Bill Vallicella – Page 619 – Maverick Philosopher

Kenny, Geach, and the Perils of Reading Frege Back Into Aquinas

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 wiederholdt 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 consists 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.

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 mainstream precincts. 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 MS and the ES are two "modes of presentation" (Fregean Darstellungsweisen) of one and the same chunk of extramental 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 wthout 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 mght be the convexity and concavity of one of the lenses. The convex surface cannot be without the concave surafce 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. I find the argument convincing.

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.

Pleonasm of the Day: ‘Negative Attack Ad’

I once heard John McCain use the phrase, 'negative attack ad.' As opposed to what? Positive attack ad? You may enjoy this Kant attack ad.

The Underground Grammarian

If you think that I am a language Nazi, then pay a visit to the Underground Grammarian. His stern visage reminds me of a passage near the beginning of Franz Kafka's Vor dem Gesetz, "Before the Law." The protagonist seeks entry into the Law, but at the door stands a guard who warns:

     Ich bin maechtig. Und ich bin nur der unterste Tuerhueter. Von Saal
     zu Saal stehn aber Tuerhueter, einer maechtiger als der andere.
     Schon den Anblick des dritten kann nicht einmal ich ertrage.

     I am powerful. And I am but the least of the gatekeepers. From room
     to room there are gatekeepers each stronger than the next. Not even
     I can bear so much as the glance of the third. (tr. BV)

Litotes

"His explanation of litotes, though not bad, was not very helpful."

On Taking Principles to Extremes

That a principle can be taken to an extreme is no argument against the principle so taken. It is rather an argument against extremism. The principle that one has the right to keep and bear arms, for example, is not refuted by the fact that some will take it to mean that one has the right to keep and 'bear' tactical nukes. Similarly in other cases.

Food Fascism Update

No Kugel for You!

Closure: Some Mathematical and Philosophical Examples

A reader asks, "What is meant by 'closure' or 'closed under'? I've heard the terms used in epistemic contexts, but I've not been able to completely understand them."

Let's start with some mathematical examples. The natural numbers are closed under the operation of addition. This means that the result of adding any two natural numbers is a natural number. What is a natural number? On one understanding of the term, the naturals are the positive integers, the counting numbers, the members of the set {1, 2, 3, 4, 5, . . .}. On a second understanding, the naturals are the positive integers and zero: {0, 1, 2, 3, 4 . . .}. Either way, it is easy to see that adding any two elements of either set yields an element of the same set. It is also easy to see that the naturals are also closed under multiplication. But they are not closed under subtraction. If you subtract 9 from 7, the result (-2) is not an element of the set of natural numbers.

Now consider the squaring operation. The square of any real number is a real number. So the reals are closed under the operation of squaring. But the reals are not closed under the square root operation. The square root of -4 cannot be 2 since 2 squared is 4; it cannot be -2 either since -2 squared is 4. The square root of -2 is the complex number 2i where the imaginary number i is the square root of -1. The square roots of negative numbers are complex; hence, the reals are not closed under the square root operation.

Generalizing, we can say that a set S is closed under a binary operation O just in case, for any elements x and y in S, xOy is an element of S. In Group Theory, a set S together with an operation O constitutes a group only if S is closed under O.

Now for some philosophical examples. Meinongian objects (M-objects) are not closed under entailment. The M-object, the yellow brick road, although yellow is not colored even though in reality nothing can be yellow without being colored. M-objects are incomplete objects. They have all and only the properties specified in their descriptions. So we say that the properties of M-objects are not closed under property-entailment. Property P entails property Q iff necessarily, if anything x has P, then x has Q.

What goes for M-objects goes for intentional objects. (On my reading of Meinong, an M-object is not the same as an intentional object: there are M-objects that are not the accusatives of any actual
intending.) Suppose I am gazing out my window at the purple majesty of Superstition Mountain. The intentional object of my perception has the property of being purple, but not the properties of being colored or being extended even though in reality nothing can be purple without being both colored and extended. Phenomenologically, what is before my mind is an instance of purple, but not an instance of colored item. What I see I see as purple but not as colored.

Now consider: If S knows that p, and S knows that p entails q, then S also knows that q. If you acquiesce in the bolded thesis, then you acquiesce in the closure of 'knows' under known entailment. For what you are then committing yourself to is the proposition that a proposition q entailed by a proposition p you know — assuming you know that p entails q — is a member of the set of propositions you know.

Of Cranks and Crackpots

London Ed quotes neurologist Steven Novella who makes an insightful observation in Cranks and Physics (the whole of which is well worth reading):

… cranks around the world have been able to form their own “alternative” community, publish their own journals, and have their own meetings. There is just one requirement in this alternative community – acceptance. All ideas are accepted (there is no chaff, all is wheat), that is except for one. Whatever is accepted by mainstream science is wrong [my emphasis]. That is “the one ring” of crank mythology, that brings all crank theories together and in the darkness of their community binds them together. Otherwise they are largely mutually incompatible. Each crank’s “theory of everything” is a notion unto itself, and is mutually exclusive to every other crank’s own theory of everything (unless there is some incidental overlap). So they get together, present their theories without criticism, and all agree that the evil conspiracy of mainstream science must be taken down. Of course, if any of them got their way and their ideas became accepted, they would instantly become rejected by the rest of the crank community as mainstream physics.

