Frege Meets Aquinas: A Passage from De Ente et Essentia

Here is a passage from Chapter 3 of Thomas Aquinas, On Being and Essence (tr. Robert T. Miller, emphasis added):

The nature, however, or the essence thus understood can be considered in two ways. First, we can consider it according to its proper notion, and this is to consider it absolutely. In this way, nothing is true of the essence except what pertains to it absolutely: thus everything else that may be attributed to it will be attributed falsely. For example, to man, in that which he is a man, pertains animal and rational and the other things that fall in his definition; white or black or whatever else of this kind that is not in the notion of humanity does not pertain to man in that which he is a man. Hence, if it is asked whether this nature, considered in this way, can be said to be one or many, we should concede neither alternative, for both are beyond the concept of humanity, and either may befall the conception of man. If plurality were in the concept of this nature, it could never be one, but nevertheless it is one as it exists in Socrates. Similarly, if unity were in the notion of this nature, then it would be one and the same in Socrates and Plato, and it could not be made many in the many individuals. Second, we can also consider the existence the essence has in this thing or in that: in this way something can be predicated of the essence accidentally by reason of what the essence is in, as when we say that man is white because Socrates is white, although this does not pertain to man in that which he is a man.

What intrigues me about this passage is the following argument that it contains:

1. A nature can be considered absolutely (in the abstract) or according to the being it has in this or that individual.
2. If a nature is considered absolutely, then it is not one.  For if oneness were included in the nature of humanity, e.g., then humanity could not exist in many human beings.
3. If a nature is considered absolutely, then it is not many. For if manyness were included in the nature of humanity, e.g., then humanity could not exist in one man, say, Socrates.
Therefore
4. If a nature is considered absolutely, then it is neither one nor many, neither singular nor plural.

I find this argument intriguing because I find it extremely hard to evaluate, and because I find the conclusion to be highly counterintuitive.  It seems to me obvious that a nature or essence such as humanity is one, not many, and therefore not neither one nor many!

The following is clear.  There are many instances of humanity, many human beings.  Therefore, there can be many such instances. It follows that there is nothing in the nature of humanity to preclude there being many such instances.  But there is also nothing in the nature of humanity to require that there be many instances of humanity, or even one instance.  We can express this by saying that the nature humanity neither requires nor precludes its being instantiated. This nature, considered absolutely, logically allows multiple instantiation, single instantiation, and no instantiation.  It logically allows that there be many men, just one man, or no men.

But surely it does not follow that the nature humanity is neither one nor many.  What Aquinas is doing above is confusing what Frege calls a mark (Merkmal) of a concept with a property (Eigenschaft)  of a concept.  The marks of a concept are the subconcepts which are included within it.  Thus man has animal and rational as marks.  But these are not properties of the concept man since no concept is an animal or is rational.  Being instantiated is an example of a property of man, a property that cannot be a mark of man.   In general, the marks of a concept are not properties thereof, and vice versa.  Exercise for the reader:  find a counterexample, a concept which is such that one of its marks is also a property of it.

Aquinas has an insight which can be expressed in Fregean jargon as follows.  Being singly instantiated — one in reality —  and being multiply instantiated — many in reality — are not marks (Merkmale) of the nature humanity.  But because he (along with everyone else prior to 1884) confuses marks with properties (Eigenschaften), he concludes that the nature itself cannot be either one or many.

To put it another way, Aquinas confuses the 'is' of predication ('Socrates is a man') with the 'is' of subordination ('Man is an animal').  Man is predicable of Socrates, but animal is not predicable of man, pace Aristotle, Categories 3b5: no concept or nature is an animal.  Socrates falls under man; Animal falls within man.  Animal is superordinate to man while man is subordinate to animal.

For these reasons I do not find the argument from De Ente et Essentia compelling.  But perhaps there is a good Thomist response.