The Rhetorical Force of the Modal Ontological Argument

Ontological arguments are fun. I don’t know of anybody who has ever been converted to theism on the basis of an ontological argument (although I had a professor once who was agnostic because he thought that the force of the ontological argument and the problem of evil balanced each other out) but they’re fun intellectual exercises. The modal version of the ontological argument developed by Plantinga is probably the most fun. While I’m not convinced by it, I’ve recently come to appreciate its rhetorical force in theism/atheism debates. Here is the argument:

P1. It is possible that God exists

P2. If it is possible that God exists, God exists in a possible world.

P3. If God exists in a possible world, then he exists in all possible worlds.

P4. If God exists in all possible worlds, then God exists in reality.

P5. Therefore, God exists in reality.

Conclusion: Therefore, God exists.

The crucial premise is premise 1. The other premises follow from axioms of modal logic. Granted, some have argued that an axiom of modal logic called S5 is controversial (it states that ‘if possibly necessarily p, then necessarily p’), but I’m going to avoid this controversy here because I have no expertise in modal logic. So assuming S5, premises 2 – 5 follow. Returning to premise 1, an atheist could deny that God’s existence is a possibility. There are a couple of options: 1) one could argue that the concept of God is logically incoherent, i.e. that some of the divine attributes entail a contradiction; 2) one could argue that the evil in the world makes God’s existence logically impossible. These strategies are possible, but I’m not sure how viable they are. They both seem to have fallen out of fashion lately. That’s not to say that they’re wrongheaded, but it is to say that both theists and atheists in the field have turned their attention to different atheistic arguments, usually probabilistic in structure.

But it is here that I feel the rhetorical force of the ontological argument. By ‘rhetorical force’ I don’t mean that I’m convinced by the argument. The atheist, when pressed, can bite the bullet and deny premise 1. But I think the atheist pays a high price for denying premise one: namely, he shoulders a heavier burden of proof. It’s not enough to show that God probably doesn’t exist; one has to show that God’s existence is logically impossible, impossible in every possible world. So in a rhetorical context, the ontological argument is quite a bit more useful to the theist than it’s often given credit for. It forces the atheist to defend a much stronger position. It makes the atheist ‘get off the fence’ about whether God’s existence is possible or not. One has to adopt a very strong form of atheism, not merely the inductive, probabilistic kind that I tend to favor. So what move should the inductive atheist make when faced with this argument? I’m not sure, which is why I feel the rhetorical force of the argument. Any thoughts?

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12 responses to “The Rhetorical Force of the Modal Ontological Argument

  1. Plantinga’s ontological argument is pure sophistry, and has no force whatsoever.

    To begin with, it’s important to understand that when you’re using the S5 modal axiom system, you cannot assume that “possible” or “modally possible” mean the same thing as “logically possible” or “logically coherent.” In fact, it’s when working in S5, it’s logically impossible for every logically coherent assertion to be true in some possible world. It is possible when working in S4, but that’s another story.

    For example, consider the three assertions “Unicorns exist in no possible worlds,” “unicorns exist in some but not all possible worlds” and “unicorns exist in all possible worlds.” All three of these statements are logically coherent. There’s nothing stopping me from making a model in S5 in which no possible worlds contains unicorns. There’s nothing stopping me from making a model in S5 in which some but not all possible worlds contains unicorns. And there’s nothing stopping me from making a model in S5 in which all possible worlds contains unicorns. But what I cannot do is make a single model in S5 in which each of those three statements is true in each of three different possible worlds. “logically coherent” and “possible” do not mean the same thing when working in S5. It’s for that reason that it is fallacious to assert that the atheist must show that the concept of God is somehow logically coherent in order to be justified in believing it is impossible for God to exist, if we’re working in S5.

    Suppose I’m in a remote city , Dullesville CT, looking for a restaurant to eat. Yet I look and I look, but I can’t find a restaurant anywhere. I begin to wonder if there is a restaurant in Dullesville.

    Suddenly I have an insight! I define a restaurant to be a “worldwide restaurant” if it has branches in every city in the world. Is there a worldwide restaurant in some city somewhere in the world? It seems very likely! There are tens of thousands of cities after all, surely one of them has a worldwide restaurant. But if there’s a worldwide restaurant in any city in the world, even in Bodhgaya India, then that worldwide restaurant must have a branch right here in Dullesville!

    Suddenly, it seems a lot more likely that there’s a restaurant in Dullesville. After all, there just has to be one worldwide restaurant somewhere, anywhere in any city in the world, and then there has to be a restaurant right here in Dullesivlle!

