Conceivability, Possibility, and the Ontological Argument for God's Existence

I don’t want to go into a full-dress exposition of the ontological argument for God's Existence, 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 accept it than to reject it-- 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 'Knowno'. Knowno 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 knowno 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 knownos 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).


bpabbott said...

1. It's possible that if a necessary being existed, there would be evidence of that being.
2. If it is possible, then the evidence exists.
3. Therefore, since there is no evidence, the being does not exist.

Anonymous said...

EA, I learn from you every single time you write something. Excellent!

Emanuel Goldstein said...

John, don't you ever wish you had had a real, medicine, engineerint, fringging real estate?

WoundedEgo said...

Andrew, what is your career?


Bill Ross

Joe E. Holman said...

Exapologist, don't you think a simpler route of attack would be Kant's response to the argument? Do you consider his objection valid?

As you know, Kant said that existence is not a defineable property by which a thing can be judged to exist. Existence does not augment; a thing exists or it does not, and thus, the argument sort of assumes what it wants to prove.

I have always considered the "being" aspect of the argument the most prominent component to attack. The "being" of the argument (the term "God" itself) cannot be defined, and therefore, an already skewed and nebulous argument is rendered useless (what the hell does a being "greater than which none can conceive" mean anyway?)


Steven Carr said...

'But that can't be right, for mathematical statements are necessarily true or necessarily false if true or false at all!'

Is Euclid's 5th Postulate true or false?

IS the Axiom of Choice true or false?

Can God exist in all possible worlds?

1) God is a necessary being and exists in all logically possible worlds.

2) God is supposedly omniscient, omnipotent, and omnibenevolent

3) Therefore , suppose a omniscient, omnipotent, and omnibenevolent being exists in all possible worlds

4) Many logically possible worlds contain large amounts of suffering with no redeeming features.

5) Therefore these logically possible worlds do not contain a being who would alleviate pointless suffering

6) Therefore there are logically possible worlds that do not contain an omniscient, omnipotent, and omnibenevolent being.

7) But this contradicts 3, showing that there is no necessary omniscient, omnipotent, and omnibenevolent being

zilch said...

The ontological argument for God's existence is perhaps the best example I know of how we can be mislead by logic when it is decoupled from reality. As joe e. holman said, Kant already defenestrated this argument: existence is not a "property" or "quality" of something. Rather, things either exist or they don't exist.

I would go further, and say that in general, the real world is not constrained to produce entities because of our conceits about the power of human concepts such as "necessity". I'll go along with bpabbott and look for "evidence" of entities, rather than trust a syllogism to tell me something about what "must" exist.

This is why I regard a great deal of philosophizing as simply words chasing their own tails: entertaining and possibly enlightening, but often content-free as regards rocks, bugs, people, and gods.

exapologist said...

Hi guys,

Nice questions and points!

Kant's objection applies to Anselm's version, but it's not clear that it applies to the modal version, such as the one under consideration. For the argument doesn't have as a premise the claim that existence is a perfection, and so it seems to get around Kant's worry. Since the modal argument is formally valid, the only way to rationally resist the conclusion is to find fault with one of the premises. And that amounts to rebutting or undercutting Axiom S5, or undercutting or rebutting the claim that it's possible that a necessary being (read: a necessarily existent object or substance or individual -- as opposed to a necessarily existent abstract entity) exists. My tack is to undercut the case for premise (1) -- i.e., that whether or not it's possible for a necessarily existent individual to exist, we just don't have sufficient evidence either way. But if not, then we're not rationally entitled to accept the premise.

Relatedly, while I sympathize with Zilch's sentiments about certain modal claims confidently asserted by some philosophers, I don't think the problem lies with claims about necessity as such -- I think it's pretty plausible that some facts about the world *are* necessary (e.g., it's not just contingently true, but necessarily true, that nothing can be red all over and green all over at the same time; that's a *modal* fact about colors and three-dimensional surfaces). Rather, I think the problem lies with our *knowledge* of modal facts. Granted, some modal claims are within our reach, viz., the humdrum modal claims common to ordinary experience (e.g., although I'm not sleeping, I *could've* went to bed at a reasonable hour, etc...). But what about modal claims *remote* from ordinary experience, such as, oh I don't know, the claim that it's possible for there to be a necessarily existent individual? ;-) That's a modal claim extraordinarily remote from ordinary experience; as such, it's truth or falsity can't be known. In short, while philosophers are justly criticized for making "remote" modal claims, it's not because there are no remote modal *facts*; rather, it's because *knowledge* of such facts is beyond our reach, and *that's* what makes philosophers look bad at times.



zilch said...

exapologist says:

I think it's pretty plausible that some facts about the world *are* necessary (e.g., it's not just contingently true, but necessarily true, that nothing can be red all over and green all over at the same time; that's a *modal* fact about colors and three-dimensional surfaces).

