Problems with Aquinas 'Third Way' Edward Moad, Department of Humanities, Qatar University Of Thomas Aquinas' five proofs of the existence of God, the "Third Way" is a cosmological argument of a specific type sometimes referred to as an argument from contingency. The Aristotelian argument for the existence of the First Unmoved Mover was based on the observation that there is change (or 'motion'), coupled with the principle that nothing changes unless its specific potential to change is actualized by an actual change undergone by some other thing. It then arrives at the conclusion that there exists something in a constant state of pure activity, which is not itself moved but sets everything else in motion. The operative sense of 'contingency' this argument turns on, then, is that of motion. That is, things have the potential to change in certain ways (depending on the kind of things they are), but may or may not do so; whether they actually do being contingent on whether they are acted on in the right way by something else. For this reason, Aristotle's argument delivers a first mover, which brings about the motion in all that exists, but not a being that brings about the very existence of everything else. The argument referred to specifically as the argument from contingency, by contrast, turns on the idea of the contingency of the very existence of anything at all. That is, if something exists which may not have, and the fact that it does exist rather than not is contingent on the action of other existing things, which are themselves contingent, then the existence of the whole lot of contingent things, taken together, is also contingent. From this, the argument ultimately concludes that there is a necessary existent – something that exists, for which it is not the case that it might not have existed, and the existence of which does not therefore depend on any other existing things, but on which the existence of all other things depends. The object of this paper is not, however, arguments from contingency in general, but specifically Aquinas's 'Third Way' as it appears in his Summa Theologica. I will raise three objections to this argument. First, the argument depends on the premise, that if everything were contingent, then there would have been a time during which nothing exists, but this is not self--‐evident and no argument is given for it here. Secondly, Aquinas tells us that a key premise in this argument, that an infinite order of things necessary through one another is impossible, has been proven just previously (in the 'second way') with respect to an infinite order of efficient causes. But this argument fallaciously equivocates between two different senses of the term 'first', and the fallacy does not disappear when applied to the 'third way'. Thus, Aquinas not only fails, in this argument, to prove the existence of a thing necessary in itself, but fails to prove that anything is necessary at all. Lastly, this argument suffers from a puzzling ambiguity as to the meaning of the term 'necessity', and either way of interpreting the term consistently in the argument raises difficulties. We will begin by quoting the key passage below, and then offer the argument in standard form for ease of analysis, posing some questions and issues that arise with certain of its premises along the way. We find some things that are possible both of existing and not existing since some things are found to be generated and corrupted, and therefore to be possible both of existing and of not existing. But it is impossible for everything of this kind to exist always since what is possible of not existing at some time does not exist. Therefore, if all things were capable Problems with Aquinas 'Third Way' Edward Moad, Department of Humanities, Qatar University of not existing, at some time no thing would exist. But if this were true, even now nothing would exist since what does not exist does not begin to exist except through something else which exists; so that if no being existed, it would be impossible for anything to begin to exist, and thus nothing would now exist, which is plainly false. Therefore, not all beings are contingent or possible; there must exist some thing which is necessary. But every necessary being either has a cause of its necessity from elsewhere, or it does not. But it is not possible to proceed ad infinitum in necessary beings which have a cause of their necessity, just as this was not possible in efficient causes, as was proved [in the Second Way]. Therefore, it is necessary to posit something which is necessary through itself, not having the cause of its necessity from elsewhere, but is the cause of necessity to other things, which is what everyone calls "God."1 The argument breaks down as follows: 1) Some things are found to be generated and corrupted. 2) Anything that is generated and corrupted is possible both of existing and not existing (implicit). 3) Therefore, there are things that are possible of both existing and not existing (1 and 2). We have inserted here, as the implicit premise (2), what is minimally necessary to take us from 1) to 3). But this leaves open the question, whether we are also to understand, here, that anything that is possible both of existing and not existing, is generated and corrupted, so that, essentially, the contingent just is the generated and corrupted; or whether the category of the contingent might include that which is not generated and corrupted. That is, can there be something that is everlasting, without beginning or end, and yet is such that it might not have existed? From the next premise, it appears not. 4) What is possible of not existing at some time does not exist. 