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.

Therefore:

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.

Therefore:

. . . 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," http://www.bu.edu/wcp/Papers/Reli/ReliMayd.htm.