Archive for September, 2008

Extension and Comprehension

Sunday, September 21st, 2008

I learned two new terms this week, courtesy of Peter Kreeft’s Socratic Logic, that are immediately applicable to De Ente et Essentia. The terms are extension and comprehension, two properties that terms have. (He also cited four pairs of synonyms; apparently, the concepts are important but the names for them are little agreed upon.)

Simply put, the comprehension of a term is its meaning; and the extension of a term is the set of things to which it refers. The comprehension of the term man, for example, is rational animal; the extension of the term man, is all men and women.

The interesting thing about comprehension and extension is that they are inversely related. If you increase the comprehension of a term, you decrease its extension, and vice versa. Thus, the term rational animal has greater comprehension than the term animal alone, it is more determinate, but at the same time it has a lesser extension, it refers to fewer beings.

And this, it so happens, is the distinction that Thomas has been making in Chapter 2 of De Ente et Essentia. In terms of extension, the genus animal contains everything that is in the species man; but in terms of comprehension the term animal means only that which all animals have in common, and is thus only a part of the species man.

Some books just seem to come along at the right time.

CT 72: The Cause of Diversity

Sunday, September 21st, 2008

Matter is the principle of individuation; this dog and that dog, while both dogs, are distinct because they contain different matter. One might say that matter is what allows us to have a diversity of dogs. But in CT 71, Thomas demonstrated that, on the contrary, matter cannot be the cause of diversity; if it were, matter would have had to exist before God created anything that includes matter. In Chapter 72 of Compendium Theologiae, Thomas shows what the true cause is of the diversity of created things.

If the unity and multiplicity of things are governed by their being, and if the entire being of things depends on God, as has been shown to be the case the cause of plurality in things must be sought in God. How this comes about, must now be examined.

All things that are have their being from God. How so?

Any active cause must produce its like, so far as this is possible. The things produced by God could not be endowed with a likeness of the divine goodness in the simplicity in which that goodness is found in God.

Any active cause must produce its like, so God, as an active cause, must produce His like. But only so far as this is possible. Nothing created can match God’s goodness and simplicity, or it would be God Himself.

Hence what is one and simple in God had to be represented in the produced things in a variety of dissimilar ways. There had to be diversity in the things produced by God, in order that the divine perfection might in some fashion be imitated in the variety found in things.

Nevertheless, creation must come as close as is possible to representing God’s goodness. Since no individual thing can do this perfectly, it was necessary for God to create a wide variety of things, each of which is, in its own way, an image of the perfection of God. It is in this sense that the very stones of the earth praise the Lord:

Furthermore, whatever is caused is finite, since only God’s essence is infinite, as was demonstrated above. The finite is rendered more perfect by the addition of other elements. Hence it was better to have diversity in created things, and thus to have good objects in greater number, than to have but a single kind of beings produced by God. For the best cause appropriately produces the best effects. Therefore it was fitting for God to produce variety in things.

Socratic Logic, by Peter Kreeft

Saturday, September 20th, 2008

Aha! Comes the dawn!

Early on in my Aquinas blogging I joked that if I ever wrote a philosophy book, it would be entitled “What Aquinas Takes For Granted,” and it would cover all of the points of Aristotelian thought that Thomas uses without explanation, for the benefit of those, like me, who came in late. But glory of glories, wonder of wonders, I no longer need to, for Peter Kreeft has already done it.

I recently received in the mail Kreeft’s book Socratic Logic, which is that most glorious of things, a college-level introduction to Aristotelian Logic. (Kreeft is a big fan of Socrates, as the title indicates, but though he is clearly fond of Plato I gather he considers Aristotle to be Socrates’ true successor.) And though I’ve just begun to read it I do believe that it is going to resolve a great many of my questions.

Just yesterday, for example, I got horribly confused by a passage in Thomas’ De Ente et Essentia about the relation between species and members of a species; and just this morning Kreeft began to explain some basic concepts that I had not understood.

I have been treating the term man as a species, as equivalent to the term rational animal; after all, “Man is a rational animal.” This is incorrect. Man is a term, a concept, the result of a simple apprehension. It is simple and indivisible. Rational animal is the species of man. It is clearly not simple and indivisible, as it composed of genus and specific difference.

