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

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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?

I know this is super late, but I would add that it's important to distinguish between two sorts of causal chains in Aristotelian/Scholastic thought. One type of chain is what is called 'accidental' and doesn't require a first cause. Aristotle and Aquinas believe this is why we can't prove that the universe had a beginning. The second sort of chain is 'essential.' That's the sort of chain going on in this argument. What this argument shows is not that 'collectively' the things can't endure, but rather that such collectivity is actually irrelevant because nothing can sufficiently sustain itself. – user28843 – 2017-10-18T22:57:40.680

@user28843 I'm aware of the distinction between accidental ordered causal chains and essentially ordered causal chains, but the part of Aquinas' Third Way that I'm asking about, i.e. the part I put in bold in the first quote, is not about causal chains. The part about causal chains is where it says "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." – Keshav Srinivasan – 2017-10-19T00:27:31.033

@user28843 To review the structure of the argument, we start with the observation that some things are contingent, i.e. they have an inherent tendency to start existing and stop existing. Then we argue that not everything can be contingent; there has to be something necessary, i.e. something which exists at all times. And then we argue that that necessary thing must either have its necessity uncaused by anything else, or it must have its necessity caused by an essentially ordered causal chain which terminates in something whose necessity is uncaused by anything else. – Keshav Srinivasan – 2017-10-19T00:46:40.627

@user28843 My question is about the part of the argument which purports to show that not everything can be contingent. It's not about the part of the argument about the causal chain which causes the necessity of a necessary thing. – Keshav Srinivasan – 2017-10-19T00:48:26.953

Yeah. I would say that the reason why Aquinas believes that not everything can be contingent is because he means by 'contingency' a sort of status that means not only 'tending to not exist' but, by a deductive inference, also 'isn't sufficient to account for its own existence.' The counterargument is that just because each part is not necessary doesn't mean the whole web isn't able to account for its own existence; in other words, it all works out so long as at least one (or more) contingent things have existed at some point in time. – user28843 – 2017-10-19T17:24:23.883

For Aquinas, this is, if not special pleading, than off the point. The mere fact that every material thing can go out of existence (or, more strongly, 'tends' to go out of existence) is proof that nothing material can really account for its own existence. Whether or not it can owe its existence to some other contingency becomes irrelevant; for Aquinas, the causal chain (an 'essential' causal chain) demands that for any material thing to exist at any moment there has to be some cause that is sufficient in itself to account for existence. – user28843 – 2017-10-19T17:27:40.477

It's important to realize that Aquinas not only believes in the tendencies of material things to go out of existence, but that such tendencies are due to the real contingency of such things (in the same way that the tendency of people to procreate is the manifestation of an actual telos or natural end that exerts causal influence in real things). It's also important to realize the role that essential causal chains play. You claim that your question is about why 'not everything can be contingent' and I say that Aquinas's distinction between essential and accidental chains has relevance here. – user28843 – 2017-10-19T17:32:17.097

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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).

How exactly does "Every object can potentially stop existing at any time (including at, say, the particular time t₁)." imply "All objects collectively can potentially stop existing at the same time (at t₁ in this case)."? It certainly follows in the modern philosophical definition of possibility, but I don't see how it follows in the hylemorphic understanding of the terms. In fact, to take an even more simple example, why does "A has a potential to stop existing at t_1 and B has a potential to stop existing at t₁" imply "A and B have the potential to simultaneously stop existing at t₁"? – Keshav Srinivasan – 2015-01-15T15:18:05.910

Fundamentally, here is what I don't understand: if A is the sort of thing that can stop existing at any time, and B is the sort of thing that can stop existing at any time, why does that imply sooner or later A and B will simultaneously stop existing? (Remember, Feser says possibility refers to an inherent tendency which must manifest itself sooner or later.) Barack Obama and Mitt Romney both have the potential to die at any given time, but that doesn't imply that eventually they're going to die simultaneously, does it? – Keshav Srinivasan – 2015-01-15T15:32:17.250

Feser explicitly says "[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." So doesn't that equally well imply that if it is possible for A and B to go out of existence together, then this possibility must actually come about. – Keshav Srinivasan – 2015-01-15T22:08:23.783

