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Conceivability, Possibility, and the Ontological Argument

I don’t want to go into a full-dress exposition of the ontological argument, because I think it would be distracting to a simple yet decisive objection to it. For our purposes, then, we can express its structure crudely as follows:

1. It’s possible that there is a necessary being.
2. If it’s possible that there is a necessary being, then a necessary being exists.
3. Therefore, a necessary being exists.

The argument is valid; so, if its premises are true, its conclusion follows of necessity. Well, what reasons can be offered for the premises?

Premise (2) is just an instantiation of Axiom S5 of S5 modal logic. The underlying idea of Axiom S5 is that what is necesssarily the case doesn't vary from possible world to possible world: if something is necessary in one possible world, it's necessary in every possible world. I accept Axiom S5; so I accept premise (2). That leaves us with premise (1). Is it more reasonable to believe it than not -- or at least: is it more reasonable to believe it than to suspend judgment either way?

No, it isn’t. For the evidence is supposed to be that it’s conceivable that such a being exists, and that whatever is conceivable is possible. Now there are a lot of points that could be brought up here, but I want to limit myself to one point based on recent work in modal epistemology, i.e., the study of how our beliefs about what is impossible, possible, and necessary are known and/or justified.

There are many objections, both classical and contemporary, that have been raised against inferences from conceivability to possibility. For example, in the past, people were able to conceive of the Morning Star existing without the Evening Star, or water existing without H20. So if everything conceivable were possible, it should follow that it’s possible for the Morning Star to exist without the Evening Star, or water without H20. But we now know that these things are impossible, since the Morning Star is the Evening Star, and water is H20.

Another example: Goldbach's Conjecture is the mathematical hypothesis that every even number greater than 2 is the sum of two primes. To date, no mathematician has proven that Goldbach's Conjecture is true (nor have they proven that it's false). Now I can conceive, in some sense, that Goldbach's Conjecture is false. I can also imagine that it's true. So if all inferences from conceivability to possibility are valid, then it follows that it's both possible for Goldbach's Conjecture to be true, and possible for Goldbach's Conjecture to be false -- in other words it would follow that Goldbach's Conjecture is only contingently true if true at all. But that can't be right, for mathematical statements are necessarily true or necessarily false if true or false at all!

Thus, it looks as though we need some criterion of legitimate conceivings to screen out illegitimate conceivings, thereby preserving the utility of inferences from conceivability to possibility.

A lot of progress has been made over the past several decades in the sub-field of modal epistemology, but for our purposes, it’s enough to mention one key distinction that’s been developed that’s helpful. Stephen Yablo[1] and James Van Cleve[2] have each pointed out that there’s a distinction between not conceiving that P is impossible, on the one hand, and conceiving that P is possible, on the other. Van Cleve calls the former, ‘weak conceivability’, and the latter, ‘strong conceivability’.

Now it turns out that pretty much all of the counterexamples to the conceivability-possibility inference are cases in which something is weakly conceivable. For example, when one says that they can conceive of Goldbach’s Conjecture being true, and that they can conceive of it also being false, they really mean that they can’t see that either conception is impossible – i.e., they only weakly conceive of such things. The same goes for conceiving of water existing without H20, and conceiving of the Morning Star existing without the Evening Star. By contrast, I can strongly conceiving of my car as being red, and of myself as a person who doesn't like to surf (albeit just barely!); thus such conceivings provide prima facie evidence that it's possible for my car to be red, and that I really could have been a person who doesn't enjoy surfing.

In light of this distinction, then, we can handle the counterexamples by limiting conceivability-possibility inferences to those that involve what is strongly conceivable – i.e., to those in which one intuits that p is possible, and not to those in which one merely fails to intuit that p is impossible.

With the weak/strong conceivability distinction before us, let’s consider premise (1) again. Is it strongly conceivable that there is a necessary being -- i.e., do we "just see" that it is possible? It doesn’t seem so. Rather it merely seems weakly conceivable – i.e. I merely can't intuit that such a being is impossible. But this isn’t enough to justify the key premise (1) of the ontological argument. For that to be so, a necessarily existing individual would have to be strongly conceivable.

To come at the point from another direction: Christian theistic philosopher Peter Van Inwagen asks us to imagine a being whom he calls 'Know-No'. Know-No is a being who knows that there are no necessary beings. If such a being is possible, then a necessary being is impossible. For then there would be a possible world in which a being knows that there is no necessary being. And if he or she knows it, then it's true that there's no necessary being.

