A Dialectical Role for the Ontological Argument
August 18, 2011 — 17:13

Author: Kenny Pearce  Category: Existence of God  Tags: , , , ,   Comments: 19

Suppose we make an ontological argument with the following general form:

  1. D (for divinity) is a consistent concept
  2. Every consistent concept is possibly instantiated
  3. D entails necessary existence
  4. Therefore,

  5. D is actually instantiated
  6. A being who instantiated D would be God
  7. Therefore,

  8. God exists

Or something like this. (Note that this formulation of the argument uses the modal principle that possibly necessarily p entails necessarily p.)
This sort of argument has a problem: If (3) is trivial, given how D is defined (for instance, if D is defined as the concept of necessary existence), then the argument is question-begging, for no one who didn’t already believe that D is instantiated would ever accept premise (1). However, if (3) is a surprising result, for which a sophisticated argument is required, then we might worry that D has other surprising consequences, some of them contradictions, and so reject (1).
Furthermore, it seems to me that for most theists the existence of God is more certain than any of the premises in the argument, so it doesn’t seem that the argument can be used to increase the confidence of someone who is already a tentative theist.
So can the ontological argument do anything? I say it can. Suppose we grant that the argument is question-begging, and that, for the theist, the conclusion is already more certain than the premises. Now, all question-begging arguments are valid, and some are sound, the problem is just that they can’t be used to convince people of the conclusion. A parallel case to this can be found in work on the foundations of arithmetic. When axiomatic set theory was being developed, people were coming up with axioms, which they weren’t sure were right, and using them to prove that 2+2=4. Now, since the premises of these arguments were quite questionable, and the conclusion was already known certainly to be true, this procedure can’t possibly have been intended to increase anyone’s confidence in 2+2=4. So what was the point? Well, they were trying to construct an axiomatic foundation for arithmetic, and 2+2=4 is a truth of arithmetic, so if the axioms don’t entail it they are obviously not the axioms we are looking for, and if they entail its contrary they are obviously false. However, if we can come up with axioms that have all the right entailments, we’ll have a reason for thinking our axioms are true, and we’ll be able to use them to answer the questions we weren’t sure about to begin with, and we also will have a much more systematic understanding of arithmetic. (Note that the method of ‘reflective equilibrium’ employed by many philosophers, especially in value theory, has a similar structure: you start by making up some proposed rules and seeing if they get the right answers in the cases where we know what the right answer is, then, if they do, apply them to the cases we aren’t sure about.)
I propose that the ontological argument might play a similar role in a theory of metaphysical theology. (Indeed, I think it does play a role somewhat similar to this in James Ross’s Philosophical Theology.) On this view, the ontological argument is not used directly to convince people of the existence of God. Rather, its premise (1) is proposed as a sort of axiom, on which a metaphysical system is to be built. This system is to be judged by its overall coherence and the plausibility of its consequences. The ontological argument might still have an indirect role to play in convincing people of the existence of God: if it turns out that assuming that the concept of, e.g., a being than which none greater can be conceived, or an infinitely perfect being, or whatever, is consistent leads to a highly attractive and systematic theory of metaphysics, wouldn’t that be a reason for accepting it? Next question: what are the consequences (apart from the existence of God) of supposing the candidate concepts to be consistent?
[cross-posted at blog.kennypearce.net]

Comments:
  • Dianelos Georgoudis

    I have a problem with the proposition “God necessarily exists” because I find it is ambiguous. If by “necessary” one means that God exists in all metaphysically possible worlds then this proposition is trivially true, simply because by definition God is the metaphysically ultimate and thus God delimits what is metaphysically possible. If, on the other hand, by “necessary” one means that God exists in all logically possible worlds then that proposition is obviously false, because God does not exist in a world where nothing exists, and that world is provably logically possible. So it is not possibly the case that God necessarily exists, for there are some possible worlds in which God does not exist.
    Now it is possibly the case that God exists in all metaphysically possible worlds, but from this it does not follow that God exists in all metaphysically possible worlds. So it seems to me that the modal argument does not get off the ground for it applies modal principles to what is really a subset of all possible worlds, namely the subset of all metaphysically possible worlds.