    Certainly the burden of proof o the skeptic has increased. The skeptic who wishes to show there are no restaurants in Dullesville now has to prove there isn’t a single worldwide restaurant in any city anywhere in the world! Has he been to all those cities? I think not!

    I hope you can see how silly this is, but it has the same structure as Plantinga’s argument. We posit the existence of possible worlds (though never precisely define what that means, except we assume one of them is the actual world). We then define “impossible” to mean not true in any of these hypothetical worlds, and “possible” to mean true in at least one of these hypothetical worlds.We then define God so that an omnipotent omni-powerful omni-etc being isn’t God unless he exists in all the possible worlds. And poof! If God exists in even one possible world, he exists in all of them, and in actuality!

    It’s all perfectly logically airtight, but it’s also completely silly. It has nothing to do with reality. Suppose an atheist was, for the sake of argument, to accept S5 as an environment for reasoning about possibility and impossibility, and to accept Plantinga’s assumptions about God. Suppose further that the atheist had a good reason for believing that God probably doesn’t exist in reality. Now the atheist has a good reason for believing God probably doesn’t exist in any possible world, as we’ve defined the notion of God and possibility so that if God doesn’t exist in even one world, he doesn’t exist in any.

    It’s pure sophistry.

  2. Thanks for the comment, Rick. I suspect the argument is sophistry, but I find it difficult to put my finger on where the sophistry lies. Note also that saying that an argument has rhetorical force, as I do, is perfectly consistent with saying it’s sophistry. Sophistry is effective precisely because it has rhetorical force, despite being logically fallacious.

    I was following you until this part: “But what I cannot do is make a single model in S5 in which each of those three statements is true in each of three different possible worlds. ‘logically coherent’ and ‘possible’ do not mean the same thing when working in S5.” Do you mean that you cannot make a model in S5 in which ALL of those three statements in true in each possible world? If you could connect the dots a little more explicitly for me here that might help.

    If I’m understanding you correctly, I’m still not clear on it’s application to Plantinga’s argument. You say that it’s fallacious to assert that the atheist must show the concept of God to be incoherent in order to show that God’s existence is impossible. But that was only one of the options I canvassed in the original post. One can show that the concept of God is incoherent OR one can show that God’s existence and the existence of evil entail a contradiction. But both options entail a denial of premise 1.

    You seem to be saying though that the atheist need not deny premise 1. What I hear you saying — and correct me if I’ve misunderstood — is that premises 2-5 don’t follow on S5. In my survey of the literature on this argument, there seemed to be a consensus that 2-5 do in fact follow. Can you point me to anyone in the relevant literature who disputes this? (Of course, some have disputed S5 itself or argued that S5 entails untoward consequences for theism, but these are different strategies.)

    Also, in your Dullesville analogy and subsequently, you use the terms “likely” and “probably.” Where do you see probability in the original formulation of the argument? You say “Suppose further that the atheist had a good reason for believing that God probably doesn’t exist in reality. Now the atheist has a good reason for believing God probably doesn’t exist in any possible world, as we’ve defined the notion of God and possibility so that if God doesn’t exist in even one world, he doesn’t exist in any.” I don’t see how this follows. I don’t see how probability is enough here. Obviously, if God necessarily doesn’t exist in the actual world, the God doesn’t exist in any possible world. But this just is to deny premise 1.

    Basically, what I’m shopping for in this post is a dialectical move that I can make in an oral debate with a theist in which the subtleties of modal logic are likely to get lost. The theist is either going to ask me what premise I’m denying or what’s wrong with the logic of the argument. It comes back (for me) to premise 1. You seem to be attacking the logic of 2-5. Again, perhaps a reference to the literature would help.

    • Thank you for your reply, and you’re quite right; something can be sophistry and still have rhetorical force. I confess I’ve been a little frustrated seeing an argument that at bottom is so silly becoming so popular. And you’re quite right; seeing there must be a problem is a lot easier than putting your finger on exactly what it is. I’ve spent weeks thinking about this myself.

