Monday, July 27, 2009

Thomas Aquinas, James Kidd, and the Attributes of God

Catholic philosopher, James Kidd, has written a fascinating and accessible article on the existence of God, published in This Rock magazine. You can read the article for yourself here: A Proof of the Existence of God. I've summarized my take on the argument below.

First of all, Kidd begins by offering a somewhat Cartesian proof of the existence of the self. Cogito, ergo sum, or "I think, therefore I am" is Descartes' oft-cited maxim. I cannot doubt my own existence without first existing.

Nevertheless, we can conceive of a state of affairs in which we do not exist. This means that in order to exist, we must possess the attribute of esse ("existence" or "being"). Another expedient example is the conception of an acorn (Kidd uses the example of a chicken egg). The difference between a real acorn and a merely imaginary one is not based on any distinction in their "acorn-ness", but simply that the former possesses esse. A real acorn exists, whereas an imaginary acorn does not.

Now, an acorn (as with any changing entity) is composed of actuality and potentiality. It is easiest to explain these terms by connotation: an acorn is an acorn in actuality, but in potentiality it is an oak tree. It is important to note that potentiality is not a thing in and of itself, but that it is a privation (an "absence" or "lack of") actuality. As Kidd points out, "a thing considered in itself contains nothing but its fullness." The nature of an oak tree, considered in itself, possesses the quality of being an oak tree, and does not possess the lack of being an oak tree.

We can now reflect on what this implies about esse (from here on, I'll refer to esse as "being"). Since every existing thing possesses being, it must be the case that being is actual. But, being cannot be composed of any potentiality, since that would require the lack of being. Hence, being itself is pure actuality.

Now we can move on to consider the attributes of pure actuality (Pure Act). Since Pure Act exists essentially, it cannot not-be - that is, it has necessary existence. Moreover, Pure Act must be distinct from everything else. The reason why is that Pure Act contains only actuality, whereas other things are composed of actuality and potentiality. Yet, if something is true of one thing and not of another, the two must be distinct. Therefore, Pure Act is distinct from other entities.

Immutability and Eternality

In order to change, a thing must first have the potentiality to change. Yet, Pure Act is not composed of any potentiality. Therefore, Pure Act is changeless. Further, whatever comes into being or goes out of being in time must have the potentiality to do so. As a result, we can soundly conclude that Pure Act exists at all times, and is therefore eternal.


If there were more than one Pure Act, then there would be distinctions between them. But, distinctions entail limitations, and limitations entail potentiality. However, it has been demonstrated that Pure Act is not composed of potentiality, so it must be one.


Everywhere that something exists, the entity in consideration must have being. As we saw above, however, every entity's existence is dependent on Pure Act. If Pure Act were not present somewhere, then nothing would exist there. Hence, Pure Act exists everywhere, e.g. it is omnipresent.

Omnipotence and Omniscience

Every entity that possesses some power and some knowledge is only partly actual. Human beings, for example, have some power and some knowledge, but we are limited in our power and knowledge. From this, we can infer that Pure Act must possess all power and all knowledge. Pure actuality is nothing less than the fullness of what potentiality may attain to.

By way of conclusion, we have seen that a single, changeless, eternal, omnipresent, omnipotent and omniscient being exists. This, as the Angelic Doctor muses, is what everyone understands to be God.

Thursday, July 16, 2009

The Thomistic Cosmological Argument - Revised

1. Every dependent being derives its existence from some other being.
2. The series of dependent beings either proceeds to infinity, or has a first being.
3. The series of dependent beings cannot proceed to infinity.
4. Therefore, a first being exists.

This argument is really a summary of Thomas' proof as found in De Ente et Essentia. I like this version, since it doesn't rely on "causation" per se, with all of its alleged deterministic connotations.

The first premise has been defended explicitly since at least the time of Parmenides. Ex nihilo nihil fit: out of nothing comes nothing. If there were literally nothing, then not even the potentiality for something to come into being would exist. But, since something exists, it must be either dependent or self-existent.* We certainly observe dependent things in the world. An oak tree is dependent on the acorn, for example.

The second premise doesn't involve a temporal succession of events. Rather, the claim is that there is a series of beings that entail rank or source. Hence, it is considered hierarchical, instead of temporal.

