Thursday, July 16, 2009

The Thomistic Cosmological Argument - Revised

1. Every dependent being derives its existence from some other being.
2. The series of dependent beings either proceeds to infinity, or has a first being.
3. The series of dependent beings cannot proceed to infinity.
4. Therefore, a first being exists.

This argument is really a summary of Thomas' proof as found in De Ente et Essentia. I like this version, since it doesn't rely on "causation" per se, with all of its alleged deterministic connotations.

The first premise has been defended explicitly since at least the time of Parmenides. Ex nihilo nihil fit: out of nothing comes nothing. If there were literally nothing, then not even the potentiality for something to come into being would exist. But, since something exists, it must be either dependent or self-existent.* We certainly observe dependent things in the world. An oak tree is dependent on the acorn, for example.

The second premise doesn't involve a temporal succession of events. Rather, the claim is that there is a series of beings that entail rank or source. Hence, it is considered hierarchical, instead of temporal.

Is it possible that this series is infinite? Several reasons are given against this conclusion. For one, a self-existent first being seems to be required in order for any dependent beings to exist. Just as a house needs a foundation, else the entire structure collapse, dependent beings likewise require something to hold them up. Moreover, if the series of dependent beings is infinite, then an infinite series would be sustaining something within a finite period of time. However, it would take infinite time for an infinite series to do anything. Hence, the series itself must be finite and therefore is grounded in a first being, in confirmation of (3).

I think this is a very reasonable conclusion to make. One might object that in a finite space, there are infinitely-many points. Of course, this argument is undermined by the fact that mathematical points are abstract and don't possess any physical dimensions. Furthermore, a finite space still has definite first and last points; so if there is any analogy between the two, a first being is still required.

The most difficult part of this argument for the Thomist, in my view, is in making the inference from a first being to the claim that this being's existence and essence
are identical. This conclusion does appear to follow from the argument above, though. The reason why is that if the first being is not dependent on anything else, then it cannot derive either its existence or its essence from another. Allow me to put this more explicitly.

The difference between a real unicorn and an imaginary unicorn is that the former is instantiated in actuality. This doesn't fall prey to the Kantian maxim that existence is not a predicate, since we're not merely adding existence to something purely conceptual. Rather, we're considering an a posteriori claim. From this it follows that a unicorn's existence is dependent on something else that brings about its existence. But, we have already seen that the series of dependent beings cannot proceed to infinity. If a being's existence is distinct from its essence, its existence is either brought about by some external being or by its own essential properties. The problem here is that nothing can be brought about by its own essential properties.** The difficulty with the former is that the first being does not derive its existence from anything else; otherwise, it wouldn't be first, which is a self-contradiction.

The conclusion seems to follow, then, that the first being's existence and essence are identical. The reason I say this is a difficulty (although there are certainly solutions) is that the divine attributes that are later inferred about this first being do appear to be distinct. Goodness seems logically distinct from power, knowledge from aseity, and so forth. The Thomist stresses the doctrine of analogy, which views the attributes of God as one and the same, so that the goodness of God really is the same as His power, etc. It's obvious that in us these characteristics are different, but what about in the divine essence?

*Something is self-existent if it exists by a necessity of its own nature. This shouldn't be confused with self-causation.

**This solution has the same problem as with self-causation. Something must already exist in order to bring about its own existence, which is absurd.


  1. Good post Doug.

    Are you defining "being" as a conscious or living entity, or merely something that exists?

    Also as promised, I have some questions around the attributes you've revealed.

    Can you define what you mean by good?

    Can you show how an idea can exist without a mind?

  2. Thanks, Vagon.

    I'm defining "being" as just "anything that exists." If you prefer "entity" or "thing," those terms work as well.

    The attributes of God I'm saving for another entry, but I'll still address your questions. In my mind, the true is what is, and the good is what ought to be. These definitions may appear simplistic, but they're also our common-sense, working standards.

    It's funny that you should ask about ideas existing without a mind. My position is actually that all ideas, and indeed all abstract objects, are concepts of a mind. Moreover, the union of all abstract objects is a concept of the divine mind. I've written a couple posts on this blog about it, but Chad McIntosh's defense of the so-called "conceptualist argument" is the best I've seen.

  3. Good reference, thanks.

    Should I continue on my line of questioning or wait for the attributes post?

  4. Well, when you say good as common sense. Do you mean good is as the majority sees fit?

    I see the Doxazo claims that "absracta" are immaterial. Can you show how these, can exist without a brain?

  5. There are a number of sophisticated defenses of the necessary existence of abstracta. One of them is based upon the S5 axiom of modal logic:

    1. Possibly numbers exist.
    2. Necessarily, if numbers exist then necessarily numbers exist.
    3. Necessarily numbers exist.
    4. Therefore, numbers actually exist.*

    To put it succinctly, if there is a possible world in which numbers possess necessary existence, then numbers exist in every possible world. This is (somewhat surprisingly) uncontroversial among modal logicians. The argument's soundness depends upon how one views the possibility of numbers via premise (1).

    I would actually appeal to the indispensability of abstracta. Let's construct a thought experiment in which there are no physical brains in some possible world. Even if this were the case, it would still be true that 2+2=4. This mathematical proposition is an abstract object, so it likewise appears to be an example of something that exists necessarily, even apart from the existence of contingent physical brains.