5) Therefore if all things were capable of not existing, at some time no thing would exist (4). A false inference This seems to entail that all that is contingent is either generated or corrupted, if not both. But is the inference from 4) to 5) valid? In purely formal terms, from the premise that, for everything, there is some time at which it is non--‐existent [∀x ∃t (∼∃x @t)]; it does not follow that there is a time at which everything is non--‐existent [∃t ∀x (∼∃x @t)]. For this inference to be valid, certain other conditions must obtain. First, the number of existing things must not be potentially infinite. If it is, then things can begin and cease to exist in succession perpetually. Then, for each thing, there could be a time at which it does not exist, and yet no time at which nothing exists. So the inference is invalid unless the potential number of existing things is finite (and, as we might safely assume, the self--‐same thing cannot begin and cease to exist repeatedly). Secondly, it must be the case that time is ontologically independent of contingent 11 ST I, q. 2, a. 3. Problems with Aquinas 'Third Way' Edward Moad, Department of Humanities, Qatar University things (e.g. time cannot be the measure of motion). Otherwise, though it is possible for nothing to exist, there can be no time at which nothing exists. But let us for now assume that true premises can be established, which will make the inference valid. Then it should also follow that, if everything other than God is capable of not existing, then at some time nothing other than God exists. And that, it seems, would constitute a philosophical proof that the world as a whole is not eternal. But as is well known, Aquinas himself argues that this cannot be proven philosophically, but only by reference to divine revelation. But if he is right about that, then it follows that 5) is false. And this means that either the inference from 4) to 5) is fallacious, or that premise 4) itself is false. What role, then, do these premises play in the overall proof? 6) What does not exist does not begin to exist, except through something else which exists. 7) Therefore, if nothing existed, it would be impossible for anything to begin to exist (6). 8) Therefore, if at some time nothing existed, then nothing would exist now (7). 9) Therefore, if all things are capable of not existing, then nothing would exist now (5,8). 10) But something does exist now. 11) Therefore not all beings are capable of not existing (i.e. contingent or possible) (9, 10). 12) Therefore, there exists something which is necessary (i.e. not capable of not existing) (11). The inference from 5) to 9) is valid. But aside from premise 5), the truth of which, as we note, has not been established, it also depends on the truth of premise 6). This is, of course, a key premise. Much of the discussion over cosmological arguments in general has focused on the principle of sufficient reason, this being taken to be a key premise in such arguments, generally. It is important to point out then, that premise (6) is not the principle of sufficient reason. For as it stands, premise (6) is entirely compatible with the proposition that there is an infinite series of things, each of which begins to exist through a previous existing thing (or things) in the series, and it is just this proposition that is normally taken as ruled out by the principle of sufficient reason, on the grounds that in such a case, there will not be sufficient reason for the existence of any member of the series. Of course, if the principle of sufficient reason is true, then premise (6), quite intuitively, follows. If there is sufficient reason for the existence of something, it is hard to see how this would not involve reference to some already existing thing. One might be audacious enough to suggest that it is simply a law of nature that some things pop into existence out of nothing, and then offer that as sufficient reason, but they would have to avoid the implication that it is the existence of such a law that constitutes the reason (whatever the existence of a law of nature, in itself, is supposed to consist in). But premise (6) does not entail the principle of sufficient reason. And this fact relieves me of the unenviable choice between attempting to defend the principle on the one hand, or of trying to conceive doing philosophy under the pretense of its falsehood, on the other. Premise (6), as distinct from the principle of sufficient reason, also has the advantage that it does not raise the same Problems with Aquinas 'Third Way' Edward Moad, Department of Humanities, Qatar University question to the coherence of the notion of a Creator endowed with voluntary will. For if the existence of the world is a consequence, as a cosmological argument traditionally aims to show, of voluntary creative choice on the part of God, then it seems to follow that there is no sufficient reason to be given for its existence, if this is to be understood as something in virtue of which He could not have done otherwise. So here, I will be content to grant premise (6), and avoid the unpleasant suggestion that it is possible that something pop into existence out of nothing. And, since something does evidently exist now, the inference to premise (12) is valid. Ambiguity in modal terms With 12), this section of the argument arrives at the existence of something that is necessary; that is, something for which non--‐existence is impossible. Consequently it is not capable of generation or corruption, since the premise (2) implicit in the inference from 1) to 3) has it that anything that is generated and corrupted is contingent (i.e. something for which non--‐existence is possible). Consequently, that