Maverick Philosopher: Strictly Philosophical

Kenny, Geach, and the Perils of Reading Frege into Aquinas

(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.

Peter Geach on the Real Distinction I

Oceans of ink have been spilled over the centuries on the celebrated distinctio realis between essence and existence (esse).  You have no idea how much ink, and vitriol too, has flooded  the scholastic backwaters and sometimes spilled over into the mainstream. Anyway, the distinction has long fascinated me and I hold to some version of it.  I will first give a rough explanation of the distinction and then examine one of Peter Geach's arguments for it.

1.  First of all, we can say that the real distinction is so-called because it is not a merely conceptual or notional distinction.  It is not like the distinction between the Morning Star and the Evening Star. It is not a distinction parasitic upon how we view things or refer to them.  It is more like the distinction between Venus and Mars.  The Morning Star and the Evening Star are two "modes of presentation" (Fregean Darstellungsweisen) of one and the same chunk of extra-mental physical reality, the planet Venus.  But Venus and Mars are not modes of presentation but entities in their own right.  Venus and Mars are distinct in reality not merely in conception.

2. But although the Venus-Mars distinction is a real distinction, the distinction between essence and existence cannot be like this.  For while each of the planets can exist without the other, essence and existence cannot each exist without  the other.  A thing's existence is nothing without the thing whose existence it is, and thus nothing without the thing's essence.  I hope it is obvious that the existence of this particular coffee cup would be nothing without the cup and the cup's individual essence.

3. It is less obvious that the individual essence would be nothing without existence.  But to make the problem more difficult I will assume that there are no nonexistent individuals, that nothing is an individual unless it exists. This implies that before Socrates came into existence there was no individual essence Socrateity.  His coming into being was not the actualization of a pre-existent wholly determinate individual essence.  (This has implications for the theory of creation: it imples that creation is out of nothing, not out of mere possibles.)  It also implies that there is no individual essence corresponding to the name 'Vulcan' when this is used to denote an intra-Mercurial planet.  My assumption is anti-Meinongian and (I believe) also anti-Avicennian.  (There was a time, long ago, when the Muslims weren't total slouches when it came to philosophy. 'Avicenna' is the Latinization of 'Ibn Sina.')

4. The essence and the existence of a particular individual are thus each dependent on the other but nonetheless really, not merely notionally,  distinct.  Really distinct (like Venus and Mars, but unlike the Morning Star and the Evening Star) but inseparable (unlike Venus and Mars).  They are really distinct like my eye glasses and my head but not separable in the manner of glasses and head. So an analogy might be the convexity and concavity of one of the lenses.  The convex surface cannot be without the concave surface and vice versa, but they are really distinct.  'Convex' and 'concave' are not merely two different ways of referring to the same piece of glass.  There is a real mind-independent difference.  But it is only  an analogy.

5. Now what reason could we have for accepting something like the the real distinction?  Here is one of Geach's arguments, based on Aquinas,  from "Form and Existence," reprinted in Peter Geach, God and the Soul (Thoemmes Press, 1994), pp. 42-64.  Geach's argument is on p. 61.  I'll put the argument in my own way.  .

Suppose you have two numerically distinct instances of F-ness.  They don't differ in point of F-ness, since each is an instance of F-ness.  But they are numerically distinct.  So some other factor must be brought in to account for the difference.  That factor is existence.  They differ in their very existence.  Since they differ in existence and yet agree in essence, essence and existence are really distinct.

Max Black was famous for his iron spheres.  (Geach does not mention Black.) He hypothesizes a world consisting of just two of them and nothing else, the spheres being alike in every relational and monadic respect.  In Black's boring world, then, there are two numerically distinct instances of iron sphere.  Since both exist, and since they differ solo numero, I conclude that they  differ in their very existence.  Since they differ in their existence, but agree in their iron sphericity, there is a real distinction between existence and nature or essence.

Suppose you deny that.  Suppose you say that the spheres do not differ in their very existence and that they share existence.  The consequence, should one cease to exist, would be that the other would cease to exist as well, which is absurd.