Friday, September 17, 2010

Aquinas's "Third Way": One Interpolation

Traditional theists believe, among other things, that there exists a “necessary being”—a being that could not have failed to exist—and that this necessary being is the fundamental or ultimate reality which explains the existence of all other things. But in the world of ordinary experience, the world we encounter through our senses, we only encounter beings which appear to be contingent—that is, beings which could have failed to exist. While there are necessary truths about the world we encounter (for example, that given an initial state of affairs and certain causal laws, a subsequent state of affairs must embody certain features), these truths are consistent with nothing actually existing, and so do not imply a necessary being.

Nothing in our ordinary experience fits with such a “necessary” thing. As Hume famously noted, everything that I can imagine existing is something I can imagine not existing. And for Hume, “imagination” is a technical term that refers to our capacity to reorganize the ideas derived from empirical experience in endless ways. As such, imagination refers to a possible way that the building-blocks of empirical experience might be arranged. Hume’s point, then, is that there is nothing in empirical experience from which we can derive the idea of necessary existence.

As such, to believe in a necessary being is to believe in the existence of something that falls entirely outside the world of ordinary experience—and furthermore, to hold that this “transcendent” reality is more fundamental and, in a sense, of greater ultimate significance than the world we encounter through our senses. This transcendent, necessary reality is the source or “creator” of the world we know. In short, to believe in a necessary being is to adopt a kind of religious stance towards the world (at least in one sense of the term "religious").

But can anything justify such a stance, or is it pure fabrication (as some critics of religion are prone to assert with great confidence)? Historically, a number of philosophers have offered arguments in favor of the existence of a transcendent reality characterized by necessary existence. Probably the most famous is St. Thomas Aquinas, the philosopher and theologian whose body of work is typically regarded as the towering intellectual achievement of the Middle Ages.

Aquinas explicitly argues for the existence of a necessary being in the third of his “Five Way” for proving the existence of God. Let me say that, although Aquinas introduces these five arguments as ways that God’s existence “can be proved,” it is pretty clear that the phrase here is intended in a very loose sense. What we get are five arguments, each for a different conclusion. The first concludes that there must exist an unmoved mover, the second an uncaused cause, the third a necessary being, the fourth something that embodies all the “perfections” that other things only approximate, the fifth an intelligence that guides the unintelligent things that exhibit goal-directed behavior. He then tacks on to the end of each argument a phrase such as “and this we name God” or “everyone understands this to be God.”

So, Aquinas is clearly speaking here to an audience of believers who have a robust idea of God—one for which all of these appellations (unmoved mover, uncaused cause, necessary being, etc.) fit admirably. Aquinas is here showing that there are several arguments which support the existence of something which has one or another of the distinctive properties typically attributed to God. But it needs to be remembered that these “Five Ways” are Aquinas’s starting point in a much more expansive case for the existence of the Christian God in which Aquinas believes.

So, what about the “Third Way”? For me, this is the most interesting of Aquinas’ arguments, but it is also the most perplexing. In fact, on an initial reading it seems as if Aquinas is guilty of a logical error. Specifically, it seems as if he moves, without justification, from asserting one proposition (which I will call PN, for “possible nothingness”) to assuming a related one (which I will call AN, for “actual nothingness”). Here are the propositions in question:

PN: “If all existing things are contingent, then it is possible that at some time nothing existed.”

AN: “If all existing things are contingent, then at some time nothing existed.”

While PN seems to be a justified assertion—and while it is the assertion that Aquinas explicitly makes—his argument’s validity depends on asserting AN. Did Aquinas inadvertently slip from one to the other without noticing? Or did Aquinas see (and assume that we would see) that PN, perhaps in conjunction with certain unstated but self-evident premises, implied AN?

Philosophically speaking, the more interesting question is not whether Aquinas in fact saw a sound inference from PN to AN, but whether there actually is such an inference. Is there? If there is, then the discipline of philosophy requires that we interpret Aquinas’ argument accordingly. That is, philosophy calls us to pursue what is called The Principle of Charity—that is, the principle of formulation the arguments of others in their strongest possible form.