      ——————
      I was following you until this part: “But what I cannot do is make a single model in S5 in which each of those three statements is true in each of three different possible worlds. ‘logically coherent’ and ‘possible’ do not mean the same thing when working in S5.” Do you mean that you cannot make a model in S5 in which ALL of those three statements in true in each possible world? If you could connect the dots a little more explicitly for me here that might help.
      ——————-

      I wish I could sit right beside you and draw diagrams, because then it would be easy to explain. Define the following sentneces

      A – Unicorns exist in no possible worlds (they are impossible)
      B-Unicorns exist in some but not all possible worlds (they are contingent)
      C-Unicorns exist in all possible worlds (they are necessary)

      What I’m saying is that it’s impossible to construct a model in S5 with 3 different worlds in which A was true in one of them, B was true in another, and C was true in a third. The reason for this is, in S5 if A is true in just one possible world it’s true in all of them, and the same for B and C.

      Now I’d argue that each of these sentences is logically coherent. A model in S5 could accommodate any one of them individually. But it’s impossible to have a single model satisfying S5 in which A is true in one possible world, B is true in another possible world, and C is true in a third.

      Because of this, the terms “modally possible” (meaning being true in a possible world) and “logically coherent” do not and cannot mean the same thing when working in S5. So an atheist does not have to believe that the idea of God is logically incoherent in order to deny that it is modally possible for God to exist. Actually, what “modally possible” is supposed to mean, apart from its technical definition, isn’t clear at all.

      ————————–
      You seem to be saying though that the atheist need not deny premise 1. What I hear you saying — and correct me if I’ve misunderstood — is that premises 2-5 don’t follow on S5. In my survey of the literature on this argument, there seemed to be a consensus that 2-5 do in fact follow. Can you point me to anyone in the relevant literature who disputes this? (Of course, some have disputed S5 itself or argued that S5 entails untoward consequences for theism, but these are different strategies.)
      ————————–

      I haven’t explained myself well. Premises 2-5 do follow from S5. Well, one could quibble about premise 3, but if one just defines God to satisfy premise as Plantinga does, then it can be made to work.

      What I’m arguing is that if we’re using S5, then “possible” no longer means “logically coherent” or “reasonable” or “likely” or “believable.” Actually it’s not at all clear what it’s supposed to mean.

      One then has two options:

      (1) Work in S4 instead of S5
      This is my preferred option, as we can now assume that anything that is logically coherent is also possible, which is how people generally use the word. If we take this route, there’s no problem in accepting premise 1.

      (2) Work in S5, but be very clear that “possible” no longer means what we usually imagine it means, especially when applied to objects that are defined to necessarily exist.

      The ontological argument works by equivocating on the meaning of the word “possible.” It starts by using the technical definition of S5. But then to get its conclusion, it invites us to refer to our intuitive understanding of “possible” as believable, or logically coherent, or even, true for all I I know.

      —————————————————–
      If I’m understanding you correctly, I’m still not clear on it’s application to Plantinga’s argument. You say that it’s fallacious to assert that the atheist must show the concept of God to be incoherent in order to show that God’s existence is impossible. But that was only one of the options I canvassed in the original post. One can show that the concept of God is incoherent OR one can show that God’s existence and the existence of evil entail a contradiction. But both options entail a denial of premise 1
      ————————————————————

      Showing that “. . .the concept of God is incoherent OR one can show that God’s existence and the existence of evil entail a contradiction.” is showing that the concept of God is logically incoherent, which is what I’m referring to.

      But this is falling into the theists trap. This is falling into the theist’s trap. It’s accepting the conclusion that the burden of proof has somehow increased on the atheist due to the ontological argument. This is false; the ontological argument is a word game.

      Of course one can make such arguments if one likes,, but one doesn’t need to make them to specifically defeat the ontological argument.

      For that matter, it’s not the job of the atheist to refute premise 1; it is the job of the theist to support it.

      —————————
      Also, in your Dullesville analogy and subsequently, you use the terms “likely” and “probably.” Where do you see probability in the original formulation of the argument?
      ———————————-

      It isn’t explicitly in the original argument. Here I’m trying to simulate why someone using this argument might be persuaded to accept premise 1, because they intuitively think of “possible” as meaning either epistemically possible or logically possible, when (if we’re using S5)

      Actually Plantinga does explicitly make an argument about probability when defending the ontological argument, arguing there might be a 50/50 chance premise 1 versus its denail might be true.

      ———————————–
      You say “Suppose further that the atheist had a good reason for believing that God probably doesn’t exist in reality. Now the atheist has a good reason for believing God probably doesn’t exist in any possible world, as we’ve defined the notion of God and possibility so that if God doesn’t exist in even one world, he doesn’t exist in any.” I don’t see how this follows. I don’t see how probability is enough here
      ———————————
      I’m not sure how to further explain this. If the atheist has a good reason for believing God probably doesn’t exist, then using the framework of S5 and the Plantinga’s definition of God, that good reason becomes a good reason for believing God is probably impossible.