I guess you never saw Yellow Submarine, which featured a cube that was red all over and green all over at the same time. Okay, it was actually alternating red and green at the framerate of the film, but it looked decidedly *weird* (is *weirdness* a modal property?)

Anyway- I guess I'm just philosophically uninformed: how is the impossibility of something that is red all over and green all over at the same time *necessary* and not *contingent*? In other words, isn't this impossibility just an observed property of our Universe? What does it add to knowledge to say something is not only *contingent*, but also *necessary*?

In my humble opinion, the world should have the last word about what's real, and not some logical construction. Not to disparage logical constructions: they enable us to make scientific generalizations. But when such constructions start out, not with observations, but with proposals about supernatural beings that bootstrap themselves into existence on a syllogism, then philosophy has overextended itself. Perhaps we agree on that anyway.

exapologist said...

Hi Zilch,

You're raising excellent and difficult questions. But I do think it matters whether a property is essentially vs. contingently had by a thing. In fact, I think the sciences would be in trouble if they couldn't determing whether the properties of things they observe and study are essential vs. contingent (for then they couldn't determine, say, whether hydrogen is essential to water, in which case they could never discern what water *is*. The problem generalizes to all the sciences. So if we can't discern essential from contingent properties, well, good-bye science!).

Philosphers are after the same thing as science, viz., investigating the nature of things. It's just that they ask much more general and fundamental questions. Since this is so, they, too, must be able to distinguish essential from contingent properties -- otherwise, they couldn't determine what things *are*.

In any case, does this go at least some way in answering your worries about philosophical investigation?



zilch said...

Hi exapologist- er, no, it doesn't really ;) but that's okay. As a thoroughgoing skeptic, I'm suspicious of all attempts to reduce the world to descriptions: the word is not the thing, the map is not the territory, as they say. Naturally, we must describe the world in order to survive, but we should always be suspicious of our descriptions, and continually check them out against the real thing. That's what science is all about, I guess.

Of course you're correct in saying that it's necessary to distinguish between *contingent* and *essential* properties: for instance, mathematics can be seen as a concatenation of *essential* properties of numbers, which does not depend upon the *contingent* fact that two apples plus two apples equals four apples (not counting worms). We wouldn't get very far if we didn't extend our understanding this way.

But I will stick to my guns and say that when one hypothesizes from a starting point of logical constructions, with no admixture of real-world observations, to a conclusion with real-world consequences, then one is fantasizing. In my humble opinion, this is precisely what's wrong with attempts by philosophy to derive morals from "pure reason" without being informed by evolutionary biology: morals make no sense unless they start from our animal evolved selves.

Of course, religions make the same mistake in spades, by appealing to a Divine Reasoner who is not around to defend his reasons, but depends upon his henchmen to enforce his laws.

speedwell said...

What about falsifiability? Logical positivists say that a claim cannot be proved true unless it can be falsified. Falsifiability requires, as best I can understand it, that there be at least one conceivable, possible, (most importantly) testable case that would, if found to be true, prove the claim false. If no such case can be proposed, then the truth of the claim cannot be determined. (If such a case can be conceived of, it is not evidence of truth, but at least it shows that the claim may be provable.)

For those not familiar with how this works in practice, here's an example. Say I claimed, "All milk is white." This claim is falsifiable because an example case can be proposed, "If we found milk that was blue, then that would falsify the claim that all milk is white."

However, if I claimed, "An unknowable, transcendent deity exists," there would be no way I could conceive of a case that, if true, might make that claim false.

zilch said...

speedwell- this is the major conceptual problem with ID: it's not falsifiable. Since there will always be gaps in our knowledge, it is impossible to prove that God is not hiding out in these gaps, so ID is not falsifiable.

Of course, the other problem with ID is that it hasn't produced any knowledge.

Joe E. Holman said...

exapologist said...

"Kant's objection applies to Anselm's version, but it's not clear that it applies to the modal version, such as the one under consideration. For the argument doesn't have as a premise the claim that existence is a perfection, and so it seems to get around Kant's worry."

My reply...

Tis true.

I have had the most experience debating Anselm's version of the OA than any other, though there seems to me to be some overlap, but I see your point: premise one is indeed subject to attack here.


exapologist said...

Hi gang,

Zilch: I understand your skepticism here. I think it would be interesting to talk about philosophical methodology, but I don't want to go to far afield on this thread about that. But for now, I should say that it looks as though we're in agreement: we both think there's no way for us to determine whether there could be a necessarily existent individual, in which case the only responsible stance to take on premise one is agnosticism.