Along with many other philosophers interested in Aquinas, I have reflected on alternative ways of justifying the inference from PN to AN in Aquinas’s Third Way. The formulation of the argument that I presented to my philosophy of religion class on Wednesday was the outcome of such reflection combined with an invocation of the Principle of Charity. What follows is a slight modification (for the sake of greater clarity) of what I presented to my class. I have also identified what is a core premise and what is an inference from prior premises.

1. There exist contingent things (core premise)

2. For each contingent thing, it is possible that it not have existed and, hence, that it not have existed at a given time T (core premise)

3. If, for each contingent thing, it is possible that it not exist at a given time T, then it is possible that no contingent things exist at time T (core premise)

4. Therefore, it is possible that at one time no contingent things existed (from 2 & 3)

5. Given infinite time, every possibility occurs (that is, as the timeline moves towards infinity, the probability that some event with a real possibility of occurring does occur at least once along that timeline approaches 1) (core premise)

6. Either the succession of contingent states extends infinitely into the past, or it has a starting point. (core premise)

7. If the succession of contingent states has a starting point, then at one time no contingent things existed. (core premise)

8. If the succession into the past is infinite, then at one time no contingent things existed (from 4 & 5)

9. Therefore, at one time no contingent things existed (from 6-8)

10. Therefore, if all existing things are contingent, then at one time nothing existed (from 9)

11. If at one time nothing existed, then nothing could ever have come into existence and nothing would exist now (core premise)

12. Therefore, it is not the case that at one time nothing existed (from 1 & 11)

13. Therefore, it is not the case that all existing things are contingent (from 9 & 12)

14. Everything that exists is either contingent or necessary (core premise)

15. Therefore, there exists something necessary (from 13 & 14)

The argument as Aquinas presents it actually goes on to distinguish between two ways in which something could be said to exist necessarily (what might be called dependent vs. independent necessity), and then argue for the existence of something with independent necessity. But the part of the argument presented here is enough to digest and reflect on by itself.

Is this the argument that Aquinas intended, or is it merely one charitable interpolation of his words? I can’t say for sure. But either way, it’s an interesting argument for the existence of a necessary being—and it’s hardly silly. Since the argument is formally valid, anyone who wants to deny the conclusion needs to deny one of the core premises (by which I mean premises that are not conclusions derived from subarguments within the broader argument).

So, for those who want to deny the conclusion, which premise are you going to challenge, and on what basis?


  1. Hi, Eric-

    While my inclination would be to ignore this whole discussion as a display of wildly excessive & egregious charity to defunct philosophy.... I can make a small point.

    That is about the status of "possible" & "contingent". I would argue that there actually don't exist any contingent things. There is no free will, and likewise everything that happens had to happen, period. The philosophical treatment of contingency seems to refer to our thoughts about things.. they could be true, but might not be true. That is fine, but it doesn't apply to actual things, which have no doubt about whether they are or not.. they just are.

    So our belief that things in the (physical) world possibly could not have existed is false. Or at least while it may describe our ignorance, it doesn't describe reality, which just runs on in one direction, with rather implacable laws and processes.

    There is then no need to posit a chooser of fates, etc. But one might then conclude that everything falls into the "necessary" class, whatever one wants to make of that, whether pantheism or atheism.

  2. Eric

    Yes, in what sense we can say contingent things exist seems to be at the centre of this for me. And that takes us into the deep dark heart of physics doesn't it?

    So, what do we even mean by things? If physical things, then these in turn appear to be made up of smaller things, until we get down to the scale where quantum uncertainty rules. At this scale, the logic of this argument doesn't appear to hold. It is not certain for example that we can speak of things existing or not existing at time A in the quantum world.

    As an interesting aside, some physicists like to suggest that even when the universe runs down to a state of maximal entropy, where no further change appears possible, quantum fluctuations will impose a limit on this level of disorder, and given enough time we should expect the circumstances required for a new burst of universe creation, and indeed calculate that this becomes a runaway process leading to infinite universes.

    There is also the unresolved problem of time's arrow. Physical equations are symmetrical with respect with time, and physicists like to suggest the reason we only experience time running in one direction is again to do with entropy. One way of interpreting this is that time itself is not directional, but rather our experience of it is, and if this is the case then I'm not sure this argument about moving back in time until a point of no contingent existence is as simple as it appears.