    The non-theist could postulate that abstracta just exist necessarily without any mind whatsoever. But, this solution runs into the enormous difficulty of explaining how we could then have knowledge of such objects:

    1. There is a causal relationship between a subject and the external object that is known.
    2. Abstract objects do not stand in causal relations.
    3. Hence, if abstract objects are external to the mind, then they cannot be known.
    4. Abstract objects are known.
    5. Therefore, abstract objects are not external to the mind (i.e. they are not mind-independent).

    So, if we take the union of all true propositions - U - then, U must be the concept of a mind. But, only an omniscient mind would know all true propositions, from which it follows that an omniscient mind exists.

    Regarding what "good" means, it's hypothetically possible for the majority to be wrong. Nevertheless, the individual has a perception of moral values that I think remains justified apart from a defeater. We can rationally conclude that something like rape, for example, is wrong because we would object if that kind of behavior were imposed on us.

  6. *Colin Cheyne, "Knowledge, Cause, and Abstract Objects," p. 106.

  7. "Let's construct a thought experiment in which there are no physical brains in some possible world. Even if this were the case, it would still be true that 2+2=4."

    I disagree. Consider another of Doxazo's abstracta, Dantes inferno:

    It is absurd to say in your no-brain possible world that Dante's Inferno is a true example of a representation of hell. Dante's concept of a place hell requires pain. Pain is a secondary quality, not an attribute. Secondary qualities require a brain.

    Mathematics is the same. The attribute, e.g. the defined quantity of molecular make-up of each of the 4 "number" units, will not change. But the meaning or relationship of the fact they can be divided into two groups (2+2) is lost.

    Put simplest, there are physical attributes and our brains have adapted to make sense of them. That adaption creates abstracta. Abstracta exist only as a result of that adaptation.

  8. You might want to bring this up to Chad, but I don't think he means what your interpretation of "Dante's Inferno" refers to.

    Why do you think the number-relationship in the quantity of molecules is lost?

  9. I don't think Chad has a comments section :)

    I do find it odd that he thinks there is no possible world where size and shape do not exist. But size and shapes are directly dependent on physics, which break down at singularity. So in a world that was still at singularity he'd have a large problem. Also he refers to the necessary existence of 0, but then you yourself have agreed that zero doesn't exist in anything other than conceptual form.

    To answer your number-relationship question:

    To assume 2+2=4 you would need to presuppose mathematics in a brainless world.

    The 4 entities still exist, but there would be nothing to interpret the tautology behind the mathematical relationship.

    It just would be, without the restatement which is just an interpretation of the situation: 4 entities.

  10. That was my mistake. Chad does have a comments section, but not on that page. Try the homepage and scroll down to the different entries.

    When he says that shapes, sizes, and numbers all have necessary existence, he means in an abstract sense. So, there may be a possible world in which no physical object exists; but, it would still be true that if there were any physical objects, they would have a size and shape. This is likewise applicable to a singularity.

    Thanks for your answer regarding the number-relationship issue. It seems to me that we need to be careful not to conflate a lack of interpretation (as you've put it) with a lack of an instantiation among concrete objects. The truth of 2+2=4 doesn't need to be validated by a physical brain any more than the law of gravity does.

  11. "This is likewise applicable to a singularity."

    I disagree.

    Size is relative, we could say the earth is big, but thats only relative to us. Similarly lengths such as inches only exist relatively.Shape refers to an object's external dimensions. But these are also relative. Both these terms are defined by the universe.

    In declaring that size and shape are necessary, Doxazo is simply pandering to the human thought process of trying to create abstract models.

    Re: Number relationship.

    Well here in lies the problem I referred to at the start. Mathematics is not instantiated without a brain. In order to consider things are instantiated a posteriori you require mathematics and by extension logic.

    We know that logic works axiomatically, you cant deny it without using it. But if there is noone using logic, where is the problem? Logic requires use to exist.

  12. Vagon, I'm going to leave the discussion of abstract objects for another entry. I do appreciate the spirited exchange, though. My next post will detail God's attributes as they are inferred from the Thomistic Cosmological Argument, as found in De Ente.

  13. Absolutely, I hope I'm not completely missing the point in places, some of the formal terms escape me, I'm sure.

    Looking forward to your other posts.

  14. Appreciate I am somewhat later to the party here...

    With regards to 2, how can you rule out a cyclic relationship? Intuitively it might not make much sense, but sometimes nature is like that, and we are thinking about some entities very much outside our every day experience (universes, God, etc.).

    "However, it would take infinite time for an infinite series to do anything."
    Is it not also the case that it would taken an infinite time before an eternal and unchanging being got around to doing something?

  15. Hi Andy,

    In regards to your last question, God's eternity is not envisaged as his having traversed an infinite amount of time before creating the universe. Rather, God is timeless, or without time.

    In fact, the TCA only attempts to argue that God exists as the first cause insofar as he is the here-and-now sustaining cause of the regress of dependent entities. As far as the proponent of the TCA is concerned, the universe may or may not be infinite in its past. In other words, the focus is on sustaining causality, as opposed to originating causality.

    I think a cyclic account of causality is self-defeating, and not just counter-intuitive. For example, an acorn may grow in an oak tree, but the acorn's sustaining causes (water, sunlight, soil, etc.) cannot be explained in terms of just another acorn. Every potentiality that is actualized has its actualization caused by something with the power to do so. No potentiality actualizes itself.