It is directly relevant to the Third Way. Part of Aquinas' argument is this: "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" – Keshav Srinivasan – 2015-01-16T03:14:43.857

So Aquinas is saying that if everything is possible not to be, then we reach an absurd conclusion, namely that nothing exists right now. In order to reach that absurd conclusion, you need to use Feser's statement that "if 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." – Keshav Srinivasan – 2015-01-16T03:17:25.327

@KeshavSrinivasan: "if A is the sort of thing that can stop existing at any time, and B is the sort of thing that can stop existing at any time, why does that imply sooner or later A and B will simultaneously stop existing?" Because if they did not, they never would've had the potential to stop existing in the first place. – Geremia – 2015-01-16T04:56:16.517

@KeshavSrinivasan: «Aquinas is saying that if everything is possible not to be, then we reach an absurd conclusion, namely that nothing exists right now. In order to reach that absurd conclusion, you need to use Feser's statement that "if 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."» Note: Feser is speaking of "every contingent thing" whereas St. Thomas is speaking of everything (contingent and non-contingent). He concludes "not all beings are merely possible." – Geremia – 2015-01-16T04:58:13.947

""if A is the sort of thing that can stop existing at any time, and B is the sort of thing that can stop existing at any time, why does that imply sooner or later A and B will simultaneously stop existing?" Because if they did not, they never would've had the potential to stop existing in the first place." Wait, are you saying it IS true that if A is the sort of thing that can stop existing at any time and B is the sort that can stop existing at any time, then sooner or later A and B will simultaneously stop existing? What about Barack Obama and Mitt Romney? Will they die simultaneously? – Keshav Srinivasan – 2015-01-16T10:01:18.740

"Feser is speaking of "every contingent thing" whereas St. Thomas is speaking of everything (contingent and non-contingent)." But Feser uses the statement "if 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" to reach the conclusion "Hence if everything really were contingent, there would have been some time in the past at which nothing existed[.]" – Keshav Srinivasan – 2015-01-16T10:09:35.070

@KeshavSrinivasan: Do Obama or Romney have the possibility to stop existing before their birth? They don't seem to fit the specifications for the A and B you're talking about, namely that they "can stop existing at *any* time." – Geremia – 2015-01-17T04:17:42.667

– Geremia – 2015-01-17T04:18:14.017

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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.

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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. :)

"Basically, it is just the matter of infinite regress, and there is no reason to think that god should be immune to it." First of all, the infinite regress part is not relevant to my question, so you should take out that part of your answer. In any case, Feser thinks there is something that makes God immune to infinite regress; see his discussion of Aquinas' First Way argument: https://docs.google.com/document/d/1WIuVBC7uhlqn647V5EDyzcttXHjO7rB4wUr0j13QjpA/edit?usp=sharing

– Keshav Srinivasan – 2015-01-12T09:43:16.313

I marked the text as you advised. As to Feser's discussion, as far as I read it's all about the definition of cause as related to the unmoved mover considered exclusively in the aristotelian framework. That's one. Two is that the only thing it might prove if we accept it (I am not going to argue for or against it now.) is UM's ability to move itself, not possibility, or even necessity of its existence. It's just a report on non-self-contradictory character of a theory. And two is that even if we assume it's fine to use it as a proof (it's doubtful), all it can do is show there is a deist god. – Borys Whittaker – 2015-01-12T10:11:05.433

Oh, plus Aristotle's Unmoved Mover did not create matter. He was just responsible for the objects' form, if I am not mistaken - I really could be, though. Ancient philosophy is ancient history to me. (; – Borys Whittaker – 2015-01-12T10:32:35.600

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• "these are not proof, they are merely leads". False, Aquinas firmly believed in the demonstrability of the existence of God (ST, Ia, 1,2).
• 2)The possible world analysis is not fit for Aquinas modal notions, as Feser clearly shows. Just read carefully, please. 3)The principle of causality (something cannot come from nothing) is argued for elsewhere by Aquinas (and Aristotle, for that matter). – Nicol – 2016-08-27T18:19:57.927