There is an argument for God called the ‘Ontological argument’ and it received an ambivalent welcome whenever it is trotted out, which seems increasingly rarely. It isn’t at all compelling, and yet that appears to be irrational because it’s rare to see someone actually attack the premises or the structure. However, that, today, is what I am going to attempt.
(Don’t get me wrong, professional and academic philosophers do attack the premises and form, but it looks like this when they do: “◇¬G” or “¬◇G”. They’re reasonably easy to parse once you understand the notation, but your average blogger or even debater isn’t going to get into all of that. The first one means ‘It is possible that God does not exist’ and the second one is ‘It is not possible that God exists’, granting that G = God exists; ◇ = It is possible; ¬ = a negation.)
The Ontological argument is a modal logic argument, which means it deals with possibilities from impossibility to necessity. It can include epistemic modality, which is an understanding of confidence in knowledge, or deontic modality, which is an assessment of a set of rules or practices and what should follow. (There is also doxastic modality, which is about confidence in beliefs, but I think you would need to do a PhD worth of work to properly distinguish between knowledge and beliefs in this case.)
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Quick quiz #1
Instead of spelling it out for you, here’s a quick quiz! Take a look at the following modal statements and decide whether they are deontic or epistemic. For extra points, also decide which are dealing with high likelihoods and which are dealing with claimed certainty:
- Don should leave the office.
- Don is most likely incompetent.
- There is no way that Don understands what he is doing.
- Don must file his tax returns.
(I do this not because Modal logic is particularly difficult, but because it is esoteric.)
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There is one more thing I want to point out before I talk about the Ontological argument directly, and it has to do with the nature of logical arguments. A logical argument is a series of propositions that, if accepted as true, should lead to a specific conclusion. This only works if the structure of the argument is sound and the premises are accepted accurate. If the structure is sound and the premises are accepted, then the argument is said to be valid.
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Quick quiz #2
Another quick quiz: what is wrong with the following arguments?
- What is Socrates?
(a) All humans are mortal
(b) Socrates is mortal
(c) Socrates is a human - It’s not a problem, but…
(a) All mammals exhibit homosexual behaviour
(b) William is a mammal
(c) William exhibits homosexual behaviour
- Have you spilt paint on my dog?
(a) Whatever colour my dog is, it must be a possible colour for a dog to be
(b) My dog is ginger
(c) Ginger is a possible colour for a dog
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If you are working on these yourself, don’t read ahead just yet. I’m about to give some answers. For argument 1, it does not follow that Socrates is a human. Socrates may be a human, but Socrates may also be a race horse. But how can it be that the conclusion doesn’t necessarily follow, if we’re not challenging any of the premises? The problem is that, although all humans are mortal, not all mortals are human.
Argument 2 is a little more complex. Although both premises are true, and the conclusion looks to follow, there is a mistake: an equivocation fallacy. This means language has been used sloppily and so confused the argument. In premise (a) the term “all mammals” is used as shorthand for ‘all mammal species have individuals that’. And yet, the structure of the argument assumes that “all mammals” means ‘all individuals that belong to a mammal species’. We, therefore, cannot tell whether William exhibits homosexual behaviour from this argument. Notice, finding fault with the argument is not the same as establishing the opposite to the conclusion is true.
Argument 3 is much simpler. You don’t know if I have a ginger dog or not. You do not have to assert that you know I have a non-ginger dog, or that you know I don’t have a dog at all, to not accept the premise and so not accept the conclusion, and therefore remain agnostic on the possibility of ginger dogs.
Sorry for the Logic 101, but it is important to get these points out of the way before we rely on some of those principles in a contentious subject.
Now, what is the Ontological Argument for God? It turns out there is no ‘the Ontological Argument for God’. It is a genre of arguments, and not a specific argument. It is any argument that tries to define a God in such a way as to conclude that God’s existence is necessary. So long as an argument attempts to mandate that the possibility of a God leads to the necessity of a God through definitions, then that is an Ontological Argument (Wikipedia contributors, 2017c).
For the sake of assessing the Ontological argument, I am going to look at the version put forward by William Lane Craig (2016) (who we have no reason to believe exhibits homosexual behaviour). It is as follows, with a few of my explanations in italics under some premises:
- It is possible that a maximally great being exists.
- If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.
This is a definition of “possible” in modal logic. If there is no possible world where a proposition is true, then the proposition is impossible. This is merely a rewording of premise 1. - If a maximally great being exists in some possible world, then it exists in every possible world.
This is taken as following from the definition of ‘maximally great’, in that it is always greater to exist in more possible universes, and so the exist in all possible universes is maximally great. - If a maximally great being exists in every possible world, then it exists in the actual world.
- If a maximally great being exists in the actual world, then a maximally great being exists.
- Therefore, a maximally great being exists.
And now for the autopsy. Remember, from the principles discussed at the start of this post, I do not have to demonstrate that the premise is false. All I have to do is validly point out that we do not have good reasons to accept the premise. It’s like my ginger dog; you don’t have to know it’s not true, you just have to realise you can’t know it is true.