    Then we can ask pesky questions about what we mean about infinity in this argument, and how good our understanding of this really is, but I'm no mathematician so I'll leave that to those better qualified.

    My point then is a familiar one. Science doesn't determine philosophy, but it does constrain it. Arguments like this only work if we understand the physical terms we're using, like time and existence (at least in the physical sense), and the state of the play in science in the moment is that we're still puzzling over them. So, we need to keep doing the science really, in the hope that one day arguments such as the one presented here can be made meaningful. Until then, this is a good one to remain agnostic about I think.

    It may be that by some things are contingent you are referring to things like the rules by which the physical universe operates, and that changes the problem somewhat, although rules regarding the behaviour of matter appear to be a necessary companion of matter (even if the rules are rules of utter chaos) so perhaps this distinction is unimportant.


  3. many people have speculative ideas. The real issue will be if you can ever demonstrate that your ideas of accurate. That will be when more people will become interested.

    But for those interested in the non-supernaturalistic study of early christianity. I am always happy to talk. I am mostly knowledgeable of the history up will the council of nicea. I am currently most interested in patristic.


  4. Burk,

    As to your first point, I guess I am just dispositionally inclined to approach the greatest minds of the past with an openness to learning something of value if I engage with them seriously and charitably.

    As to your second point, the idea that everything is necessary is an interesting idea--but, I would say, a controversial philosophical one. It's truth value doesn't seem to be a function of empirical facts, and so the assessment of it might benefit from critical but charitable engagement with thinkers of various stripes, past and present, who have wrestled with these ideas. I certainly wouldn't want to rule out any source of insight just because they lived long ago in an intellectual climate very unlike ours and without a body of knowledge we possess.

    That said, I'm not convinced by your claim that the categories of contingency and necessity don't apply to actual things but only to thoughts about them. It is true that these modal concepts are ones we most comfortably and routinely employ with respect to propositions. We say that a proposition is true necessarily when the proposition is such that its negation implies a contradiction. When there is no contradiction involved in negating a proposition, we say it is true contingently.

    But some of the propositions we make are existential ones (of the form "X exists,"). And none of the existential propositions involving ordinary objects of experience (where X refers to an actual or possible object of sensory experience) are such that, in isolation from other propositions, their negation implies a contradiction. And this is what is meant, I think, when it is said that the objects of ordinary experience are all contingent.

  5. Bernard,

    Here, at least, I’m very Kantian: Kant thought that modal categories such as contingency and necessity were “categories of the understanding” which we use to make sense of the empirical world. More precisely, empirical objects are *constituted* by the categories of the understanding, which include modality.

    If this is right, then further scientific inquiry won’t instruct us concerning the meaning of these concepts, because our understanding of what science delivers is a FUNCTION of our modal concepts (among others). Put another way, we wouldn’t have any capacity to organize and make sense of the deliverances of science if we did not do so in terms of concepts (including modal ones) that were already in place.

    But our scientific understanding might adjust what we ultimately apply these modal concepts TO—and this may be part of your point. Of WHAT can we properly say that it exists contingently or necessarily? To answer that, we need to ascertain of what we can properly say that it exists AT ALL.

    Still, why couldn’t Aquinas sidestep this problem and present his argument as having force no matter what counts as a properly existing thing? Why couldn’t he say, “Well, whatever it is that is properly an existing thing, it either exists contingently or necessarily,” and then just push his argument along to the conclusion that some existing thing must exist necessarily?

    Perhaps the problem with THAT is something along the following lines: Perhaps we have become convinced by scientific study of the world that every macro-level “thing” is just a structured collection of smaller things—and if this macro-level thing falls apart, nothing has ceased to exist in a strict sense. It’s just that things have been rearranged. Likewise for some macro-level thing coming to be: It’s just old stuff arranged in a new way, not a new thing.

    So then, that of which we can properly say, “here is an existing thing,” would have to be the most basic building block of matter. But if one thinks quantum indeterminacy entails that we cannot make ordinary existence claims about these basic elements, then perhaps we might think quantum mechanics has shown that there is nothing of which we can properly say that it exists.