What I was missing was the notion of the “five predicables”, the five kinds of things that can appear as the predicate of a proposition: genus, specific difference, species, property, and accident. These terms have to be thought of as predicates; and if I had realized this, I’d not have confused man and rational animal. These two concepts are related, but not identical.

I am just scratching the surface of Socratic Logic, but I can confidently say that it’s going to be an eye-opener all the way along.

What joy!

DE&E: Chapter 2:12

Friday, September 19th, 2008

Have discoursed at length on the relation between the genus and species, now Thomas spends some time on the relation between the species and individual. And all I can say is, Oh Dear! But let’s take it little by little and see where we get. (Be warned: I make some false steps, here and there, though I think I come out at the right spot.)

Furthermore, since, as said above, the nature of the species is indeterminate with respect to the individual just as the nature of the genus is with respect to the species, and since, further, the genus, as predicated of the species, includes in its signification (although indistinctly) everything that is in the species determinately, so too does the species, as predicated of the individual, signify everything that is in the individual essentially, although it signifies this indistinctly. In this way, the essence of the species is signified by the term man, and so man is predicated of Socrates.

I think I understand the above; but I’m confident I’m missing something. Thomas says, “the nature of the species is indeterminate with respect to the individual just as the nature of the genus is with respect to the species”. I get that. Just as saying that X is an animal doesn’t tell you which species X belongs to, saying that X is a man doesn’t tell you which man X is. But why does he say “the nature of the species” and “the nature of the genus” instead of simply “the species” and “the genus”? The term nature is usually used concerning the operation of some being, but I don’t see how that fits in. And then, at the end of that bit, he says “the essence of the species is signified by the term man”. Why “the essence of the species” instead of just “the species”? Isn’t “man” the name of the species?

Either Thomas is speaking carelessly, which seems unlikely, or the translation is bad, which is possible, or there are subtleties that are eluding me like ghosts in the mist, which is likely.

But wait! It gets worse!

If, however, the nature of the species is signified in such a way as to exclude designate matter, which is the principle of individuation, then the species is related to the individual as a part; and this is how the term humanity signifies, for humanity signifies that by which a man is a man.

Is “designate matter” the same as the “signate” matter Thomas spoke of some paragraphs back? It seems that it is; he says it’s the principle of individuation, and signate matter was that matter found in individual composite beings, as opposed to non-signate matter which was found in the essence of composite beings.

In that case, by “the nature of the species” he means the essence, which is form and non-signate matter. But then, he draws a distinction between “man” and “humanity”, and says that “humanity” is the nature of the species signified in such a way as to exclude designate matter, and that “humanity” is a part of the human individual. Which leads me to the opposite conclusion, that “designate matter” is non-signate matter, or perhaps any kind of matter, signate or non-signate, and that humanity is simply the form of man: essence without matter. In which case, it certainly is just a part of man, as man is form and matter together.

So I’m going to assume, unless corrected, that “man” is the essence, and “humanity” the essential form, indeed, the special form.

Designate matter, however, is not that by which a man is a man, and it is in no way contained among those things that make a man a man.

Ummm…a man isn’t a man without some kind of matter. But it’s the form that makes a man a man, rather than a dog.

Since, therefore, the concept of humanity includes only those things by which a man is a man, designate matter is excluded or pretermitted, and since a part is not predicated of its whole, humanity is predicated neither of man nor of Socrates.

You know, I looked at this right after I got home from work. I was tired, and fuzzy-headed, and it made no sense. Since then I’ve had a nice leisurely dinner out with Jane, and some good conversation, and a nice stroll, and I’m feeling rested and the house is quiet, and I can think without being disturbed. And this still doesn’t make any sense. It appears to be saying that I can’t say that Socrates is human.

Let’s try some propositions:

  1. Socrates is a man. He’d better be; this proposition is to logic as “Now is the time for all good men” is to typewriters.
  2. Socrates is humanity. OK, that’s not true. Like Zaphod Beeblebrox, he’s just this guy, you know?
  3. Socrates has humanity. That looks better. And I suppose it translates to
  4. Socrates is a being of which humanity is a part.