which is necessary exists at all times. So, if (6) provides the only condition by which a thing needs a cause for its existence, then that which is necessary needs no cause for its existence. So, in (12), we will have arrived at an uncaused cause of the existence of other things. With an additional proof that there can only be one uncaused cause of existence, we might be justified in identifying that as God. The fact that everything else is contingent could be a premise for an additional proof that the necessary existent causes the existence of everything else by a voluntary act of will (i.e. it might not have created any of them). And the premise (4), again, would entail that the world is not eternal. But this is not what Aquinas does here. Instead, he goes on to argue that: 13) Every necessary being has a cause of its necessity from elsewhere, or it does not. 14) But it is not possible to proceed ad infinitum in necessary beings which have a cause of their necessity, as has been already proved in regard to efficient causes. 15) Wherefore, it is necessary to posit something which is necessary through itself, not having the cause of its necessity from elsewhere, but is the cause of necessity to other things, which is what everyone calls God. Here, we are presented with a distinction between a necessary being, the necessity of which is caused by something else, and a necessary being that is necessary 'through itself.' For a thing to be necessary, is for it to be impossible that it not exist. So, the cause of its being necessary will be the cause, not only of its existence, but also of its being impossible not to exist. Avicenna had also distinguished the 'necessary through another' from the 'necessary in itself', but the former was just the contingent – the 'possible in itself', where its being caused to exist was just its being necessary, given the cause. In this case, the cause of a thing's being necessary could be understood just as the cause of the existence of that which is contingent in itself, but necessary through that which caused it to exist. But here, Aquinas distinguishes the contingent thing that is Problems with Aquinas 'Third Way' Edward Moad, Department of Humanities, Qatar University caused to exist by something else, from the necessary thing the necessity of which is caused by something else. But what does this mean? We might say, contra Avicenna, that a contingent thing might be caused to exist by something else, and yet not be necessary through that cause, if it remains that it might not have been caused to exist by it. By contrast, something is necessary through another, if it is caused to exist by another, and it is not the case that it might not have been. In the latter case, the cause would have to be something that is itself necessary, and necessarily causes the existence of its effect. In the former case, however, even if the cause itself exists necessarily, it must at least be a contingent matter that it caused its effect – it has to remain the case that it might not have caused its effect. This leaves the way open for the traditional understanding of God, as creating the universe by a voluntary act of will. For even though God Himself is understood to exist necessarily, it need not be the case that He necessarily creates this world, or any world at all. All that is caused to exist by His voluntary act would remain ultimately contingent, since His causing them to exist does not entail causing them to be necessary. Conversely, if being caused to exist were equivalent to being made 'necessary through another', as in Avicenna's system, then the argument would lead us, not only to a being that exists necessarily, but one who necessarily causes the existence of exactly that which does exist, and who could not have done otherwise. This would rule out creation as a voluntary act of will, and that would not be the sort of God that Aquinas aims to prove. So there is good reason for Aquinas to want to distinguish the contingent that is caused to exist (but remains contingent), from that which is made necessary through another. But if there is something that is necessary through another, in this sense, then it follows that there is something that God causes involuntarily, because again, if he created it voluntarily, then it would remain contingent. Now, the only reason we have been given here to believe in the existence of the necessary at all, is the fact that contingent things exist, and their existence depends on the existence of the necessary. Thus, the only necessary through another, which we have been given reason to believe exists, is one on which the existence of contingent things depends. But, if these things depend on the existence of this necessary through another, and they remain contingent, then it would be as if God involuntarily causes the existence of another voluntary creator (or at least a random 'existence generator' if such a thing is possible). Conversely, if this necessary through another is not another voluntary creator or random existence generator, involuntary caused by God, then those things on which it depends are not contingent after all, but additional things made necessary through another. In that case, according to premise (2) they are not susceptible of generation and corruption, and should presumably exist at all times. But according to the first (and strongest) premise in this argument, that is false. Then anything necessary through another, for which we have any reason to believe exists, will be a voluntary creator or random existence generator that God involuntary causes to exist for all time. According to premise (14), it is not possible to proceed ad infinitum in