And so, the argument stumbles before the first premise. What are the defining features of a ‘maximally great being’? People don’t tend to hesitate to put ‘maximal potence’ in there (they say ‘omnipotence’, but then limit it according to all sorts of theologically necessary excuses), or ‘maximal knowledge’ (i.e. omniscience, as limited to make way for other maximal traits). Plantinga puts ‘moral goodness’ in there (Plantinga, 1998), but some theologians recognise the subjectivity problem or the circular reasoning (when you consider theological definitions of morality) in there.
This uncertain definition of ‘maximally great’ allows us to not accept premise 1 on the grounds of it being ill-defined, which makes it impossible to demonstrate. It also allows us to reject premise 3, in that it is not established that ‘existence in more possible worlds’ is not obviously or necessarily greater and it wouldn’t follow that existence in all possible world is ‘maximally great’.
We can also reject premise 1, even if the definition of ‘maximally great’ is clear, on the grounds that it cannot be demonstrated to actually be the case that such a being is ‘possible’. There are contentions here between ‘rationalist’ and ‘empiricist’ definitions of possible. Rationalists define ‘possible’ as any given thing that has a definition that is not internally contradictory. Empiricists require a demonstration of possibility. This gets a little confusing, but we can simplify it: if the definition of a ‘maximally great being’ were contradictory, we would have demonstrated the impossibility of it. However, a lack of a contradiction only fails to demonstrate impossibility, it is not a demonstration of possibility.
Gödel has a version of the Ontological argument that tries to save the definition of ‘maximally great’. He defined ‘maximally great’ as the full realisation of only parameters that can only be expressed in ‘positive’ terms. This is not a subjective argument; positive terms are those which are not expressed as the negation of something else. For example, “potence” is positive, but “impotence” is the negation of potence and so is not positive. This leads to some weird conclusions, like the ‘maximally great being’ being maximally hot (but not maximally cold, as cold can be expressed as the absence of heat). But, this also leads to contradictions: it is a quirk of language that some things can be expressed in positive terms, but neither good nor evil is expressed as the negation of the other, and neither dense nor sparse, neither. The negation of “good” is not “evil”, it is nihilism. The negation of density is not sparsity, but absence. And so Gödel’s definition leads to contradictions, and so is not possible.
(The weaker, but still relevant version of the argument in the previous paragraph is this: it is possible that “evil” is not the negation of “good” ― but, instead, the negation of either is nihilism ― and therefore it is possible that Gödel’s definition leads to contradictions. It is therefore not necessarily the case that Gödel’s ‘maximally great being’ is possible, and so premise 1 can be rejected.)
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Fun game
There are other contradictory pairs where their negation doesn’t lead to the other member of the pair, but a middle ground: sexiness and ugliness, when negated, leave plainness. A maximally sexy and maximally ugly God? There are also cases where things we woud consider negative are the positively expressed state: cleanliness is actually the absence of dirt, and so this would lead to a maximally dirty God. You can play around with a lot more of these in the comments section.
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(There is another interpretation of Gödel’s Ontological argument, that “positive” is actually to be understood in moral and aesthetic terms, and that parameters such as ‘density’ can be ignored because they are not ‘necessary’. This leads to the legitimate concern of not being able to define ‘necessary’ and the subjectivity problem with “positive”, and so the first premise can still doesn’t have to be accepted. There are other significant criticisms of Gödel’s argument available on the relevant Wikipedia page, which several doubts and refutations (Wikipedia contributors, 2017a))
If you don’t accept premise 1, it is not just the case that the remaining premises are insufficient to conclude a God. It’s worse than that. If you don’t accept premise 1, premises 2 – 4 fall as well. And if premise 4 is fallen, so is premise 5. That’s all the premises, which evaporates the conclusion.
And yet the fatality is not over. You could accept premise 1, but not premise 3. This would mean rejecting the idea that ‘maximally great’ somehow entails existence in all possible worlds. But, there is a valid reason for doing that: the modal fallacy. The modal fallacy is the fallacy of confusing “possibility” and “necessity” in modal arguments (Wikipedia contributors, 2017b). And yet, the entire purpose of premise 3 is to force the “possibility” from premise 1 into “necessity”, by simply defining a maximally great being that way. It defines God as a fallacy.
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If you don’t accept that premise 3 is the modal fallacy, I shall use it in an argument that God does not exist:
An Ontological argument for the nonexistence of a God
(1) It is possible that a maximally great being does not exist
(2) There is some possible world where a maximally great being does not exist
(3) (taken from William Lane Craig’s Ontological argument) If a maximally great being exists in some possible world, then it exists in every possible world
(4) (From (3)) If there is some possible world where a maximally great being does not exist, then a maximally great being does not exist in any possible world
(5) (from (2) and (4)) A maximally great being does not exist in any world
(6) Reality is a possible world
(7) (From (5) and (6)) A maximally great being does not exist in reality
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There’s one more fallacy I think I can see, and it is the equivocation fallacy. This fallacy is a little more tenuous, but I think it is worth talking about. The original Ontological Argument was from Anselm of Canterbury, and it spoke of a ‘Greatest Conceivable Being’ (Oppy, 2014). This is exactly the same as a ‘maximally great being’, but highlights the equivocation fallacy. The argument starts talking about the idea of a being inside a conceptual world. Using imprecise language, in then shifts the meaning to an actual being in the actual world. The argument confuses concepts with reality. Even if we follow the argument (tidying up a little as we go), it only follows that an actually greatest being would exist inside a conceptual reality, not actual reality (Loptson, 1980).