    August 19, 2011 — 1:50
  • Kenny Pearce

    Danielos – I’d like to know more about the (alleged) proof that the empty world is logically possible. Many things (e.g. the denial of the incompleteness theorem) contain very complicated and non-obvious contradictions. Also, it seems to me that your claim that “by definition God is the metaphysically ultimate” is not obvious or uncontroversial. “being the metaphysically ultimate” (i.e. the ground of being for everything there is, or some such) might be a possible substitution for D in my schema, but it is certainly not an agreed upon definition of the word ‘God’ – indeed, many philosophers take that word as a proper name.
    Your basic point that we need to be careful to use the same species of modality throughout the argument is well taken. I used the word ‘consistent’ in part because I had the broadly logical modalities in mind.

    August 19, 2011 — 10:13
  • “because God does not exist in a world where nothing exists, and that world is provably logically possible”
    Whether an empty world is possible in some logical system L depends on the axioms and rules of inference you allow in that system. In classical (non-free) first order logic, it is provable that something exists, and so in any modal logic that accepts classical FOL plus Necessitation, it is provable that it is impossible that nothing exists.
    Of course, you can say that the rules of classical FOL are objectively incorrect by the lights of the objectively correct logic because the objectively correct logic is a free logic. But why think that, apart from an earlier conviction that it is logically possible that nothing exists? And that conviction isn’t going to be based on anything as strong as proof, I suspect.

    August 19, 2011 — 11:05
  • I find the claim that possibly nothing exists puzzling. Suppose nothing exists. Then the number of things is zero. If the number of things is zero, then something is the number of things. So there is something if there is nothing. So there must be something.
    This reasoning rests on some less than obvious claims. But none of them seem to be logically false. So it does not seem to be logically true that there might have been nothing at all.

    August 20, 2011 — 21:07
  • Dianelos Georgoudis

    Kenny,
    The proof I had in mind goes like this: A world is impossible when it is internally incoherent, i.e. when two true propositions about it conflict with each other. But there only one true proposition that applies to an empty world, namely the proposition “nothing exists” (for it fully describes it), and thus there are no propositions about it that conflict with each other. Therefore that world is possible.
    About God being by definition the metaphysically ultimate my understanding of the ontological discourse is as follows: One starts by assuming that the world (our world) is such that it is not “turtles all the way down”, i.e. that there is the metaphysically ultimate. According to naturalism, which is one ontological theory, the nature of the metaphysically ultimate is mechanical, i.e. it evolves in a mechanical way all knowledge about which can be described by a mathematical model. According to the opposite ontology, supernaturalism, reality evolves in a way that cannot be modeled mathematically, but is intrinsically creative in the sense that genuinely new facts can obtain. Of all the different supernaturalistic ontologies there is one, theism, according to which the ontologically ultimate is no less than the greatest conceivable being we can conceive, and is thus (according to virtually universal judgment) one, personal, perfect in goodness, power, and knowledge, etc. That person we call “God” in English, “Dios” in Spanish, “Allah” in Arabic, “Theos” in Greek, etc. So “God” is both a proper name of a particular person, and the concept which denotes the metaphysically ultimate according to theism.

    August 20, 2011 — 21:10
  • Dianelos Georgoudis

    Alex,
    First order logic is a epistemological method that applies to our world. Now any epistemological method uses concepts which refer to something. In an empty world there is nothing concepts may refer to, and there is thus no epistemological method which applies.
    A different way to see the same is as follows: Epistemology is contingent on ontology. An empty world has nothing in it which can be the object of knowledge, and thus no epistemology, including FOL, applies to it.
    Since there is no epistemology which applies to an empty world, one cannot use an epistemology which applies to prove that something exists in that world, which would then indeed render that world impossible.

    August 20, 2011 — 21:24
  • Kenny Pearce

    But one proposition can be impossible all by itself, for instance, there is a round square. Perhaps there is nothing at all is a proposition like that.

    August 20, 2011 — 21:31
  • Jason

    Danielos,
    Does it make sense to say, there is a proposition, “Nothing Exists”, but at the same time literally claim that, “Nothing exists is possibly instantiated”? For in that *possible* world, there is at least one thing, namely, the proposition, “Nothing exists”. It seems that would be self-referentially incoherent. Thus, it is impossible for a world in which nothing exists to obtain.
    Moreover, does not your claim that “Nothing exists is possibly instantiated” contradict the two claims that “Somethings necessarily exists” and “Some propositions are necessarily true”? If so, that is problematic since it more obvious (at least by my lights) that “There are necessary truths” and “There are necessary existents” than the claim that “Nothing exists is possible”.
    I agree with you that the term “God” can function as a proper name and refer to some metaphysical ultimate.