Is it possible that this series is infinite? Several reasons are given against this conclusion. For one, a self-existent first being seems to be required in order for any dependent beings to exist. Just as a house needs a foundation, else the entire structure collapse, dependent beings likewise require something to hold them up. Moreover, if the series of dependent beings is infinite, then an infinite series would be sustaining something within a finite period of time. However, it would take infinite time for an infinite series to do anything. Hence, the series itself must be finite and therefore is grounded in a first being, in confirmation of (3).

I think this is a very reasonable conclusion to make. One might object that in a finite space, there are infinitely-many points. Of course, this argument is undermined by the fact that mathematical points are abstract and don't possess any physical dimensions. Furthermore, a finite space still has definite first and last points; so if there is any analogy between the two, a first being is still required.

The most difficult part of this argument for the Thomist, in my view, is in making the inference from a first being to the claim that this being's existence and essence
are identical. This conclusion does appear to follow from the argument above, though. The reason why is that if the first being is not dependent on anything else, then it cannot derive either its existence or its essence from another. Allow me to put this more explicitly.

The difference between a real unicorn and an imaginary unicorn is that the former is instantiated in actuality. This doesn't fall prey to the Kantian maxim that existence is not a predicate, since we're not merely adding existence to something purely conceptual. Rather, we're considering an a posteriori claim. From this it follows that a unicorn's existence is dependent on something else that brings about its existence. But, we have already seen that the series of dependent beings cannot proceed to infinity. If a being's existence is distinct from its essence, its existence is either brought about by some external being or by its own essential properties. The problem here is that nothing can be brought about by its own essential properties.** The difficulty with the former is that the first being does not derive its existence from anything else; otherwise, it wouldn't be first, which is a self-contradiction.

The conclusion seems to follow, then, that the first being's existence and essence are identical. The reason I say this is a difficulty (although there are certainly solutions) is that the divine attributes that are later inferred about this first being do appear to be distinct. Goodness seems logically distinct from power, knowledge from aseity, and so forth. The Thomist stresses the doctrine of analogy, which views the attributes of God as one and the same, so that the goodness of God really is the same as His power, etc. It's obvious that in us these characteristics are different, but what about in the divine essence?

*Something is self-existent if it exists by a necessity of its own nature. This shouldn't be confused with self-causation.

**This solution has the same problem as with self-causation. Something must already exist in order to bring about its own existence, which is absurd.

Monday, July 6, 2009

The Third Way

Thomas Aquinas' tertia via ("third way") has been the subject of criticism by theists and atheists alike. William Rowe, for example, discusses this argument, summarizing it as follows:

i. Whatever is a contingent being at one time did not exist.


ii. If everything is contingent then at one time nothing existed.

iii. If at one time nothing existed then nothing would exist now.

iv. Something does exist now.


. . . Not every being is a contingent being.

Rowe objects, "Even if we concede (i) to Aquinas, . . . the inference of (ii) from (i) is clearly invalid. From (i) it follows that if everything is contingent then for each thing there is a time at which it does not exist. That is, where Cx = x is a contingent being, Ty = y is a time, and Exy = x exists at y, from (i) it follows that

"2a. . . . Each contingent thing is such that there is some time or other when it did not exist.

"But from (i) it does not follow that

"2b. There is some definite time such that no contingent being existed at that time." [1]

If this is what Thomas is saying, then Rowe is correct that the argument is unsound. However, to Rowe's credit, he does make this qualification:

"It is sometimes suggested that there may be a plausible premise or principle that, when added to (i), will give us a logically valid inference to (ii). Father Copleston suggests, for example, that Aquinas is supposing that in an infinite time any real potentiality inevitably would be realized. Accordingly, the questionable inference is not from (i) to (ii) but from (i) and the proposition that in an infinite time any real potentiality would be realized." [2]

I think this is a reasonable inference to make. I'll attempt to reformulate the argument in a way that clarifies Thomas' original meaning, along with Copleston's interpretation. It should be pointed out, though, that when Thomas writes of "contingent" things, he doesn't mean logically contingent; he means temporally contingent, or corruptible. Likewise, "necessary" does not refer to logical necessity, but to temporal necessity.