these things. But there could still be quite a large number (you might call it a pantheon). Of course, however many they may be, it would be argued, they all ultimately depend, for their existence, on the necessary through itself (which we call God). The troubling thing remains that, Problems with Aquinas 'Third Way' Edward Moad, Department of Humanities, Qatar University their being necessary, He would not have any choice in the matter. Assuming that Aquinas is committed to an omnipotent God Who has complete voluntary control over whatever else exists, he would not want to admit the existence of any such things necessary through another, in this sense. Of course, premise (13) does not entail the existence of such. It merely acknowledges the logical possibility of it. But to be effective in proving the existence of the sort of God that Aquinas presumably wants to prove, an additional argument ruling out this possibility is required, and the fact that this is missing here constitutes a weakness of this argument. But another possible explanation is that by 'necessary' here, Aquinas really means, not that it is impossible for the thing not to exist, but simply that it is 'not subject to generation and corruption.' In this case, the 'necessary through another' connotes a thing that exists at all times (angels, immortal souls, etc.). But, since they exist at all times by the voluntary will of God, of course, we cannot strictly say that it is impossible for them not to exist, unless we simply define the possibility of a thing's non--‐existence as the actual non--‐existence of the thing at some time. In this case, what Aquinas means by 'necessary through another' is really just 'everlasting', while true necessity (as in, non--‐existence really being impossible for a thing) is limited to the necessary in--‐itself (which in this case really means, everlasting through itself, but arguably amounts to the same thing). The problem with this interpretation is that it contradicts premise (4), that 'what is possible of not existing at some time does not exist.' Because the 'necessary through another', understood this way, is possible of not existing and yet, there is no time at which it does not exist. But if, to resolve this, we understand the 'possible of not existing' as simply that which is generated and corrupted, then the premise is a tautology: that which at some time does not exist, at some time does not exist. Likewise, for the whole inference from (1) to (3): premise (2) essentially becomes 'anything that is generated and corrupted is generated and corrupted', and therefore (3) 'there are things that are generated and corrupted.' So, on this interpretation, we purchase consistency with premise (4) at the cost of making it, along the first section of this argument, largely vacuous. So the problem, here, is that there is an ambiguity in the meaning of the modal terms in the argument. If we understand 'necessary thing' as that the non--‐existence of which is impossible, then the argument fails to prove the existence of the kind of voluntary creator that it presumably aims to prove. On the other hand, if we understand a 'necessary thing' as simply 'everlasting', then either premise (13) contradicts premise (4), or everything from (1) to (4) on the argument is rendered vacuous. Fallacy of equivocation But whichever way that goes, why is it not possible to proceed ad infinitum in things necessary through another? This has been proved, says Aquinas, in the case of efficient causes, which was dealt with in his 'second way.' It appears then, that the force of the 'third way' proof depends on that of the 'second way'. So to the latter we must turn. This proof is given as follows. In the world of sensible things, we find that there is an order of efficient causes. There is no case known (neither is it, indeed, Problems with Aquinas 'Third Way' Edward Moad, Department of Humanities, Qatar University possible) in which a thing is found to be the efficient cause of itself; for so it would be prior to itself, which is impossible. Now in efficient causes it is not possible to go on to infinity, because in all efficient causes following in order, the first is the cause of the intermediate cause, and the intermediate cause is the cause of the ultimate cause, whether the intermediate cause be several, or one only. Now, to take away the cause is to take away the effect. Therefore, if there be no first cause among efficient causes, there will be no ultimate, nor any intermediate cause. But if in efficient causes it is possible to go on to infinity, there will be no first efficient cause, neither will there be any ultimate effect, nor any intermediate efficient causes; all of which is plainly false. Therefore, it is necessary to admit a first efficient cause, to which everyone gives the name of God.2 Here is how this argument breaks down: 1) In the world of sensible things, we find that there is an order of efficient causes. 2) It is impossible for a thing to be the efficient cause of itself. 3) In all efficient causes following in order, the first cause is the cause of the intermediate cause, and the intermediate cause is the cause of the ultimate cause, whether the intermediate cause be several, or one only. 4) To take away the cause is to take away the effect. 5) Therefore, if there be no first cause among efficient causes, there will be no ultimate, nor intermediate cause (3 and 4). 6) If, in efficient causes, it is possible to on to infinity, there will be no first efficient cause. 7) If, in efficient causes, it is possible to on to infinity, there will be no ultimate effect, nor any intermediate efficient causes (5 and 6). 