    But this entire line of thinking presupposes a reductionistic metaphysics that treats an entity like a cow as simply a sum of its parts and not a single entity in its own right. And so my instinct is to take all of this as a reductio ad absurdum argument against reductive materialism.

    ==> cont.

  6. But I am thinking about the relation between contingency and possibility in the sense of possibility in which we can assign a probability. Specifically, I'm not sure that asserting that something is contingent--even if in a sense it means that it is POSSIBLE that it not exist--has any clear implications for how probable it is that it be the case or not be the case. And if so, the inference in the early part of the argument may not hold--it may turn on an equivocation on senses of "possible."

    And I wonder if your invocation of the "block universe" idea (the idea that time is a dimension such that past and present and future are all "there" all at once, so to speak) may not expose the same problem in a different way. But I need to think about that some more.

  7. Hi, Eric-

    "But some of the propositions we make are existential ones (of the form "X exists,"). And none of the existential propositions involving ordinary objects of experience (where X refers to an actual or possible object of sensory experience) are such that, in isolation from other propositions, their negation implies a contradiction. And this is what is meant, I think, when it is said that the objects of ordinary experience are all contingent"

    I am afraid this isn't making sense to me. If you say, "the moon exists" and I say "the moon does not exist", then we have a contradiction on our hands. Existential propositions necessarily involve contradiction depending which position they take, as far as I can see.

    Again, you seem to be talking about propositions rather than about what the propositions are about. What exists exists, and isn't contingent as far as we know. Our propositions can range from accurate to deluded and be as contingent as you like.

    This whole tack reminds me of the fourth way, likewise a measure of imagination rather than reality. Whatever I can imagine, that must be, including the greatest of all things, ergo god.

  8. Consider this:

    By (1) there exists a contingent being.
    If we assume (2) then it is possible that it didn't exist at some past time.
    By (5), there was a time it didn't exist.

    How did it come to exist? We have three possibilities:

    a) Every contingent being is caused by another one.
    b) A contingent being can begin to exist without a cause.
    c) A contingent being can be caused to exist by a non contingent one.

    If (a) is true then there was always an existing being and the inference (8) is invalid (5 cannot be applied) and the argument fails.
    If (b) is true then (11) is false and the argument fails.
    If (c) is true then the argument begs the question and fails.

  9. Eric

    Yes, I would treat an entity like a cow as in fact a collection of atoms at the most basic level. A cow however is a helpful category for us to use, because it gives a useful shorthand for dealing with that particular lump of atoms that behaves in certain characteristic ways (and tastes a certain characteristic way too I might add.) Having understood how the category cow then comes about (and our failure to understand this has plagued populist interpretations of evolution) does I think force us to consider how Aquinas' argument would work at the quantum level.

    The alternative is to propose that there is some essence of cowishness greater than the sum of its parts that comes into being when a cow is conceived/born. But nobody thinks that any more do they? It's a very hard notion to square with evolution.

    Another thing I was thinking is to do with time. So core premise number 7 says at some time no contingent thing existed (if the succession of contingent states had a starting point). This too seems to potentially clash with physics, where under general relativity time and space are intimately connected to the point that we describe time and space coming into existence through the big bang. So, outside of the existence of space time, we can not properly talk of a time where no contingent thing existed because there is no time without matter (assuming matter is contingent, and if it isn't, then what is?)

    And there's also an interesting question of probability here. JP may have already covered this, but premise 5 says, given enough time all possible things will happen. However, once a thing exists, it may be that the probability of its existence remains 1 (after the event, all probabilities collapse to 1 don't they?) and hence no matter how long you run the tape for, in either direction, there is no possibility of it not existing. This might be close to Burk's original point, that if a thing exists, then it must exist, and here the idea of contingency becomes fuzzy for me.

    This would accord with my basic understanding of the physics. Almost 14 billion years ago, the big bang occurred. Since then there has been no time where no matter existed, and some physicists predict there will be no such time afterwards, due to regeneration. And this is all the time we have available to consider. Any other state involves moving outside of space time which, I submit, our imaginations are incapable of.


  10. About the cow...

    What does that refer to? It seems reasonable to assume that our brain builds a (extremely simplified) representation of the outside world, a model, and that, within this model, there are entities like cows and chairs and so on. This is very similar to what we do all the time with computers. Thinking would consist in the manipulation of these entities.