      Let me refer back to the worldwide restaurant story, because everything is in there. The story operates by defining a worldwide restaurant to be one that has a branch in every city. We then argue that this makes it reasonable to believe a restaurant exists in Dullesville, since we only need to find one worldwide restaurant in any city anywhere. Meanwhile, the restaurant skeptic has a huge burden of proof, because to prove no restaurant exists in Dullesville, he has to prove no restaurant exists in any city whatsoever.

      But this is ridiculous! Because how would one verify a worldwide restaurant existed in some city? By verifying that it had branches in all cities everywhere, including a branch in Dullesville! So as part of verifying a worldwide restaurant exists in some city somewhere, we have to verify it exists in Dullesville. The burden for the person trying prove the existence of such a restaurant has increased, not lessened!

      In the same way, accepting S5 and Plantinga’s definition of God, yes, one would only have to show that such a God exists in some possible world. But what would be involved in verifying that that God was God? One would have to verify it existed in every possible world, including reality! Veryifying that God exists in some possible world is not easier than verifying God exists in reality if part of the definition of a possible God is that such a possible God is only a possible God if it exists in reality as well.

      And it’s silly to assert that the modal ontological argument increases the burden of proof on the atheist; if anything it decreases it. The atheist merely needs to show it’s possible God doesn’t exist for it to follow that God doesn’t exist, and couldn’t possible exist.

      I hope this is helpful, and I’d be glad to keep talking about it. I too ham looking for the perfect refutation of the ontological argument that makes everything crystal clear. ^^ As for literature, I don’t have anything that directly applies unfortunately. I have been reading Fitting and Mendelsohn’s modal logic and Plantinga’s the Nature of Necessity.

      • Thanks for the follow up, Rick. Your above remarks go a long way toward clarifying the issues for me. I think you’ve definitely targeted the faults in the argument. I’m trying to boil your criticisms down to a concise counter-argument that one could deploy in a debate context. If you want to take a stab at that, please be my guest. Your second to last paragraph suggests that one might flip the argument on it’s head and come up with an atheistic version.

        I think you’ve adequately addressed my worries about premise 1 being the only way out of the argument. Indeed, this is falling into the theist’s trap as you say. It seemed clear to me that this strategy couldn’t be the only way to combat the argument. Of course, what the better move would be wasn’t so clear to me. Thanks for the insights and check out some of my other posts if you’re so inclined.

  3. Hello,

    I’ve been thinking further about the ontological argument, and my views have been shifting. I still find it unpersuasive, but I’m beginning to believe that there is no pithy clever way to explain why, because the issues involved are subtle.

    Boiling it down though, it is simply not the atheist’s responsibility to show premise 1 is false to show the argument is not sound. Rather, it is the theist’s reponsibility to support premise 1 for a nonbeliever to take the argument seriously. I think a theist would see this if the positions were reversed. Suppose an atheist gave a proof of the nonexistence of God, and when the theist asked why he should accept such and such a premise as true, the atheist demanded he prove it false. It is the responsibility of a person who finds a proof persuasive to support the premises, not that of the skeptic to show the premises false.

    This is particularly important in the case of the modal ontological argument, as its use of S5 assumes a very particular meaning for the word “possible.” To be metaphysically possible (alethic possibility) as required in S5 is not the same thing as logically coherent (apodictic possibility). It’s possible for an assertion to be metaphysically impossible, and yet for it to be impossible to prove false.

    So what the theist does in this argument is to construct a valid argument that relies on the definition of possible as metaphysical (or alethic) possibility. He then challenges the atheist to prove God is not possible. But just because something is not metaphysically possible doesn’t mean it can be proved impossible, so this is a non-sequitor.

    In short, the modal ontological argument equivocates with the meaning of the word “possible.” It uses an alethic sense to establish the validity of the argument, then an apodictic sense to justify the premises.

    It is still important for the atheist not to fall into the trap of attempting to disprove premise 1, because doing so is to share in this fallacy. Rather, the atheist should point out that it is up to the person making the argument to justify the premises, not to the unpersuaded party to prove them false. And furthermore, arguing that the idea of God appears logically coherent is irrelevant, as logical coherence in that sense is not the same thing as metaphysical possibility.