Hi Speedwall: the logical positivist's criterion was a criterion of meaningfulness -- i.e., a criterion to determine when a string of letters was capable of being true or false. The criterion was one of verifiability, not falsifiability. The criterion stated that a sentence is meaninful if and only if it was either a tautology or empirically verifiable via a sense-experience. The problem with the criterion was that (i) it was self-refuting (since it itself was neither a tautology nor capable of verification via a sense-experience), and (ii) it entailed that theoretical claims in the sciences (e.g., "there are quarks") are meaningless strings of jibberish.

The philosopher of science Karl Popper came up with the falsifiability criterion. Unlike the verifiabiliity criterion, it wasn't a criterion of *meaningfulness*, but rather a criterion to demarcate science from non-science. Philosophers of science ultimately rejected the falsifiability criterion, since it assumed a naive view of scientific confirmation and disconfirmation. It turns out that in the typical case, if an experiment doesn't confirm a hypothesis, it's not clear which claim got falsified -- the primary hypothesis, or one of the auxiliary hypotheses. It turns out that scientific testing is much more convoluted than falsification implies. Scientists typically abandon a hypothesis on the basis of a number of factors: e.g., it's no longer heuristically fertile, it no longer makes novel predictions, etc.

But about the claim that there is a necessariliy existent person with maximal power, knowledge, virtue, etc.: It does seem capable of direct and indirect confirmation and disconfirmation. For example, if the hypothesis is the simplest one that explains all the relevant data better than competing theories (e.g., the beinginng of the the universe, the fine-tuning of the fundamentall constants of nature, morality, religious experience, etc.), then it accrues abductive support; if not, then it receives indirect disconfirmation (think of the problem of evil, the problem of religious diversity, etc.). And if one could show that the notion of such a being is incoherent, then the claim is demonstratively falsifiable.

I think the same thing goes with Intelligent design theory: it's not that it's non-science, it's that it's bad science. It's a degenerative research program that makes few if any novel predictions; its criteria of design detection admit of counterexamples; Michael Behe has been shown wrong (the structures he claimed to be irreducibly complex have been shown not to be so), etc.

Great discussion, all!


zilch said...

Hi exapologist-

Of course you're right- this is not the time and place to discuss philosophical methodology. And I suspect we agree more than we disagree anyway.

I'm not sure, though, about your characterization of ID as being bad science, rather than non-science. Invoking supernatural assistence to help life around the tight corners, and thus drawing lines beyond which further research is useless, qualifies as a science-stopper to me. But that's just quibbling about definitions.

After having read a fair amount of ID "stuff" (to be neutral), it seems that ID has made one correct prediction after all: "Life can be expected to be really complicated and really hard to understand." Hardly a novel or useful prediction, though...

WoundedEgo said...

I have weighed Christianity in the balance and found it wanting. No other religion holds any more appeal for me.

But I must confess that I often feel like I am living in someone's fishbowl.

Did you know that there is a guy who can solve the Rubik's Cube in 20.09 seconds with one hand?

Not bad for an overgrown amoeba!

And what, exactly, would an Orangutan walk away with from a Ben Lee concert?:

I have cats. I see how much they look like rabbits without ears, or monkeys without a pre-hensile tail. I get that.

But I am both self-aware and cognizant of various events in distant galazies, and of the bizarre interation of electrons.

What I am saying is that I KNOW that Christianity is falsifiable, as are the other religions... but it defies my ability to accept explanations for THIS world that are completely devoid of intelligence.

This might be another sleepless night...

Bill Ross

GordonBlood said...

While im not positive on this one I think almost all philosophers, Christian or not, no longer consider the ontological argument to be valid in its conclusion. I think for me I fifnd a variant that was suggested by Descartes where the fact that we can even comprehend anything like God is indicative that such a being may exist, especially in the light of Darwinian evolution. That however is ultimately a subjective evaluation.

John said...


I think we discussed this before.
But the argument that I heard isn't based on the conceivability of God. Rather, it's based on the fact that I can't conceive of His non-existence therefore He must exist. It's inconceivable that God not exists. He must be. He cannot not exists. He exists necessarily.
If I can conceive of a possible world where God didn't exist I would actualize His non-existence.
I can't do that so He must exist.

Have I made a mistake here?
I realize this isn't very popular and I could be wrong.

John said...

If I can conceive of a possible world where God didn't exist He would be contingent and not necessary. I can't conceive of the non-existence of Necessary Being therefore it must exist.

Karl Betts said...

(1) Ontology implies more reality "in actu" than mere conceptual possibility or even logical necesssity in a proposition or syllogism.

By that I mean that existence is ultimately concrete--not in terms of "physical material," but in terms of actual being vs. merely propositional. Propositions by themselves do not, by necessity, entail the concreteness of an ontology. Anselm's "that than which nothing greater can be conceived" was more of a negation (in terms of abstraction) than a proposition justifying ontological existence.