Now both possibilities can't be true -- either a necessary being is possible, or a being like Know-No is possible, but not both, since the possibility of each one precludes the possibiliity of the other. But notice: both possibilities are conceivable in the weak sense: on reflection, I fail to see an incoherence in the conception of either one. So, if weak conceivability were sufficient evidence for possibility, it would follow that I'm justified in believing that necessary beings and Know-Nos are both possible, which, as we've just seen, is false -- if either one is possible, the other is impossible. Thus, again, the notion of a necessarily existent individual is only weakly conceivable, and weak conceivability isn't good evidence for possibility.[3]

Thus, it looks as though the ontological argument is not a successful piece of natural theology. Whether or not the key premise is true, I don’t have sufficient reason to think so. Thus, the argument is of no help in the task of justifying theism.
---------------------------
[1] “Is Conceivability a Guide to Possibility?”, Philosophy and Phenomenological Research 53 (1993), 1-42.
[2] “Conceivability and the Cartesian Argument for Dualism”, Pacific Philosophical Quarterly 64, (1983), 35-45.
[3] This objection to the ontological argument can be found in Peter Van Inwagen's textbook, Metaphysics, 2nd edition (Westview, 2002).

Comments

Mike Almeida said…
So if everything conceivable were possible, it should follow that it’s possible for the Morning Star to exist without the Evening Star, or water without H20. But we now know that these things are impossible, since the Morning Star is the Evening Star, and water is H20

Not so fast! The metaphysically possible and the logically possible diverge only when other worlds are considered counterfactually, not when other worlds are considered as actual. So it is false that, from the point of view of every other world, 'H20 is water' is true. That is just what the conceiveablity that water is not H2O tells us. It is true that, from the point of view of our world, 'H2O is water' is true in all other worlds. So there is a very important sense in which concievability does entail possibility. The question is whether it is a sufficiently important sense for the point under discussion. Would it matter that, from the point of view of some world, God is possible? That's the question we should be considering, since, even if metaphysically impossible, it is true that from the point of view of some worlds, that God is possible (assuming that God is conceivable).
exapologist said…
Hi MIke,

Good point. So your point is that, as Kripke taught us in Lecture III of Naming and Necessity, we need to avoid conflating actual-world referents with their epistemic counterparts when we make conceivability-possibility inferences, and that we can avoid this by keeping them separate (with your use of the considering a world as actual/considering a world as counterfactual terminology, it sounded like you were recommending Chalmers-style 2D modal epistemology as a regimented way to keep them separate, correct?). And so you want to say that once we get around the conflation problem, it's pretty much smooth sailing for justified modal claims?

Here's how I would reply: It's good that Kripke taught us not to conflate actual-world referents with their epistemic counterparts. It's also good that Chalmers provided a regimented way to avoid conflating the two by (i) distinguishing primary from secondary conceivability, and (ii) distinguishing (counteractual) 1-possibility from (counterfactual) 2-possibility, and finally by (iii) restricting primary conceivability to 1-possibility and secondary conceivability to 2-possibility. However, while avoiding such conflations is a necessary condition for a worthy modal epistemology, it's not sufficient; it also requires an account of when conceivability is evidence of possibility in the first place.

Now there are two ways to construe Chalmers' account of primary conceivability as evidence of 1-possibility: (i) as mere epistemic possibility (in the sense that, roughly, P is conceivable iff one can't rule out P as impossible, and (ii) as his more souped-up, Yablo-esque version of conceivability spelled out in his "Does Conceivability Entail Possibility?" Construal (i) falls prey to the Goldbach's Conjecture problem (as Yablo, Van I, and Van Cleve have pointed out), as well as the equal conceivability of the existence of an Anselmian being and a knowno (as Yablo and Van I have pointed out). And construal (ii) falls prey to a vacuity problem raised in Van I's paper, "Modal Epistemology". For on construal (ii), Chalmers' adds the Yablo-esque requirements that a primary proposition receive epistemic backing from an objectual imagining that (i) is strongly conceivable, and (ii) entails the target modal claim. But then pretty much no modal claim remote from ordinary experience passes the modal appearance test, rendering construal (ii) vacuously true (well, at least if we leave to the side more humdrum modal claims about things closely similar to what we experience in the actual world).

So it seems to me that there is a formidable dilemma against any modal epistemology that tries to allow for justified modal claims that are remote from ordinary experience: all such accounts are such that either their criteria for adequate conceivings are satisfiable but admit of counterexamples, or they don't admit of counterexamples but they're not satisfiable.

Of course, the worries for modal epistemology I mention here require much more argument and elaboration. I have attempted to do so in the first two chapters of my dissertation, but I don't want to bore you with that!

At any rate, those are the worries I have about the nice points you raise.