    So, in this view, a “cow” is an idea, a concept, a symbol, an “object” inside our brain. As quintessential pattern matchers, we map some configurations of sensory input to this idea and we say “here is a cow”. But I don't understand how we could define a cow as a real, single, well delimited, unambiguous entity. Even defining it in terms of its constituents seems problematic because, for one, they are constantly replaced.

    The “model” approach, it seems to me, presents none of these difficulties. Of course, it has some import on what exactly are the “things” or “beings” at the core of Aquinas' arguments.

  11. One could probably challenge the third premise on the basis of the first law of thermodynamics; that “energy can be transformed, i.e. changed from one form to another, but cannot be created or destroyed.” It might be a fact that no contingent being can ever simply cease to exist without giving rise to one or more other contingent beings of the same net amount of energy.
    If this is the case, even if all beings were contingent, then there would never be a time in which nothing existed. One could then argue that the first law of thermodynamics, or the net amount of energy, was some form of necessary being in an abstract sense, but I don’t think this is what Aquinas would have meant by the word God.

  12. Eric,

    I have trouble with premise (5):

    5. Given infinite time, every possibility occurs

    Imagine a world that consists of a machine that can possibly be in three different states. Further that machine is wired in such a way that it alternates between the first two states. No matter how much time passes, the machine will never reach the third state, so that third state even though possible will never obtain.

    Coming back to the idea that God exists necessarily, doesn’t this say that God exists in all possible worlds? But I can imagine a world in which God does not exist, say a world that consists of a single immutable sphere and nothing else. Such a world is possible, isn’t it? Am I missing something?

  13. In order to accept Aquinas' argument two things must be true: (a) the model implicit in the argument must be a sufficiently good fit to reality and (b) the logic must be sound

    As for (a), the argument describes a reality composed of “things” set on a background of absolute time extending infinitely into the past. The latter is problematic on two counts: there is no such a thing as absolute time and, moreover, time is part of the fabric of the universe – not external to it. In particular, there is no “before” the big bang – the phrase is simply meaningless. As for “things”, it is not clear what they should be but the best choice might be the ultimate elementary particles. This is also problematic: for one, there might not be such things (a particle physicist would be helpful here) and, second, if it's meaningful to speak of these, they might have always existed (from the BB on), creating all the higher level objects by constant recombinations. As time originates at the BB, there could have been no time at which these particles did not exist.

    As for (b), there is a problem with premise (3):

    If, for each contingent thing, it is possible that it not exist at a given time T, then it is possible that no contingent things exist at time T.

    This assumes that “things” are independent from each other. If they are independent, and finite in number, then (3) may hold. In reality, however, they are not. Once a “thing” exists at some time, the situation changes completely and the existence of some other things may no longer be contingent. For example, if a thing A is caused to exist by a previously existing thing B, then B becomes necessary (or at least the existence of some antecedent thing is necessary). We then have a succession of contingent things extending indefinitely into the past.

    As Dianelos suggests, premise (5) is also problematic:

    Given infinite time, every possibility occurs

    The problem is similar to the problem with premise (3): it assumes that possible events are independent. But they are not necessarily so. Suppose that a large number of events are each individually possible. It does not imply that all of them can happen because the occurrence of one may prevent the occurrence of another.


  14. On a lighter side, here's a good piece in the Onion: God Angrily Clarifies 'Don't Kill' Rule.

  15. Some thoughtful comments here--comments which reveal, I think, how our assessment of Aquinas's thinking (or one interpretation of it) is bound up with such puzzles as the nature of time and what constitutes an existing thing (contingent or otherwise).

    Unfortunately I haven't had time to dig into the specifics of your respective comments because I have been and still am preparing for an upcoming conference.

  16. One quick point with respect to the following (from Burk's post):

    "If you say, 'the moon exists' and I say 'the moon does not exist', then we have a contradiction on our hands. Existential propositions necessarily involve contradiction depending which position they take, as far as I can see."

    Of course, the negation of any proposition contradicts the original proposition. But when one says that the negation of a proposition implies a contradiction, one means that one can deduce a contradiction from the negation of the proposition taken by itself.