    Working in S5, the statements “P is possible” and “Either P is necessary or it is possible that P is true contingently” are logically equivalent. Hence when working in S5, defending the statement “It is possible God exists” is equivalent to defending the statement “Either God necessarily exists or it is possible God exists contingently.” Since the theist making the argument believes it’s not possible that God exists contingently he cannot defend this premise without showing that God exists necessarily. But this is what the modal ontological argument purports to prove; hence it is circular.

    • Thanks for the additional thoughts, Rick. I think I was being tripped up by the equivocation of ‘possible’ that you mentioned. I also suspect you’re right that there’s no quick way to explain where the argument goes wrong.

      • Paul Almond described a useful example that helps to think about the modal ontological argument.

        Goldbach’s conjecture from mathematics states that every prime number greater than four can be written as the sum of to odd prime numbers. Goldbach’s conjecture remains unproven to this day, and no one has found a counter-example.

        Goldbach’s conjecture is an example of a statement that cannot be contingently true or false if anything is. If it is false, and there is an even number that cannot be written as the sum of two primes, then there is no possible world in which it can be so written. And if it’s true, then there is no possible world where an even number greater than 4 could be written as the sum of two prime numbers.

        So, using S5 logic, if it’s possible for Goldbach’s conjecture to be true, it must be true necessarily. Contingent truth for statements of number theory doesn’t make sense.

        But now suppose someone asked me if I thought if it was possible Goldbach’s theorem was false. On an epistemic level, I would have to say yes, I am not able to prove there is no even number greater than four that isn’t write-able as the sum of two primes (if I could prove that, I’d be famous!).

        If the person then told me that because I’d admitted it was possible Goldbach’s conjecture was false, I must now admit it is necessarily false, I’d laugh at them. Apodictic or epistemic possibility is different than the alethic or metaphysical possibility assumed in S5. If they further asserted that it was my responsibility to prove Goldbach’s conjecture true, and if I couldn’t we should conclude there was a counter-example, I would say they didn’t understand mathematics. Ever since Godel, we’ve known it’s there are theorems that are true which cannot be proven. If someone thinks there’s a counter-example to Godel’s theorem, it’s up to them to demonstrate it, it’s not up to anyone else to prove they can’t.

        And if a theist wishes to argue in favor of the ontological argument, ti’s up to them to demonstrate that it’s possible God exists; they don’t get to challenge atheists to prove it’s impossible and declare victory if we can’t (how would we even prove the impossibility of such a vaguely defined concept?). Oh, and as they’ve defined God in such a way that he must exist in all possible universes to exist at all, as part of proving it’s possible God exists they must prove he exists in all possible universes, as by their own peculiar definition anything that fails to do so isn’t God. Good luck with that.

  4. Thanks. That’s a helpful example.

  5. Pingback: Further Reflections on the Prosblogion Survey | dude ex machina

  6. Keith Brian Johnson

    I hope you are still reading comments on this post! I think I can help you with that “pithy argument” you’re looking for. It’s this: when God is so characterized that his possible existence implies his necessary existence–which one may start with as a characterization of God or else derive from the characterization of God as being such that his actual existence would imply his necessary existence–then for God, possibility and necessity have been collapsed. But then any justification for the possibility of God’s existence–which the ontological argument needs–will also have to be sufficiently strong justification as to support the necessity of God’s existence. If the theist had such strong justification, he wouldn’t need the ontological argument; lacking it, he has no good reason to accept the premise of God’s possible existence, and the argument is toothless.
    I love Rick Taylor’s examples, and I wonder whether they are original or derived from elsewhere (I’d like to give proper credit when citing his sorts of examples). I wish I knew how to get in touch with you people! My own e-mail address is joyfuloctopus at yahoo dot com, should you see this and want to write to me.

    • Heya. I’m still here, and still get notified when people make comments through this thread. I agree with your assessment of the problem with the modal OA. People who support the argument want to use axiom 5 when it says we can conclude necessarily exists if it possibly exists, but ignore that very same axiom when it says in order to show it’s possible a MGB exists, we need to show it necessarily exists.

      The Goldbach conjecture example I got from Paul Almond originally, though I don’t know if it original with him. The worldwide restaurant example is my own invention.

  7. Hi Keith and Hello again Rick. Thanks for your comments. I’ve been in the midst of Christmas traveling and haven’t had a chance to respond until now. Keith, I do like your pithy reply and it does seem to take the teeth out of the argument. I’m afraid I don’t have that much more to add to the discussion. I’m satisfied with both of your responses to the argument and the ‘rhetorical force’ has been largely neutralized for me. Feel free to carry on any further discussion on this thread. If I have something to add, I’ll chime in.

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