    August 21, 2011 — 17:56
  • Jason

    CORRECTIONS:
    Change first half of the first sentence above from
    –Does it make sense to say, there is a proposition, “Nothing Exists”
    to
    –Does it make sense to say that, “There is some proposition, nothing Exists”
    and
    insert “is” between “it” and “more” in the second paragraph third line down.

    August 21, 2011 — 18:29
  • Dianelos Georgoudis

    Kenny,
    Strictly speaking the proposition you propose is the union of two propositions, (1) X is round, (2) X is square, from which one can easily derive two propositions of the form (3) P, (4) not-P, which instantiate a logical contradiction. Thus I don’t here see a counterexample to my claim that a world is logically impossible only when two true propositions about it conflict with each other.

    August 22, 2011 — 6:33
  • Dianelos Georgoudis

    Jason,
    I think that propositions about a world do not form part of that world. True propositions about a world form part of the map of that world, whereas the world itself is the territory being mapped.
    There is also an argument to be made from absurdity. Suppose we hold that a world W includes the true proposition about it. For each true proposition this produces an infinite regression of elements that exist in that world, namely “p forms part of W”, “(p forms part of W) forms part of W”, etc. So we get a very heavily populated W. Now consider a world W* which is identical to W except does not include any true propositions about it. On the one hand W* would seem to be vastly different than W, on the other hand W* and W would be epistemically identical: you couldn’t say anything significant about W* that is not true about W also, and vice-versa.
    As for the idea in your second paragraph, if I understand it correctly, I think that the propositions “Something necessarily exists” and “Some propositions are necessarily true” are true in all metaphysically possible worlds. In other worlds, reality (our world) in any possible state it may have will include some particular existents, which we therefore call necessary. Similarly some propositions remain true in all possible states reality may have, and are therefore called necessarily true. An example of a necessary existent would be the number 2, and an example of a necessarily true proposition would be “2+2=4”. Now I am not claiming that the empty world is a metaphysically possible world, I am only claiming that it is a logically possible world.
    We may define the set of all metaphysically possible worlds thus: A world is an element of the set of all metaphysically possible worlds if and only if that world is identical to a logically possible state of the actual world (i.e. of reality). On theism the empty world is metaphysically impossible for it can come about only by an act of God’s will, which entails the logically incompatible propositions “God values existence” and “God does not value existence”.

    August 22, 2011 — 6:49
  • Dianelos Georgoudis

    Douglas,
    “The number of things in an empty world is zero” is a true proposition about the empty world. But I think it does not follow that there is something in that world. After all, what exactly is the “something” you think must exist for that proposition to be true? It seems you mean “the number of things in that world”. But numbers do not exist in the empty world, nor do they have to exist for that true proposition to be meaningful or to be true. After all it’s we living in the actual world (which is certainly not the empty world) who form that proposition, understand its meaning, and ponder about its truth value.
    See the distinction between map and terrain in my comments to Jason above. All propositions exist in our world (for our world is the only world where things actually exist). When discussing the empty world as a logical possibility, such propositions have no causal power on that world. So I don’t see anything puzzling in the claim that possibly nothing exists, in the logical sense.

    August 22, 2011 — 7:23
  • If it’s questionable to talk about an empty possible world, could we instead talk about a possible world with no being or with no consciousness? I’m not sure that an empty world is all that problematic, but surely we could agree that the latter type of world is logically possible.

    August 22, 2011 — 11:41
  • Douglas

    Dianelos.
    (1) Possibly, nothing exists (assumption).
    (2) Possibly, zero is the number of things (from 1).
    (3) Possibly, zero exists and zero is the number of things (from 2).
    (4) Possibly, at least one thing exists and it is false that at least one thing exists (from 3).
    That’s impossible. So it must be that something exists. I guess you would deny the inference of (3) from (2) or the inference of (4) from (3). I think that both inferences are plausible. I think the weakest inference is of (2) from (1). Perhaps if nothing exists, then nothing is the number of things.