Best,

EA
evangelical said…
I think it is best in premiss one, and the surrounding context to limit "possibility" and "necessity" to the "logically possible" and "logically necessary."

There is nothing self-contradictory in the concept "necessary being" so premiss one stands. Bringing in Goldbach's Conjecture and a Know No only muddies the water as I'll now explain.

Goldbach's Conjecture really is true, or, instead, it really is false. Nobody thus far has been smart enough to say if it is the former or if it is the latter. However, I cannot conceive of it being that which it is not for it is logically impossible to conceive of the logically impossible. There are two and only two possibly mental states of affairs on the question. Either a. I do not know if Golbach conjectured accuretly or b. I know that he did (or did not, if that is the case). I simply am not able to conceive that true if false or false if true. It is not entirely clear to me it this is the point you are trying to make with you weak vs. strong conceivability or are using those concepts to say, "we really can conceive the logically impossible afterall." I think it is the latter but perhaps I've misread you.

Now, I have very great problems conceiving of a Know No since it's existence is logically impossible in light of the fact that a necessary being possibly exists (and I've already said such a being is logically possible).
exapologist said…
Hi Evangelical,

I think it is best in premiss one, and the surrounding context to limit "possibility" and "necessity" to the "logically possible" and "logically necessary."

I think that's unwise. I agree with Plantinga that it's a mistake to construe the argument in terms of logical possibility. For a statement p is logically possible if and only if it doesn't entail a contradiction in first-order logic. But as Plantinga points out, logical impossibility is too coarse-grained to depict metaphysical possibility. Take Plantinga's example from The Nature of Necessity:

1. There is a prime number that is a prime minister.

Letting 'Px' denote 'x is a prime number', and letting 'Qx' denote 'x is a prime minister', we can express (1) in first-order logic as follows:

1. (Ex)(Px & Qx)

Thus, we see that (1) doesn't entail a contradiction in first-order logic; it is therefore a logical possibility. However, (1) is clearly metaphysically impossible. This problem applies to infinitely many logical possibilities; therefore, I agree with Plantinga that logical possibilities are too coarse-grained to suitably depict metaphysical possibilities.

Furthermore, neither

2. Possibly, there is a necessarily existent individual.

nor

3. Possibly, there are no necessarily existent individuals.

entails a contradiction in first-order logic. So if logical possibility entailed metaphysical possibility, then (2) and (3) would both be possible. But, necessarily both cannot be possible. Therefore, logical possibility doesn't entail metaphysical possibility.

For reasons such as these, Plantinga, and the philosophical community in general, have moved away from logical possibility as either a reliable guide or a reliable depicter of metaphysical possibility.

There is nothing self-contradictory in the concept "necessary being" so premiss one stands.

See my previous point. We've just seen that logical possibility isn't metaphysical possibility; nor is it a reliable guide to metaphysical possibility. So from the fact that premise (1) of the modal ontological argument doesn't entail a contradiction in first-order logic, it doesn't follow that it's metaphysically possible. That's why modal epistemologists work so hard at coming up with accounts of conceivability that are reliable guides to possibility. And that's why I brought up the distinction between weak and strong conceivability -- weak conceivability isn't a reliable guide to metaphysical possibility. And since (1) is only weakly conceivable, we lack sufficient reason to accept it.

Goldbach's Conjecture really is true, or, instead, it really is false. Nobody thus far has been smart enough to say if it is the former or if it is the latter. However, I cannot conceive of it being that which it is not for it is logically impossible to conceive of the logically impossible. There are two and only two possibly mental states of affairs on the question. Either a. I do not know if Golbach conjectured accuretly or b. I know that he did (or did not, if that is the case). I simply am not able to conceive that true if false or false if true. It is not entirely clear to me it this is the point you are trying to make with you weak vs. strong conceivability or are using those concepts to say, "we really can conceive the logically impossible afterall." I think it is the latter but perhaps I've misread you.

Yep, you've misread me. ;-) I'm not claiming that we can conceive the impossible in the discussion of the Goldbach's Conjecture case. Rather, I'm claiming that we can weakly conceive it -- that is, we fail to see an incoherence or contradiction in denying it; the same thing goes with affirming it. By contrast we can strongly conceive neither one -- i.e. we can't see that either claim is possible. And the worry is that premise (1) of the ontological argument is in the same boat as Goldbach's Conjecture: we can't strongly conceive its truth; we can only weakly conceive it. That's the crux of the problem with the ontological argument that I'm arguing in this post.

Best,

EA
evangelical said…
If we do not use logical possibility as a test of metaphysical possibility, then what do we use? What is your alternative test?
exapologist said…
See my dissertation. ;-)

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