Ed comments:

Correct. My enemy's enemy is my friend, whatever my enemy believes. I have seen this effect in Wikipedia a number of times. Cranks unite to defeat the mainstream, orthodox view. Orthodox editors get blocked or banned. Cranks then war with each other, and get banned themselves. The orthodox editors mount appeals to the powers that be – the arbitration committee, none of whom have any expert credentials as far as I can see, and get unbanned. Or they just open 'sockpuppet' accounts and start editing again under a different name. So do the cranks, and the whole nightmare begins again. Another difficulty that Novella omits is 'mainstream' crankery. That is, bad science or quackery that unites its practitioners by financial interest. Homeopathy and 'Neurolinguistic programming' are good examples of this.

This would not matter at all, if Wikipedia were not increasingly used as a 'reliable source' by students, and even some medical researchers, as I noted in an earlier post.

Philosophy, Superman, and Richard C. Potter

I was pleased to hear from Patrick Kurp of Anecdotal Evidence this morning. He inquired:

About four or five years ago you wrote about an American writer and thinker, perhaps an academic philosopher, who published, I believe, two books and seemed to disappear. You had difficulty finding information about him online. I believe you said he had an interest in East Asian thought. His “career” was eccentric by conventional standards and he seemed to be something of a loner.

Then I remembered a post of mine which begins:

This post examines Richard C. Potter's solution to the problem of reconciling creatio ex nihilo with ex nihilo nihil fit in his valuable article, "How To Create a Physical Universe Ex Nihilo," Faith and Philosophy, vol. 3, no. 1, (January 1986), pp. 16-26. (Potter appears to have dropped out of sight, philosophically speaking, so if anyone knows what became of him, please let me know. The Philosopher's Index shows only three articles by him, the last of which appeared in 1986.)

I don't know whether Potter is the man Kurp had in mind, but the former does satisfy part of Kurp's description. In any event, the Richard Potter story is an interesting one.

I recall talking to him, briefly, in the summer of 1981 at Brown University. I was a participant in Roderick Chisholm's National Endowment for the Humanities Summer Seminar, and Potter, who I believe had recently completed his Ph.D. at Brown, sat in on a few sessions. My impression was he that he was unable to secure a teaching position. I also recall a slightly derogatory comment I made about the Midwest and how one might have to go there to find employment. Potter's mild-mannered reply was to the effect that he preferred the Midwest over other geographical regions. His name stuck in my mind probably because of a paper on the paradox of analysis he co-authored with Chisholm and because of the F & P article mentioned above. See here. But then he dropped out of philosophical sight.

A few years back, I did a search and he turned up again as a George Reeves and Superman aficionado. So here is part of the rest of the Potter story. Here is Potter's George Reeves site.

A checkered career, his.

I too enjoyed the Superman series while growing up in the '50s. Some thoughts of mine on George Reeves are in Superman: The Moral of the Story.

The Immorality of Contemporary Liberalism

Another outstanding column by Victor Davis Hanson.

Hats Off to Hentoff: Abortion and Obama

It is often assumed that opposition to abortion can be based only on religious premises. This assumption is plainly false. To show that it is is false, one need merely give an anti-abortion argument that does not invoke any religious tenet, for example:

   1. Infanticide is morally wrong.
   2. There is no morally relevant difference between abortion and
   infancticide.
   Therefore
   3. Abortion is morally wrong.

Whether one accepts this argument or not, it clearly invokes no religious premise. It is therefore manifestly incorrect to say or imply that all opposition to abortion must be religiously-based. Theists and atheists alike could make use of the above argument.

And as a matter of fact there are pro-life atheists. Nat Hentoff is one. In The Infanticide Candidate for President, he takes Barack Obama to task:

     But on abortion, Obama is an extremist. He has opposed the Supreme
     Court decision that finally upheld the Partial-Birth Abortion Ban
     Act against that form of infanticide. Most startlingly, for a
     professed humanist, Obama — in the Illinois Senate – also voted
     against the Born Alive Infant Protection Act. I have reported on
     several of those cases when, before the abortion was completed, an
     alive infant was suddenly in the room. It was disposed of as a
     horrified nurse who was not necessarily pro-life followed the
     doctors' orders to put the baby in a pail or otherwise get rid of
     the child.

Internet Crackpots and the Perils of Autodidacticism

One of the (very minor) drawbacks of having a Web presence is that one becomes the target of crackpot e-mail from people like this. He describes himself as an autodidact, thereby illustrating the perils of autodidacticism.

And yet some negotiate the straits of autodidacticism quite well, Eric Hoffer for example. In general, however, he who educates himself has a fool for a pupil. That being said, I advise a modicum of skepticism concerning academic credentials.

If you expect to have 'cred' in the 'sphere, it helps to have established credibility in peer-reviewed venues. Some of my publications are listed here, at PhilPapers.

It comes as no great surprise that the crackpot in question is an anti-Semite.

The Voter Photo Identification ‘Issue’

Some positions are so absurd as to be beneath refutation. To respond reasonably to the unreasonable lends them a veneer of credibility to which they are not entitled. Mockery, derision, and ridicule are often much more appropriate and effective. Oftentimes, all it takes is a cartoon to refute a stupid liberal. By the way, this voter ID 'issue' — pseudo-issue, actually — is a perfect example of the lunacy of contemporary liberalism. But it is worse than lunacy given that the motive (not the reason, they have none) is to encourage voter fraud. For a leftist, the end justifies the means. Does it take fraud to win? Then you commit fraud.