Aquinas’ Third Way Argument

0. Introduction

I recently listened to a podcast, where the host, David Smalley, was interviewing a christian apologist, Tom Peeler. The conversation was prefaced by Peeler making the claim that he could prove that God existed without the use of the bible.

The first argument offered by Peeler was essentially Aquinas’ ‘Third Way’ argument, but done in a way that made it particularly easy to spell out the problem with it. In fact, Peeler gave two arguments – or, rather, I have split what he said into two arguments to make it easier to explain what is going on. Once I have explained how the first argument fails, it will be obvious how the second one fails as well. The failures of Peeler’s argument also help us to see what is wrong with Aquinas’ original argument.

1. Peeler’s first argument

Peeler’s first argument went like this (at about the 23 minute mark):

1. If there were ever nothing, there would still be nothing
2. There is something
3. Therefore, there was never nothing

As Peeler pointed out, the argument is basically a version of modus tollens, and so is definitely valid. But is it sound? I will argue that even if we grant that the argument is valid and sound, it doesn’t establish what Peeler thinks it does.

Here is the sort of consideration that is motivating premise 1. In the interview, Peeler was keen to stress that his idea required merely the fact that things exist and the principle that “existence precedes causal influence”. There is an intuitive way of spelling out what this principle means. Take some everyday object, such as your phone. This object exists now, but at some point in the past it did not exist. It was created, or made. There is some story, presumably involving people working in a factory somewhere, which is the ‘causal origin’ of your phone. The important part about this story for our purposes is that the phone was created via the causal powers of objects (people and machines) that pre-existed the phone. Those pre-existing objects exerted their causal influence which brought the phone into existence; or, more mundanely, they made the phone. The idea is that for everything that comes into existence, like the phone, there must be some pre-existing objects that exert causal influence to create it. As Aquinas puts it: “that which does not exist only begins to exist by something already existing”.

One way to think about what this principle is saying is what it is ruling out. What it is ruling out is that there is a time where no objects exist at all, followed immediately by a time at which some object exists.

Imagine that at time t0, no objects exist at all. Call that an ‘empty time’. Then, at t1 some object (let’s call it ‘a‘) exists; thus, t1 is a ‘non-empty time’. This situation violates Peeler’s causal principle. This is because a has been brought into existence (it has been created), but the required causal influence has no pre-existing objects to wield it. We can picture the situation as follows:

At the empty time, t0, there is nothing (no object) which can produce the causal influence required to bring a into existence at t1. Thus, the causal influence seems utterly mysterious. This is what Peeler means by ‘nothing can come from nothing.’ So we can understand Peeler’s causal principle in terms of what it rules out – it rules out things coming into existence at times that are immediately preceded by empty times, or in other words it rules out non-empty times immediately following from empty times. Let’s grant this principle for the sake of the argument to see where it goes.

If we do accept all this, then it follows that from the existence of objects, such as your phone, that there can never have been a time at which no objects existed (i.e. that there are no empty times in the past). That’s because of the following sort of reasoning. If this time has an object, such as your phone, existing at it, then this time must not be preceded by a time at which no objects existed. So the phone existing now means that the immediately preceding time has objects existing at it. But the very same reasoning indicates that this prior time must itself be preceded by a time at which objects existed, and so on for all times.

We can put it like this: if this time is non-empty, then so is the previous one. And if that time is non-empty, then so is the previous one, etc, etc. Thus, there can never be an empty time in the past if this time is non-empty.

This seems to be the most charitable way of putting Peeler’s argument.

2. Modelling the argument

For all we have granted so far, at least three distinct options are still available. What I mean is that the argument makes certain requirements of how the world is, for it’s premises and conclusion to be true. Specifically, it requires that a non-empty time not be immediately preceded by an empty time. But there are various ways we can think about how the world is which do not violate this principle. A model is a way that the world is (idealised in the relevant way). If the model represents a way that the world could be on which the premises and conclusion of an argument are true, then we say that the model ‘satisfies‘ the argument. I can see at least three distinct models which satisfy Peeler’s argument.

2.1 Model 1

Firstly, it could be (as Peeler intended) that there is a sequence of non-necessary objects being caused by previous non-necessary objects, which goes back to an object which has existed for an infinite amount of time – an eternal (or necessary) object. Think of the times before t1 as the infinite sequence: {… t-2, t-1, t0, t1}. God, g, exists at all times (past and future), and at t0 he exerted his causal influence to make a come to exist at t1 alongside him:

On this model, there are no times in which an object comes into existence which are immediately preceded by an empty time, so this model clearly does not violate Peeler’s principle. Part of the reason for this is that there are no empty times on this model at all, just because God exists at each time. Anyway, the fact that this model doesn’t violate Peeler’s causal principle means that there is at least one way to model the world which is compatible with Peeler’s argument. The world could be like this, for all the truth of the premises and conclusion of Peeler’s argument requires.

But, this is not the only option.