In summary, it is not the case that rejecting an argument means accepting the opposite of the conclusion; rejecting an argument only supports agnosticism. However, rejecting the Ontological argument is the rational thing to do because the possibility of a God existing isn’t demonstrated and so the first premise can be rejected. The leap made from “possibility” to “necessity” is a fallacy being masked over by the definition of ‘maximally great’, and all Ontological arguments have this step (it is premise 3 in the William Lane Craig version discussed here). There are other problems with the definition of ‘maximally great’, and yet attempts at resolution made by Gödel only lead to other problems. Finally, the interpretation of possible worlds leading eventually to reality is an equivocation fallacy.
References
Craig, W.L. (2016) Struggling with the Ontological Argument. Available from: https://www.reasonablefaith.org/writings/question-answer/struggling-with-the-ontological-argument [Accessed 7 November 2017].
Oppy, G. (2014) Ontological Arguments. In: Ed Zalta (ed.). Stanford Encyclopedia of Philosophy.
Wikipedia contributors (2017a) Gödel’s ontological proof. Available from: https://en.wikipedia.org/w/index.php?title=G%C3%B6del%27s_ontological_proof&oldid=806709869 [Accessed 7 November 2017].
Wikipedia contributors (2017b) Modal fallacy. Available from: https://en.wikipedia.org/w/index.php?title=Modal_fallacy&oldid=808628417 [Accessed 7 November 2017].
Wikipedia contributors (2017c) Ontological argument. Available from: https://en.wikipedia.org/w/index.php?title=Ontological_argument&oldid=807420087 [Accessed 7 November 2017].
Allallt in discussion 
I think the “maximally great” concept is fatally flawed. Consider a “tallest” human contest. There could be found which of the human beings in the entire world is tallest. Assume, that all humans can be checked or that we can provide an incentive that all would check themselves. The winner is “The World’s Tallest Human!” Is this person the maximally tallest human being? To claim so would entail arguing that a teller person was impossible.
Consider the claim that a maximally great being was possible? This is a claim that none could be greater, but it is not a claim that the second most great being was far behind. The tallest person contest may have been won by someone by a fraction, a small fraction of an inch/cm. Aside that, has there ever been a maximally great anything? Mountain? Warrior? Donald Trump? galaxy? star? universe? Has anything ever qualified as being maximally anything?
I think you will be very hard pressed to find such an example. Consequently, the first premise should be re-written as “(1) It is possible that a maximally great being does exist, but the probability is vanishingly small.” I think you can see where this leads. To me it leads to “Therefore, the probability that a maximally great being exists is vanishingly small.”
Premises that are likelihoods or unlikelihoods can be tucked into premise sets under the guise of being “possible”. It is possible that there is a teapot in orbit around a moon of Mars, is one example of such possibilities. But possibles are not certainties, so turning a possibility into a certainty has a certain stink about it, as does William Lane Craig.
Sorry about the typos, written with some passion is my excuse and I am sticking to it.
The problem with the Ontological argument is that if you grant three things, then the argument works.
(1) A maximally great being is possible, no matter how vanishingly unlikely.?
(2) Part of the definition of ‘maximally great’ leaps the barrier between concepts and reality.
(3) Existence is a trait that relates to greatness, such that ‘existing more’ (i.e. in more possible worlds) is greater. (Or that God transcends possible worlds, and so if it’s possible in one it is necessarily in them all.)
There is another problem that jumps out at me based on your comment, though: If you can establish the possibility of a God existing, you can establish the likelihood, too. From the likelihood, you can establish what fraction of possible worlds the Maximally great being exists in. That very idea contradicts the step that turns the possibility to a necessity.
I had a mere philosophy minor in college (long, long ago) and have read some/much since then. You are clearly better educated in this subject than I but that doesn’t mean my bullshit detector no longer functions. Love your stuff, man! Keep it coming!
You’ve got the great problem with this, in all its iterations, in that you can’t make the jump from a possibility to an actuality by words alone. The biggest problem with Craig’s argument is that he’s just rewording Anselm’s to make it sound more modern without even making an attempt at covering up the flaws. It’s just the same with Descartes’ version (though Descartes’ is in a weird place and seems like a non-sequitur in the Meditations). I’m a philosophy adjunct and teach this argument on almost a yearly basis (though I omit the discussion of modal logic). I’m surprised you didn’t mention Kant–who is the one that drove the nail in this thing’s heart in his initial pointing out of the problem.