(2) Possibilities are always contengencies and therefore do not meet the criterion for "necessity." Contingencies tell us that they are contrasted to necessities, but contingencies do not make-up the building blocks of necessity, they merely provide value and meaning for necessities.

(3) Without "being," per se, ontological arguements are, in the end, more like empty tautologies.

This is not to diss the logical brilliance behind the ontological arguments and the like. My sense is that you are appreciating them for what they bring to the table, both in terms of their strengths and their weaknesses. The fact that apologists and philosophers still re-introduce them shows that there is stuff to learn from them.

It seems to me that the best contribution ontologcial arguements make is that they lead us to probablistic propositions, in which case, "necessity" by definition, is out the window.

exapologist said...

Hi Cole!

I see what you're saying, but can't you conceive of a world that lacks gods? If not, then I worry that it's because you're trying to conceive something like the following:

1. The being who exists at all possible worlds does not exist in at least one possible world.

The worry is that if this were a valid way to infer the necessary existence of something, then by parity of reasoning so should this:

2. The winged horse that exists at all possible worlds does not exist at possible world W.

In both (1) and (2), it's part of the *concept* of the being in question that they exist at all possible worlds. And given that, you're right that the non-existence of such a being is inconceivable (for propositions describing such a state of affairs contain a contradiciton). But from that, it doesn't follow that any being *satisfies* the concept in either proposition.

Hi Zilch!

It would be interesting to discuss the scientific status of ID. Perhaps we could have a "dialogue post" on that some time down the road? That would be interesting.



John said...


I can't conceive of the non-existence of NECESSARY BEING.

If I did I would actualize it's non-existence.

It must exist. It cannot not exist.

Since it exists then it exists in every possible world.

exapologist said...

Hi Cole,

I'm not seeing how this answers the worry in my previous comment.


John said...

Let me think about it.
I'll get back to you.

zilch said...

hi exapologist! You beat me to the punch in your reply to cole- instead of the winged horse, I would have said The Perfect Ice-Cream Sundae, which cannot be conceived not to exist, because then it would not be perfect...

Sure, we could have a dialogue post about the scientific status of ID, but I suspect we pretty much agree on it- we would simply define it with different words. Given that the borders of what exactly constitutes science are fuzzy and debatable, I think it's moot to try to pin down what's inside and what's outside.

For instance: I'm an instrumentmaker. When I make an instrument, say a harp, some of the decisions I make about dimensions, materials, and proportions are solidly in the realm of science (or engineering, if you prefer)- the sounding lengths of the strings for particular pitches, for instance. But many other decisions are hazy- my sense of which wood will sound "best" for the soundboard, for instance. There's no place where I can draw a line and say "this is where my scientific knowledge stops, and intuition (or guesswork, or chance) begins".

The difference between my work and ID, of course, is that I don't claim that my productions are scientific through and through.

In any case, getting back to the topic, I've never understood why the Ontological Argument, at least in Anselm's formulation, was ever taken seriously. If one imagines a being or an object (or an idea, or a word, or a dream...) which has the quality, by definition, that it must exist, it is not magically called into existence by your "mistaken" conceiving of it to not exist. It seems an elementary falsehood to me...

Shygetz said...

It would be interesting to discuss the scientific status of ID. Perhaps we could have a "dialogue post" on that some time down the road? That would be interesting.

While I find ontological arguments to be silly (which may be my professional chauvinism coming out), be sure to invite me to the ID party.

John said...


I think you're right.

I still like William Lane Craig's version of the argument though.

I'm trying to find Jonathan Edward's version. I think Sproul has a version of it.

kachow007 said...

i have a question for ya'll.......Where did ya'll get that there was no evidence to support God's existence? I have seen plenty of evidence all around us proving that there is a for example, a Universal Moral Law.....what exactly is your opinions on that? i would like to know.

speedwell said...

A "Universal Moral Law?" We've been over that before. There is no such thing. If there was, everyone would think it was so obvious as to not need mentioning, and follow it without question.

You may also be interested in a FAQ that's lying around here somewhere. Anyone have the link?

The other purported evidence that you've been reading about in your apologetics books has similarly been disposed of. Poke around on this blog for a while and you'll probably find it all discussed here.

Shygetz said...

There are a few widespread moral laws (not universal) that are present in most humans. They also happen to be present in "lower" social animals as well. They exist for evolutionary reasons; organisms that rely upon socialization for reproductive success don't last long if they kill each other at whim.

A lot of scientific work has been (and is being) done on the evolutionary basis of social structures in animals (and in humans, although that is a much stickier question).

zilch said...

As far as "universals" go, here's a list of some two hundred concepts, which, according to Donald E. Brown, have been found in every known human society. Food for thought.