2.2 Model 2

Here is another. In this model, each object exists for only one time, and is preceded by an object which itself exists for only one time, in a sequence that is infinitely long. Each fleeting object is caused to exist by the previous object, and causes the next object to exist. On this model there are no empty times, so it is not a violation of Peeler’s principle. Even though it does not violate the principle, at no point is there an object that exists at all times. All that exists are contingent objects, each of which only exists at one time.

Think of the times before t1 as the infinite sequence { … t-2, t-1, t0, t1}, and that at each time, tn, there is a corresponding object, bn:

Thus, each time has an object (i.e. there are no empty times) and each thing that begins to exist has a prior cause coming from an object. No object that begins to exist immediately follows from an empty time. Therefore, this model satisfies Peeler’s argument as well.

2.3 Model 3

There is a third possibility as well. It is essentially the same as the second option, but with a merely finite set of past times. So, on this option, there is a finitely long set of non-empty times, say there are four times: {t-2, t-1, t0, t1}. Each time has an object that exists at that time, just like in model 2. The only real difference is that the past is finite:

In this case, t-2 is the first time, and b-2 is the first object.

However, there might be a problem with this third option. After all, object b-2 exists without a prior cause. It isn’t caused to exist by anything that preceded it (because there are no preceding times to t-2 on this model). Doesn’t this make it a violation the causal principle used in the argument?

Not really. All that Peeler’s causal principle forbids is for an object to begin to exist at a time immediately following an empty time. But because there are no empty times on this model, that condition isn’t being violated. Object b-2 doesn’t follow an empty time. It isn’t preceded by a time in which nothing existed. It just isn’t preceded by anything.

Now, I imagine that there is going to be some objection to this type of model. Object b-2 exists, but it was not caused to exist. Everything which comes into existence does so because it is caused to exist. But object b-2 exists yet is not caused to exist by anything.

We may reply that object b-2 is not something which ‘came into existence’, as part of what it is for an object x to ‘come into existence’ requires there to be a time before x exists at which it does not exist. Seeing as there is no time before t-2, there is also no time at prior to t-2 at which b-2 does not exist. So b-2 simply ‘exists’ at the first time in the model, rather than ‘coming into existence’ at the first time. Remember how Aquinas put it: “that which does not exist only begins to exist by something already existing”. There is no prior time at which b-2 is “that which does not exist”. It just simply is at the first time.

No doubt, this reply will seem to be missing the importance of the objection here. It looks like a technicality that b-2 does not qualify as something which ‘comes into existence’. The important thing, Peeler might argue, is that b-2 is a contingent thing that exists with no cause for it. That is what is so objectionable about it.

If that is supposed to be ruled out, it cannot be merely on the basis of Peeler’s causal principle, but must be so on the basis of a different principle. After all, Peeler’s principle merely rules out objects existing at times that are preceded by empty times. That condition is clearly not violated in model 3. The additional condition would seem to be that for every non-necessary object (such as b-2), there must be a causal influence coming from an earlier time. This principle would rule out the first object being contingent, but it is strictly more than what Peeler stated he required for his argument to go through.

However, let us grant such an additional principle, just for the sake of the argument. If we do so, then we rule out models like model 3. However, even if we are kind enough to make this concession, this does nothing to rule out model 2. In that model, each object is caused to exist by an object that precedes it in time, and there are no empty times. Yet, there is no one being which exists at all earlier times (such as in model 1).

The existence of such an eternal being is one way to satisfy the argument, but not the only way (because model 2 also satisfies the argument as well). Thus, because model 2 (which has no eternal being in it) also satisfies the argument, this means that the argument does not establish the existence of such an eternal being.

So, even if we grant the premises of the first argument, it doesn’t establish that there is something which is an eternal necessary object. It is quite compatible with a sequence of merely contingent objects.

2. Peeler’s second argument

From the conclusion of the first argument, Peeler tried to make the jump to there being a necessary object, and seemed to make the following move:

1. There was never nothing
2. Therefore, there is something that has always been.

The fact that the extra escape routes are not blocked off by the first argument, should give you some reason to expect the inference in the second argument to be invalid. And it is. It is a simple scope-distinction, or an instance of the ‘modal fallacy’.

There being no empty times in the past only indicates that each time in the past had some object or other existing at it. It doesn’t mean that there is some object in particular that existed at each of the past times (such as God). So long as the times are non-empty, each time could be occupied by an object that exists only for that time (as in our second and third models), for all the argument has shown.

The inference in the second argument is like saying that because each room in a hotel has someone checked in to it, that means that there is some particular individual person who is checked in to all of the rooms. Obviously, the hotel can be full because each room has a unique individual guest staying in it, and doesn’t require that the same guest is checked in to every room.

When put in such stark terms, the modal fallacy is quite evident. However, it is the sort of fallacy that is routinely made in informal settings, and in the history of philosophy before the advent of formal logic. Without making such a fallacious move, there is no way to get from the conclusion of Peeler’s first argument to the conclusion of the second argument.

3. Aquinas and the Third Way

In particular, medieval logicians often struggled with scope distinctions, as their reasoning was carried out in scholastic Latin rather than in symbolic logic. That they managed to make any progress at all is testament to how brilliant many of them were. Aquinas is in this category, in my view; brilliant, but prone to making modal fallacies from time to time. I think we can see the same sort of fallacy if we look at the original argument that is motivating Peeler’s argument.