    August 22, 2011 — 19:10
  • Dianelos:
    You wrote:
    “God does not exist in a world where nothing exists, and that world is provably logically possible”
    I pointed out that in FOL one can prove that something exists. You responded:
    “First order logic is a epistemological method that applies to our world. Now any epistemological method uses concepts which refer to something. In an empty world there is nothing concepts may refer to, and there is thus no epistemological method which applies.”
    I don’t see how you can both say this and maintain that an empty world is provably logically possible. Maybe by “provably” you mean in a logic that isn’t first-order. But then you’d need to say why your “epistemological method” argument applies to first-order logic but not to your preferred logic in which one allegedly can prove an empty world to be possible.

    August 23, 2011 — 12:13
  • Dianelos Georgoudis

    Douglas,
    (1) and (2) strike me as being synonymous, for they both make the same claim, namely that an empty world is possible, i.e. that among all possible worlds there is one with nothing in it. I have a problem with the inference from (2) to (3). From the premise that “zero is the number of things” in the empty world it does not follow that the number zero exists in the empty world. Rather it only follows that the number zero exists in our world, the real world in which we are thinking about the possibility of an empty world, and ponder propositions about it.
    I understand you are only sketching the argument, but it looks kind of strenuous. On the contrary the claim that an empty world is logically possible strikes me as entirely plausible. After all a logical impossibility obtains only when there is some kind of conflict, and the empty world includes nothing which may conflict with something else.

    August 24, 2011 — 0:14
  • Dianelos Georgoudis

    Alex,
    I analyze whether a world is possible or impossible by considering the “book on it”, i.e. the set of all true propositions about this world. In the case of analyzing the logical possibility of an empty world I am not applying logic to it (since the empty world does not support any logic), but to the book on it, which I conceptualize within our world (where logic does apply).
    Specifically I use the broadly accepted criterion that a world is logically impossible if and only if the book on it includes two propositions which logically contradict each other. Since the book on the empty world includes only exactly proposition it is easy to prove that the empty world is not logically impossible. Please observe that I am not using any kind of “preferred logic” in that proof, but applying standard logic to prove a proposition about the book on the empty world, a book which exists in our world.

    August 24, 2011 — 0:22
  • “Since the book on the empty world includes only exactly proposition it is easy to prove that the empty world is not logically impossible.”
    I assume you mean “exactly one”.
    There are just as many propositions true at the empty world as at the actual world. Let p be any proposition true at the actual world. Then either p will be true at the empty world or not-p will be true at the empty world.
    Moreover, that a set of propositions contains only one proposition does not imply that the set is consistent. For it could be that the one proposition is, in fact, self-inconsistent.

    August 24, 2011 — 10:04
  • Dianelos Georgoudis

    Alex,
    You write: “There are just as many propositions true at the empty world as at the actual world. Let p be any proposition true at the actual world. Then either p will be true at the empty world or not-p will be true at the empty world.”
    To be true a proposition must first be meaningful on its domain. Thus propositions such as “George Washington was the first president of the US” or “2+2=4” are meaningful and true in our world, but are not meaningful in the empty world. Nor is their negation meaningful in the empty world. Thus neither they nor their negation belong to the book on the empty world.
    Another way to see this is as follows: The book on a world represents a perfect description (or map) of that world. A book which includes just one proposition, namely “nothing exists”, perfectly describes the empty world.
    “Moreover, that a set of propositions contains only one proposition does not imply that the set is consistent. For it could be that the one proposition is, in fact, self-inconsistent.”
    Do you see any self-inconsistency in the proposition “Nothing exists”? And in any case, as far as I know, self-inconsistent propositions always imply two propositions which explicitly contradict each other, as required by the criterion I use for deciding that a world is logically impossible.
    Incidentally, I was thinking about alternative single proposition books on the empty world, and came up with two, namely: “All propositions of the form ‘x exists’ are false”, and “There are no meaningful propositions except this one” (the advantage of which is that it does not refer to the concept of existence in the first place). The empty world is certainly a weird one, but I think not a logically impossible one.
    I understand that if it is the case that the empty world is logically possible, then it is also the case that there is no logically necessary being. Do you see any reason why this latter belief might be problematic on theism?

    August 24, 2011 — 13:26