Thus, humanity is not predicable of Socrates directly.

Thus Avicenna says, Metaphysicae V, cap. 5, that the quiddity of a composite thing is not the composite thing of which it is the quiddity, even though the quiddity itself is composite, as humanity, while composite, is not man. On the contrary, it must be received in something that is designate matter.

Blast. I was right about designate matter the first time. Here Thomas indicates clearly that he means humanity to be the quiddity of man in general or of Socrates in singular; and quiddity is essence. And while the quiddity of a composite thing is composite, it is not the same as the composite thing–why? Because the quiddity includes non-signate matter, not signate, or designate, matter. Humanity becomes man only when it is received in something that is designate matter, which is the principle of individuation.

So where did I go wrong? Clearly, I was conflating the species, man, with its essence or quiddity. And since humanity was not man, I concluded that it could not be essence. So species is not essence. The nature of the species is its essence. Socrates is a man; he has the essence of a man.

Could it be that this is a distinction that is often glossed over? That species and essence are often used interchangeably, because most of the time the distinction doesn’t matter? Or have I simply been oversimplifying for the last couple of months?

I’m reminded of that joke about how, having gone through four years of college, we are now confused at a higher level about more important things.

CT 71: Matter Not the Cause of Diversity in Things

Thursday, September 18th, 2008

Having established that God and only God can create from nothing, there being nothing pre-existing for Him to work with, Thomas begins in Chapter 71 to investigate the causes of the great diversity of things we see in the world:

The foregoing exposition shows clearly that the cause of diversity in things is not diversity on the part of matter. For, as we have proved, the divine action which brings things into being does not suppose the pre-existence of matter. The cause of diversity in things could not be on the side of matter unless matter were needed prior to the production of things, so that the various forms induced would follow diversity in matter. Therefore the cause of diversity in the things produced by God is not matter.

There are many kinds of things that are made of matter, and they all seem to contain different kinds of matter…but that’s not because God had a bunch of kinds of matter all ready to hand before he got started. The matter didn’t exist until the things containing it were created.

Again, the plurality or unity of things is dependent on their existence. For, to the extent that anything is a being, it is also one. But forms do not possess existence on account of matter; on the contrary, matter receives existence from form. For act is more excellent than potency; and that which is the reason for a thing’s existence must be the more excellent component. Consequently forms are not diverse in order that they may befit various types of matter, but matter is diversified that it may befit various forms.

Remember that form is act and matter is potency. Would it be correct, then, to say that form is logically prior to matter? We’ve seen that a composite being must have both; but we’ve also seen that the intellect can abstract form from matter and retain the form in the intellect as a concept.

A human artisan can have a concept of a new kind of chair, say, firmly in mind without actually building such a chair; and he probably needs to have such in mind before he actually does build a new kind of chair. It seems reasonable that the form of man, or dog, or brine shrimp existed in the mind of God before ever being paired with matter; and indeed, Thomas tells us that all perfections that are in creatures first existed in God.

DE&E: Chapter 2:11

Wednesday, September 17th, 2008

In the previous paragraph Thomas continued to discuss the relation of the genus, the specific difference, and the species to a composite being contained in that genus and species. In this paragraph, he focusses in on the relation of the genus to the species.

Although the genus may signify the whole essence of the species, nevertheless there is not just one essence of the various species under one genus, for the unity of the genus proceeds from its very indetermination or undifferentiation.

In other words, there’s no such thing as a generic animal. (Something is generic, of course, if it belongs to a genus.) Every animalis a dog or a cat or a slug or a sea-cucumber or a brine shrimp or a dust mite. All brine shrimps are animals and all dogs are animals, and in fact the genus includes all animals of all kinds, because of that which all animals have in common. But that which they have in common is not an essence; it’s incomplete, or as Thomas puts it, it is indeterminate.

Nor is it the case that what is signified through the genus is numerically one nature in the various species such that to it there supervenes some other thing, which is the difference that determines it, as a form determines matter, which is numerically one. Rather, the genus signifies some form (though not determinately this one or that one), which the difference expresses determinately, the very one that is signified indeterminately through the genus.