Here is how Aquinas states the Third Way argument:

“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.” Aquinas, Summa Theologiae, emphasis added)

This argument explicitly rests on an Aristotelian notion of possibility. The philosopher Jaakko Hintikkaa explains Aristotle’s view:

“In passage after passage, [Aristotle] explicitly equates possibility with sometime truth, and necessity with omnitemporal truth” (The Once and Future Seafight, p. 465, emphasis added)

This is quite different from the contemporary view of necessity as truth in all possible worlds. On the contemporary view, there could be a contingent thing that exists at all times in some world. Therefore, being eternal and being necessary are distinct on the modern view, but they are precisely the same thing on the Aristotelian view. We will come back to this in a moment. For the time being, just keep in mind that Aquinas, and by extension Peeler, are presupposing a very specific idea of what it means to be necessary or non-necessary.

We can see quite explicitly that Aquinas is using the Aristotelian notion of necessity when he says “…that which is possible not to be at some time is not”. This only makes sense on the Aristotelian view, and would be rejected on the modern view. But let’s just follow the argument as it is on its own terms for now.

The very next sentence is: “Therefore, if everything is possible not to be, then at one time there could have been nothing in existence.” What Aquinas is doing is imagining what would be the case if all the objects that existed were non-necessary objects. If that were the case, then no object would exist at every time, i.e. each object would not exist at some time or other. That is the antecedent condition Aquinas is exploring (i.e. that “everything is possible not to be”).

What the consequent condition is supposed to be is less clear. As he states it, it is “at one time there could have been nothing in existence”. We can read this in two ways. On the one hand he is saying that if everything were non-necessary, then there is in fact an earlier time that is empty. On the other hand, he is saying that if everything were non-necessary, there could have been an earlier time that is empty.

Let’t think about the first option first. It seems quite clear that it doesn’t follow from the assumption that everything is non-necessary that there is some time or other at which nothing exists. Model 2 is an example of a model in which each object is non-necessary, but in which there are no empty times. If Aquinas is thinking that “if everything is possible not to be, then at one time there could have been nothing in existence” means that each object being non-necessary implies that there is an empty time, then he is making a modal fallacy. This time, the fallacy is the other way round from Peeler’s example: just because each guest is such that they have not checked into every room of the hotel, that does not mean there is a room with no guest checked in to it. Think of the hotel in which each room has a unique guest in it. Exactly the same thing applies here too; just because every object is such that it fails to exist at some time, that does not mean that there is a time at which no object exists. Just think about model 2, in which each time has its own unique object.

Thus, if we read Aquinas this first way, then he is committing a modal fallacy.

So let’s try reading him the other way. On this reading he is saying that the assumption that everything is non-necessary is compatible with there being an empty time. One way of reading the compatibility claim is that there is some model on which the antecedent condition (that every object is non-necessary) and the consequent condition (that there is an empty time) are both true. And if that is the claim, then it is quite right. Here is such a model (call it model 4):

On this model, there are two objects, a and b, and they are both non-necessary (i.e. they both fail to exist at some time). Also, as it happens, there is an empty time, t2; both a and b fail to exist at t2. So on this model, the antecedent condition (all non-necessary objects) and the consequent condition (some empty times) are both satisfied.

However, while this claim is true, it is incredibly weak. The difference is between being ‘compatible with’ and ‘following from’. So for an example of the difference, it is compatible with me being a man that my name is Alex; but it doesn’t follow from me being a man that my name is Alex. If we want to think about the consequent following from the antecedent condition, we want it to be the case that every model which satisfies the antecedent condition also satisfies the consequent condition, not jus that there is some model which does. But it is clearly not the case that every model fits the bill, again because of model 2. It satisfies the condition that every object is non-necessary, but it doesn’t satisfy the condition that there are some empty times.

So what it comes down to is that the claim that there are only non-necessary objects is compatible with the claim that there are empty times, but it is equally compatible with the claim that there are no empty times. Being compatible with both means that it is simply logically independent of either. So nothing logically follows from the claim that there are only non-necessary objects about whether there are any empty times in the past or not.

So on the first way of reading Aquinas here, the claim is false (because of model 2). On the second way of reading him, the claim is true, but it is logically independent of the consequent claim. On either way of reading him, this crucial inference in the argument doesn’t work.

And with that goes the whole argument. It is supposed to establish that there is an eternal object, but even if you grant all of the assumptions, it is compatible with there not being an eternal object.

4. Conclusion

Peeler set out an argument, which was that if nothing ever existed, there would be nothing now. The truth of the premises and the conclusion is satisfied by, or compatible with, model 2, and so does not require that an eternal object (like God) exists. The second argument was that if it is always the case that something exists, then there is something which always exists. That is a simple modal fallacy. Lastly, we looked at Aquinas’ original argument, which either commits a similar modal fallacy, or simply assumes premises which do not entail the conclusion.