8) There are ultimate effects and intermediate efficient causes. 9) Therefore, in efficient causes it is not possible to go on to infinity (7 and 8). 10) Therefore, there is a first efficient cause. The conclusion of this argument is that there is a first efficient cause, which is absolutely first in the sense that it is not the effect of any prior cause. In premise (3) however, we are told that, in all efficient causal orders, the first cause is the cause of the intermediate cause, etc. So either this is a circular argument, or the term 'first' is to take a different sense in the premise, from that which it takes in the conclusion. The efficient causal orders that have been shown to exist are those we observe among sensible things. Among these, obviously, we do not observe the first cause referred to in the conclusion. Otherwise, there would be no need for a proof. In the causal orders we do observe, we find first causes in a relative sense – that is, 'first' in relation to an intermediate cause or causes, and an ultimate effect, in a circumscribed series of causes, and not 'first' in the absolute sense, of not being the effect of any prior cause. 2 Ibid Problems with Aquinas 'Third Way' Edward Moad, Department of Humanities, Qatar University So, when we get to (5), the inference is valid, so long as we mean, by 'first', the same thing we mean in (3). But when we come to (6), the meaning of 'first' shifts. It is true that an infinite causal series would have no 'first' cause in the absolute sense (that is, of a cause that is not the effect of any prior cause), but not that there would be no 'first' cause in the relative sense in which the term is used in the previous premises. If we were to stick with this sense of 'first' cause, as the prior cause in any circumscribed set of causes within a larger series, then it would be more plausibly to say that, if the series goes on to infinity, there are an infinite number of 'first' causes. Thus, when Aquinas infers (7) from (5) and (6), it is based on an equivocation in the operative sense of the term 'first'. So this argument is invalid. Will it make a difference, if this argument were given in terms of things 'necessary through another' rather than in terms of efficient causes? It does not look promising. The first premise would go 'in the world if sensible things, we find there is an order of things necessary through another.' This is manifestly not the case. What we observe of sensible things is subject to generation and corruption. And even if we did observe something that is everlasting, we could never observe it as such. Our first premise, rather, would have to be, 'from what we observe of the world of sensible things, we may deduce the existence of something necessary'. But this premise would only hold, if the first section of the 'third way' – namely, the inference from premise (4) to (5) – is valid, and we have seen that it is not. That is, it has not been proven that, if everything is non--‐ existent at some time, then there is some time at which everything is non--‐ existent. The second premise of the 'second way' was that 'it is impossible for a thing to be the efficient cause of itself.' In that context, the premise is sound. But in the context of the 'third way', this premise will say 'it is impossible for something to be necessary in itself.' And this, of course, is in direct contradiction to the very conclusion of the 'third way'. So there must be some substantial differences between the argument for premise (13) of the 'third way', against an infinite order of things necessary through one another, and the argument against an infinite order of efficient causes, as given in the 'second way'. Following the pattern of the latter as closely as possible, however, our argument for premise (13) of the 'third way' would be: 1) In all things necessary through on another, following in order, the first necessary thing is that through which the intermediate necessary thing is necessary, and the intermediate necessary thing is that through which the ultimate necessary thing is necessary. 2) To take away that, through which a thing is necessary, is to take away the necessity of that thing. 3) Therefore, if there were no first necessary thing among things necessary through one another, there would be no ultimate, nor intermediate necessary thing (1 and 2). 4) If in things necessary through another, it is possible to go on to infinity, there will be no first necessary thing. Not surprisingly, the same equivocation in the sense of the term 'first' appears here, as in the previous case. Premise (4) is true so long as we mean an absolute first necessary thing (for which there is no prior thing through which it is necessary). But that is not the same sense in which the term appears in the Problems with Aquinas 'Third Way' Edward Moad, Department of Humanities, Qatar University premises. In that sense of 'first' – that is, a first necessary thing in relation to any given order of three things necessary through one another – premise (4) is arguably false. If it is possible to go on to infinity in the order of things necessary through one another, then arguably there are an infinite number of 'first' necessary things. Thus, to infer, on the basis of (3) and (4), that with an infinite series of things necessary through one another, there will be no such things at all, would constitute the same fallacy of equivocation that we found in the argument against an infinite order of efficient causes. So this argument is no more effective in proving premise (13) of the 'third way' than it was in the case of 'second way'. Thus, there is no valid inference, given here, to the conclusion that there exists a thing necessary in itself.