In other words, a dog isn’t a generic animal with the optional dog package bolted on. If you took away from your dog that which makes him a dog, there’d be nothing left. You can’t draw a diagram of a dog and say “These parts are the animal parts, and those parts are the dog parts.” It simply doesn’t work that way.

Consequently, the essence of a dog and the essence of a slug are different, even though they belong to the same genus.

I have to say, I’m not entirely comfortable with the language Thomas uses here. I’m tempted to say that a genus is the collection of all special forms for which some proposition or set of propositions is true. The specific difference is then a proposition or set of propositions that is true of only one special form and hence determines it. But I might well be missing something.

By a thing being numerically one I’m assuming that Thomas means that it is an individual, an existing being, this dog, or this slug.

And thus the Commentator says in Metaphysicae XII, com. 14, that prime matter is called one by the removal of all forms, but the genus is called one through the commonality of forms signified. Hence, the indetermination, which was the cause of the unity of the genus, having been removed through the addition of the difference, the species remain essentially diverse.

As I indicated above: the specific difference selects the particular special form, which along with (non-signate) matter is the species of the composite being.

CT 70: Creation Possible for God Alone

Tuesday, September 16th, 2008

In CT 69, Thomas showed that God can create other beings ex nihilo, from nothing. In Chapter 70, he shows that only God can so create:

From this it appears, further, that God alone can be Creator. For to create is the prerogative of that cause which does not presuppose another cause that is more universal, as we saw in the preceding chapter. But such causality pertains to God alone. He alone, therefore, is Creator.

Hmmm. I can see that God necessarily must be able to create ex nihilo; being the first cause, there’s nothing available to make anything from. I don’t see (from this argument) why some created being–let’s call him “Fred”–couldn’t also have this ability. Oh, wait, I get it. Fred was created by God, and has the perfections that God gave him. If Fred had the ability to create ex nihilo, that ability was given him by God–which is to say, in exercising that ability, Fred is really making use of God’s power. But gosh, it sure would look like Fred was creating completely out of nothing.

If Thomas is saying here that not even that can happen, I can’t see why.

Besides, the more remote a potency is from act, the greater must be the power that reduces it to act. But whatever distance may be imagined between potency and act, the distance will ever be still greater if the very potency itself is withdrawn. To create from nothing, then, requires infinite power. But God alone is infinite in power, since He alone is infinite in essence. Consequently God alone can create.

OK, this I can see: creation isn’t simply moving something from potency to act, it’s causing there to be act (and potency) that wasn’t there before. I still don’t see why God can’t delegate this power, as it were.

DE&E: Chapter 2:10

Monday, September 15th, 2008

In the previous paragraph, Thomas explained how, for composite beings, the genus determines the matter, the specific difference determines the form, and species determines both. In this paragraph, he elaborates on just what the genus, difference, and species are:

From this is it clear why the genus, the difference, and the species are related proportionally to the matter, the form, and the composite in nature, although they are not the same as these things. For, the genus is not the matter, though it is taken from the matter as signifying the whole; nor is the difference the form, though it is taken from the form as signifying the whole.

I’m not sure why Thomas uses the word proportionally here; does he simply mean respectively? I dunno. But let’s elaborate on the distinctions between the genus and the matter, the difference and the form, and the species and the composite:

Thus we say that man is a rational animal, but not composed of the animal and the rational in the sense that we say that man is composed of soul and body: man is said to be composed of soul and body as from two things from which a third thing is constituted different from each of the two.

To use a bad analogy: an axe is a tool that chops. But you can’t combine a generic tool and a chopping capability and make an axe. You need to combine a lever (the axe handle) with a wedge (the axe blade).

The difference is not the form; it determines the form given the genus. My substantial form is not rational; my substantial form is Man.

Man, surely, is neither body nor soul.

Rather, he is the marriage of the two.

But if man is said in some sense to be composed of the animal and the rational, it will not be as a third thing composed from these two things, but as a third concept composed from these two concepts.

Right. It’s an analytical breakdown.