1. Every existing entity is either corruptible or necessary.
2. Something has always existed.
3. Every corruptible entity potentially fails to exist.
4. Given infinite time, every real potentiality will be actualized.
5. Hence, there is some time in the infinite past in which every corruptible entity collectively fails to exist.
6. Therefore, a necessary entity exists. (From 1, 2, and 5).

(1) gives us our available options. If something exists, but is not corruptible, then it must exist necessarily. (2) is based on the principle that something cannot come from nothing. If there were ever a time in which nothing existed (is such a state of affairs contradictory, anyway?), then not even the potentiality for something to come into being would exist. As a result, nothing would be able to exist.

(3) is true by definition. If corruptible entities cannot not-be, then it follows that they exist necessarily, and (6) already concludes that something necessarily exists. As it is, however, there are many corruptible entities: trees, tables, planets, stars, galaxies, people, and so forth.

(4) is likely the most controversial premise, but it's not hard to see why Thomas (following Maimonides) came to this conclusion. If we were talking about a finite period of time, then we might have more of an incentive to deny this premise. However, if there is even the potential that every corruptible entity fails to exist, then given infinite time, it seems quite rational to say they would.

One way to get around this is by pointing to the one-to-one correspondence of actual infinites:

{2, 4, 6, 8, ... n} has just as many members as {1, 2, 3, 4, ... n}, where the first set includes all even positive numbers and the latter includes all positive numbers. Perhaps given infinite past time, only some of the infinitely-many potentialities are actualized?

The problem, I think, with this objection is that past time isn't like Cantorian set theory, even assuming that the past is infinite. The moments of the past did not arrive at the present from {8, 6, 4, 2, p}, where p = present time. On the other hand, I agree that the objection does show that there is no logical contradiction, broadly speaking, with a rejection of (4). What the proponent of the third way will have to argue, then, is that it is more likely that (4) is true than its negation.

(5), of course, follows from (3) and (4). So, if our tentative (4) is correct, then it follows that a necessary entity exists. Is there any way to strengthen the argument, so that we don't have to rely on (4)? I briefly sketched an argument in an earlier post, inspired by Robert Maydole [3], that shows we can modalize the third way in such a manner that we can be confident that a necessary entity exists:

Where x = an entity; C = temporally contingent; t = time; P = past time; y = explicandum; and Eyx = x explains y.

1. (x) (Cx □ → ◊ (t) ~xt).
2. (x) ◊ (□t) ~xt □ → ◊ (□t) (x) ~Pxt.
3. ~(x) (◊x □ → ◊ (y) (x ^ Eyx)).
4. ~[(□x) ◊ (□y) Eyx □ → ~(□t) (x) ~Pxt].
5. ~Pxt → ~C(x).
6. :. ~C(x).

In English:

1. Every temporally contingent entity possibly fails to exist at some time.
2. If all entities possibly fail to exist at some time, then it is possible that all entities collectively fail to exist at some past time.
3. It is necessarily the case that possible truths are explicable.
4. It is necessarily the case that something is explicable if and only if there was not a time when nothing existed.
5. If there could never have been a time when nothing existed, then a temporally necessary entity exists.
6. Therefore, a temporally necessary entity exists.

Notice that we have gone from a purely metaphysical analysis to an inclusion of possible worlds. (1) and (2) should not be at all controversial, since there is no contradiction in asserting that a given temporally contingent entity doesn't exist. The old Yankee stadium existed, but it doesn't logically have to, as is evidenced by its closing.

(3) states that possible truths are explicable, but not that possible truths must have an explanation, so there isn't a dependence on even a moderately strong version of the PSR. A state of affairs need not have an explanation in order for it to have an explanation in some possible world.

(4) points out that if literally nothing existed, then there wouldn't even exist possible explanations, or time itself. The idea of an existing time in which nothing exists is self-contradictory. But, since it's not possible for nothing to exist, then from (2) and (4), we know that (5) is true, and therefore (6) follows: a temporally necessary entity exists. Q.E.D.

Works Cited

[1] William L. Rowe, The Cosmological Argument, Fordham University Press, 1998, pp. 42-43.

[2] ibid., pp. 43-44.

[3] Robert Maydole, "Aquinas' Third Way Modalized,"