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:
Some things are created and destroyed.
Therefore, some things are such that it's possible for them to exist and possible for them not to exist.
If it is possible for something not to exist, then there must be a time at which it will not exist.
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.
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?