And, as Aquinas points out, if animal were included in rational, then the genus animal would be included twice in the definition of the species man. That would be like saying: Man is rational and as rational an animal, and an animal. But this is not the case: animal occurs only once in Man is a rational animal.
What is it for one concept to be included in another? A concept C is included in a concept D just in case, necessarily, everything that falls under D falls under C. Thus, unmarried is included in bachelor because every bachelor is unmarried. We could also put this in terms of analytic entailment. C is included in D if and only if D analytically entails C. Thus swan is included in cygnet just in case cygnet analytically entails swan.
Therefore (from 4)
6. If being were a GENUS, then being would NOT be included in every specific difference whereby this putative genus would be divided into species.
7. If BEING were a genus, then being would HAVE TO BE included in every specific difference. For being applies to everything inasmuch as everything is. So being would have to be included in each concept: necessarily, if x falls under any concept C, x falls under being, whence it follows that being is included in every specific difference whereby this putative genus would be divided into species.
Therefore (from 6 and 7)
8. If being were a genus, then being would and would not be included in every specific difference.
Therefore (from 8 by RAA)
9. Being is not a genus.
To put the point rather more simply, when we say of a thing that it is a being, or even more simply, that is is, we are not saying anything about what kind of thing it is. We are not saying anything about WHAT it is: we are underscoring that it IS. Being is not a highest quidditative determination. For when we speak of the being (esse) of a being (ens) we are referring to its sheer existence, not its nature or essence or quiddity.
This is an absolutely fundamental point. But I have learned from hard experience that there are those who cannot 'see' it, people like my friend 'Ocham.' These are the people I call 'existence-blind.'