What do necessity and possibility mean in Aquinas' Third Way argument for the existence of God?

Question

In his famous Summa Theologica, the Scholastic theologian Thomas Aquinas presents Five Ways to demonstrate the existence of God. Here is Aquinas' Third Way, the argument from contigency:

The third way is taken from possibility and necessity, and runs thus. We find in nature things that are possible to be and not to be, since they are found to be generated, and to corrupt, and consequently, they are possible to be and not to be. But it is impossible for these always to exist, for that which is possible not to be at some time is not. Therefore, if everything is possible not to be, then at one time there could have been nothing in existence. Now if this were true, even now there would be nothing in existence, because that which does not exist only begins to exist by something already existing. Therefore, if at one time nothing was in existence, it would have been impossible for anything to have begun to exist; and thus even now nothing would be in existence – which is absurd. Therefore, not all beings are merely possible, but there must exist something the existence of which is necessary. But every necessary thing either has its necessity caused by another, or not. Now it is impossible to go on to infinity in necessary things which have their necessity caused by another, as has been already proved in regard to efficient causes. Therefore we cannot but postulate the existence of some being having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity. This all men speak of as God.

I want to focus on the part I put in bold. Here is the basic logic as I understand it:

1. Some things are created and destroyed.

2. Therefore, some things are such that it's possible for them to exist and possible for them not to exist.

3. If it is possible for something not to exist, then there must be a time at which it will not exist.

4. If all things are such that it's possible that they do not exist, then it is possible for there to be a time at which nothing exists.

5. If it is possible for there to be a time at which nothing exists, then there must be a time at which nothing exists.

My question is primarily about step 3 (although step 4 will also enter into the discussion later). If possibility and necessity are being used in the standard way we use them today, for instance in alethic modal logic, then it seems to me that step 3 is simply false; it is fallacious to go from "for any time t, it is possible for X not to exist at time t" to "there exists a time t at which X does not exist". After all, you can have a situation where X existed at all times, and yet it was possible for X not to have existed at some time t. So at least on this interpretation of the terms possibility and necessity, Aquinas' argument seems invalid.

But Edward Feser, in his book Aquinas, claims that Aquinas is using the terms possibility and necessity in a different way:

In other words, given that the matter out of which the things of our experience is composed is always inherently capable of taking on forms different from the ones it happens currently to instantiate, these things have a kind of inherent metaphysical instability that guarantees that they will at some point fail to exist. They have no potency or potential for changeless, indefinite existence; hence they cannot exist indefinitely. By “possible not to be,” then, what Aquinas means is something like “having a tendency to stop existing,” “inherently transitory,” or “impermanent”; and by “necessary” he just means something that is not like this, something that is everlasting, permanent, or non-transitory. Thus there is no fallacy in his inference from “such-and-such is possible not to be” to “such-and-such at some time is not,” for this would follow given an Aristotelian understanding of the nature of material substances.

Now under Feser's definitions of possibility and necessity, step 3 makes some measure of sense. But then I don't see how step 4 is valid. Here is what Feser says (while justifying step 5):

[I]f it is even possible for every contingent thing to go out of existence together (which even Aquinas’s critic must concede), this possibility must actually come about. For (again, at least given an Aristotelian conception of possibility) it would be absurd to suggest both that it is possible for every contingent thing to go out of existence together, and yet that over even an infinite amount of time this will never in fact occur. “Possibility” here entails an inherent tendency, which must manifest itself given sufficient time, and an infinite amount of time is obviously more than sufficient. Hence if everything really were contingent, there would have been some time in the past at which nothing existed[.]

In the beginning of that quote, Feser is just casually stating step 4 as if it's obvious. Now if we were to adopt a modal definition of possibility and necessity, I agree that step 4 makes a lot of sense; in modal logic the statement "for every object X and for every time t, it is possible for X not to exist at t" doesn't imply "there exists a time t such that it is possible that no objects exists at time t", but it's not that big a leap to go from one to the other. But under the definitions that Feser adopts, it's not clear to me at all that step 4 is true. How can you go from "Every object has a tendency to stop existing at some point or the other." to "All the objects collectively have a tendency to go out of existence simultaneously at some point."?

So to sum up, under the standard model definitions of possibility and necessity, step 3 doesn't make sense but step 4 does. Under the definitions Feser adopts, step 3 makes sense but step 4 does not. So what definitions is Aquinas actually relying upon? And whatever definitions he adopts, what is the justification for steps 3 and 4?

