(Written 23 December 2013)
I have been studying Anthony Kenny, Aquinas on Being (Oxford 2002). I cannot report that I find it particularly illuminating. I am troubled by the reading back of Fregean doctrines into Aquinas, in particular in the appendix, "Frege and Aquinas on Existence and Number." (pp. 195-204) Since Kenny borrows heavily from Peter Geach, I will explain one of my misgivings in connection with a passage from Geach's important article, "Form and Existence" in God and the Soul. Geach writes,
Frege, like Aquinas, held that there was a fundamental distinction in rebus answering to the logical distinction between subject and predicate -- the distinction between Gegenstand (object) and Begriff (concept). [. . .] And for Frege the Begriff, and it alone, admits of repetition and manyness; an object cannot be repeated -- kommt nie wiederholt vor. (45-46)
So far, so good. Geach continues:
Understood in this way, the distinction between individual and form is absolutely sharp and rigid; what can be sensibly said of one becomes nonsense if we try to say it of the other. [. . .] Just because of this sharp distinction, we must reject the Platonic doctrine that what a predicate stands for is is some single entity over against its many instances, hen epi pollon. On the contrary: the common nature that the predicate 'man' (say) stands for can be indifferently one or many, and neither oneness nor manyness is a mark or note of human nature itself. This point is made very clearly by Aquinas in De Ente et Essentia. Again we find Frege echoing Aquinas; Frege counts oneness or manyness (as the case may be) among the properties (Eigenschaften) of a concept, which means that it cannot at the same time be one of the marks or notes (Merkmalen) of that concept. (46)
I smell deep confusion here. But precisely because the confusion runs deep I will have a hard time explaining clearly wherein the confusion consists. I will begin by making a list of what Geach gets right.
1. Objects and individuals are unrepeatable.
2. Concepts and forms are repeatable.
3. Setting aside the special question of subsistent forms, no individual is a form, and no object is a concept.
4. Frege distinguishes between the marks of a concept and the properties of a concept. The concept man, for example, has the concept animal as one of its marks. But animal is not a property of man, and this for the simple reason that no concept is an animal. Man has the property of being instantiated. This property, however, is not a mark of man since it is not included within the latter's conceptual content: one cannot by sheer analysis of the concept man determine whether or not there are any men. So there is a sense in which "neither oneness nor manyness is a mark or note of human nature itself." This is true if taken in the following sense: neither being instantiated singly nor being instantiated multiply is a mark of the concept man.
But how do these points, taken singly or together, support Geach's rejection of "the Platonic doctrine that what the predicate stands for is some single entity over against its many instances"? They don't!
It seems obvious to me that Geach is confusing oneness/manyness as the relational property of single/multiple instantiation with oneness/manyness as the monadic property of being one or many. It is one thing to ask whether a concept is singly or multiply instantiated. It is quite another to ask whether the concept itself is one or many. It is also important to realize that a Fregean first-level concept, when instantiated, does not enter into the structure of the individuals that instantiate it.
Aquinas is a constituent ontologist, but Frege is not. This difference is deep and causes a world of trouble for those who attempt to understand Aquinas in Fregean terms. For Frege, concepts are functions, and no function enters into the structure of its argument. The propositional function x is a man is not a constituent of Socrates. What's more, the value of the function for Socrates as argument is not a state of affairs with Socrates and the function as constituents. The value of the function for Socrates as argument is True; for Stromboli as argument, False. And now you know why philosophers speak of truth-values. It's mathematical jargon via Frege the mathematician.
The Fregean concept man is one, not many. It is one concept, not many concepts. Nor is it neither one nor many. It can have one instance, or many instances, or no instance. The Thomistic form man, however, is, considered in itself, neither one nor many. It is one in the intellect but (possibly) many in things. In itself, however, it is neither. And so it is true to say that the form is not "some single entity over against its many instances." It is not a single entity because, considered in itself, it is neither single nor multiple.
But this doesn't follow from point (3) above. And therein lies Geach's mistake. One cannot validly move from the "sharp distinction" between individuals/objects and forms/concepts to the conclusion that what a predicate stands for is not a single entity. Geach makes this mistake because of the confusion exposed two paragraphs supra. The mutual exclusion of objects and concepts does not entail that concepts cannot be single entities.
There is another huge problem with reading Frege back into Aquinas, and that concerns modes of existence (esse). A form in the intellect exists in a different way than it does in things. But if Frege is right about existence, there cannot be modes of existence. For if existence is instantiation, then there cannot be modes of existence for the simple reason that there cannot be any modes of instantiation.
I'll say more about this blunder in another post. It rests in turn on a failure to appreciate the radically different styles of ontology practiced by Aquinas and Frege. In my jargon, Aquinas is a constituent ontologist while Frege is a nonconstituent ontologist. In the jargon of Gustav Bergmann, Aquinas is a compex ontologist while Frege is a function ontologist.