The concept of animal is without determination of a special form and expresses, with respect to the ultimate perfection, the nature of the thing from that which is material; the concept of the difference, rational, consists in the determination of the special form. From these two concepts are constituted the concept of the species or the definition. Thus, just as a thing constituted from other things does not have predicated of it these other things, so too a concept does not have predicated of it the concepts of which it is constituted: clearly, we do not say that the definition is either the genus or the difference.

I had to puzzle over the term special form for a while; the meaning is obvious in context, but why did Thomas call it that? Then it hit me–D’oh! It’s the form of the species. The species is the definition of the composite being, and specifies the being’s form and matter; and that form is clearly the special form.

CT 69: Creation from Nothing

Sunday, September 14th, 2008

In CT 68, Thomas shows that all that exists, apart from God, has its existence from God. In Chapter 69, Thomas shows that God creates ex nihilo, from nothing, and what that means.

This makes it clear that, in creating, God has no need of pre-existing matter from which to fashion things.

And why not?

No agent needs, prior to his action, what he produces by his action; he needs only what he is unable to produce by his action. The builder requires stones and lumber before he can set to work, because he is unable to produce these materials by his action. On the other hand, he does not presuppose a house, but produces it by his activity. But matter must be produced by God’s action since, as has just been proved, everything that exists in any way at all has God as the cause of its existence. Therefore the conclusion follows that God does not presuppose matter in His activity.

But, of course, there’s more:

Besides, act naturally precedes potency, and hence the notion of principle primarily befits act. But any principle that in creating would presuppose some other principle, would verify the concept of principle only in a secondary way. Accordingly, since God is the principle of things as the first act, whereas matter is a principle as a being in potency, it is unthinkable that matter should be presupposed before God can act.

This is a little tricky. First, “act naturally precedes potency.” This is one of Aquinas’ maxims: possibility always arises from actuality, as seeds come from full-grown plants. Next, “the notion of principle primarily befits act”. The term principle is one I’m still wrestling with; although I’ve seen it used many a time, I’ve not seen a definition. Time to find one.

Rune’s Dictionary of Philosophy says (in part):

Principle: (Lat. principe, from principium, a beginning) A fundamental cause or universal truth, that which is inherent in anything. That which ultimately accounts for being. According to Aristotle, the primary source of all being, actuality and knowledge.

So when we say, for example, that “matter is the principle of individuation” we are saying that “matter is the cause of their being many things with the same essence.” And when Thomas says “the notion of principle primarily befits act” he is saying that it is usually act which is the fundamental cause of something.

But a fundamental cause that presupposes some other fundamental cause isn’t particularly fundamental. Now God, as Thomas has established over and over again earlier in the book, is the first cause of everything, is, in fact, the principle of everything that exists, and God is pure act. Matter is required for things to exist, and is the principle of individuation; but matter is potency; it simply cannot be more fundamental than pure act. So God cannot require pre-existing matter in order to create.

Furthermore, the more universal a cause is, the more universal its effect is. Particular causes make use of the effects of universal causes for something determinate; and such determination is related to a universal effect as act to potency. Hence any cause that causes something to be in act, utilizing pre-existing material that is in potency to that act, is a particular cause with respect to some more universal cause. But this sort of procedure cannot pertain to God, since He is the first cause, as we showed above. Consequently God does not need matter as a prerequisite to His action.

This, I think, is another way of saying the same thing. Particular causes depend on the effects of prior causes, which are more universal. A particular cause takes something from potency to act, which presupposes that there’s already something in potency due to some more universal cause. But God is the first cause; there is no more universal cause than He. Hence, there is nothing for Him to bring from potency to act.

Well, actually, I suppose that God can act as a particular cause as well, acting on that which He has already created. But the point is, there’d be nothing for Him to act on if He had not already created it.

Therefore He has the power to bring things into existence from nothing or, in other words, to create. This is why the Catholic faith professes that He is the Creator.

QED.

Truth Cancer

Saturday, September 13th, 2008

Mark Shea recently used the term “truth cancer”. Truth cancer takes root when you latch on to one truth out of many and proceed to exalt it to the detriment of the others. This leads to the syndrome Uncle Screwtape called “Christianity and …”. This one truth, which is undeniably true, becomes an idol.

Or, as it occurred to me to put it the other day, while cancer metastasizes, truth cancer hypostasizes.