Answer 1

Possibility and necessity in St. Thomas's sense cannot be understood without Aristotle's doctrine of matter and form (hylemorphism). Possibility (or necessity) in the modern philosophical sense (the Humean sense) is more about whether we can conceive another world in which something can be (or must be).

Regarding how
"All the objects collectively have a tendency to go out of existence simultaneously at some point."
follows from
"Every object has a tendency to stop existing at some point or the other.":

Perhaps rephrasing it as the following would help:
Every object can potentially stop existing at any time (including at, say, the particular time t₁).
All objects collectively can potentially stop existing at the same time (at t₁ in this case).

Answer 2

First of all, these are not proofs, but merely leads. It is a common misconception.

I would not say that alethic modality is standard in any way. We do not need this special, logical meaning of contingency to get rid of Aquinas's third way.

[Irrelevant according to the asker] { Basically, it is just the matter of infinite regress, and there is no reason to think that god should be immune to it. (Unless you define him as immune to infinite regress, but well...) (Dawkins has written quite well on the topic in his famous "God Delusion".) }

Now, the interesting part - Feser's understanding of necessity and possibility. It does not seem so different. This view can be easily translated into the possible-worlds model. In this case stating that god is necessary would mean that he exists in every possible world, whilst other things do not. It does not really make things better for the following reasons:

1) There are stronger or at least equally strong claims. The fact that god exists in every possible world comes from our definition of god which is not verifiable, nor could be applied to anything else. But, for instance, the fact that 2 + 2 = 4 or that ¬(p = ¬p) is true for all possible worlds as well and is far more corroborated, quite verifiable and applicable to infinite number of objects and situations. They are more sure, and thus godly, than god himself.

2) It does not solve the problem of infinite regress. Let's assume that god does exist in every possible world, etc. Alright, but how did he get there? Same thing about logic - how did it get here? Where from? [This part keeps its relevancy. The possible-worlds interpretation of necessity without an additional, topic-specific interpretation does not say a word about the source of facts and objects marked by it as necesary.]

As to the transition from ∀x∀t {Object(x) ∧ Time(t) ∧ ♢¬[∃x En(x, t)]}, for "Object(x)" standing for "x is an object", "Time(t)" standing for "t is a moment in time", and for "En(x, t)" standing for "x endures at t", to ∃t∀x {Object(x) ∧ Time(t) ∧ ♢¬[En(x, t)]} for predicates as before - it surely depends in which modal logic. Frankly, I am quite sceptic about that happening at all. A logic allowing non-negated general statements to be transformed into non-negated existential statements is somewhat fishy.

Also, this whole argument is founded on the underlying assumption that something cannot come from nothing. (And this is partly why I think the matter of infinite regress is relevant.) Well, it might seem natural, but how the heck could we possibly take the statement like that as sure or even probable? We just do not know. It is a bit like in the case of identity. How can we know there won't come a quantum superposition-like law that will explain existence ex nihilo? Or a proof for eternity of everything that exists, like ancient Greeks wanted it?

So, answering your final questions: I do not think we can ascribe such sophisticated modern logic to Aquinas. We could interpret him with their aid, but I would not ascribe beliefs in them to a medieval monk. I am not a specialist in scholasticism, but it seems to me that he treated the terms rather naturally. And I do not really see a way in which this argument could be held and defended.

If you would like to consider a more convincing proposition for the necessity of existence of god, try reading on Gödel's ontological argument which is a developed version of Anzelm's ontological argument.

And if you would like to stop seeking a more convincing proposition for the necessity of existence of god, read Wittgenstein's lectures on religious belief. :)

Answer 3

Feser is using the correct definition of necessity and possibility. Were he not, the proposition "But it is impossible for these always to exist, for that which is possible not to be at some time is not" would be clearly false. I think that in Feser's understanding the argument goes about some way like this:

Suppose that everything which exists here and now is contingent, and there is no necessary being. Now, what we want to do now is to prove that under this assumption we must admit that the world (made only of contingent things) must have had a beginning in time, i.e., there was a time when no contingent thing (and thus nothing, under our assumption) existed. Suppose that the thesis were false, that is, that the world has always existed. This means that all contingent things have existed for an infinite amount of time. But this is impossible, since, given a long enough amount of time, contingent things will eventually corrupt.

I think, however, that the Third Way, even as Feser puts it, contains a logical mistake. What we have proven is that if everything is contingent, that only those things which exist here and now, the world of contingent things at a given instant must have had a beginning in time, before which other contingent things, which do not exist anymore now, existed and generated the current world.

I don't know if I've got my point across. Feel free to ask for clarifications.