A modal ontological argument for atheism?

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There have been several recent discussions in this forum of the modal ontological argument for theism, so I thought members might be interested in a recently published paper arguing that a form of this argument actually favours atheism:

https://onlinelibrary.wiley.com/doi/10.1111/nous.70009

It’s a very technical paper and I make no claims for being able to understand it. But, fortunately, one of its authors is Joe Schmid, a YouTuber with a knack for explaining complex philosophical ideas in a manner accessible to laypeople. He has explains the article in this interview by Phil Halper (skydivephil):

I’ll try summarize the video;

First of all, let’s review the original modal ontological argument. It exists in a few forms, and in the video Schmid gives two examples. First, the simplified “airplane” version:

  1. God possibly exists.
  2. God’s existence is either impossible or necessary.
  3. Therefore, God necessarily exists.

A more rigorous version of the argument is:

  1. If God exists, then it is necessary that God exists.
  2. Possibly, God exists.
  3. Therefore, God exists.

The argument is valid in the system of modal logic known as S5. If God is defined as a necessary being, as is often the case, then the only way the argument could be refuted is by denying premise 2. This gives rise to the negative ontological argument (or the ontological argument for atheism).

  1. God possibly does not exist.
  2. God’s existence is either impossible or necessary.
  3. Therefore, God does not exist.

or, more the more rigorous version:

  1. If God exists, then it is necessary that God exists.
  2. Possibly, God does not exist.
  3. Therefore, God does not exist.

We, therefore, have two arguments that appear symmetrical, both of which are valid (in S5) but which lead to opposite conclusions. Anyone wishing to defend one argument over the other needs to find a way to break this symmetry.

Or so it has usually seemed. Schmid and his co-authors believe they have found a way to avoid this symmetry altogether, and accept all the premises of both argument. Interestingly, when one does so, it turn outs that only the negative (atheistic) argument is valid.

To explain, Schmid provides a brief overview of modal logic. Without going into the same degree of detail that he does, there are several systems of modal logic. A modal system of logic is said to be “stronger” than another if it entails more axioms. In the video, Schmid is primarily concerned with two logics, S4 and S5. Of the two, S5 is the stronger by virtue of including an axiom, the B axiom, that can be formulated as follows: If p is true, then it is necessarily possible that p. It could also be worded as Whatever could be necessary is true, or as If something is possibly necessarily true, then it is true. (All wordings are equivalent.

S4 differs from S5 only by not including the B axiom, and is therefore “weaker.”

The crucial point: Although in S5 both the theistic and atheistic versions of the ontological argument are valid, and are therefore symmetrical, in S4 this symmetry does not exist. In S4, only the negative (atheist) argument is valid. The theistic argument is now invalid.

That is to say, while the theist argument is only valid in the strongest system (S5), the atheist argument is also valid in at least one, weaker, system. (Despite what it might sound like, being valid in a weaker system actually means the argument is stronger, as it requires fewer axioms to attain validity.)

Schimid goes on to explain that whether the B axiom is actually true, and therefore whether S5 actually accurately describes metaphysical reality, is a matter of some controversy and debate, whereas there is less disagreement over the axioms that make up S4. So whether the theistic argument is valid depends on whether the B axiom is true, a problem not faced by the atheistic argument.

As it happens, Christian apologist William Lane Craig has responded to Schmid in a video of his own. Disappointingly, but probably not surprisingly, Craig completely misconstrues and misrepresents the argument, and Schmid has issued a response of his own, where he is uncharacteristically blunt:

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My own thinking tends to short-circuit a lot of this:

  1. I do not accept that God exists.
  2. I therefore do not accept that God-as-a-necessary-being is possible.

I’m not at all sure that I accept the concept of “necessary beings” more generally – this would appear to be an assumption or axiom at least as strong and problematic as anything that is being attempted to ‘prove’ based upon it.

As an agnostic atheist, I am willing to accept the possibility of God-as-a-contingent-being, but I feel that only a theist (and probably only a non-doubting-theist at that) would, knowing the full implication of their admission, accept the possibility of God-as-a-necessary-being.

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When I’ve discussed the modal ontological argument on other occasions, people often make the mistake of thinking that in order not to accept the premise “Possibly God does not exist” one must assert that existence of God is logically impossible. That is not the case, because in this instance it is metaphysical, not logical, possibility that is being discussed. I have a hard time believing WLC does not understand the difference, which is why I believe his response is disingenuous.

I am really not sure how one would go about determining whether it is metaphysically possible for a god to exist necessarily. The example Shmid gives is that it is metaphysically impossible that water could be H3O. But we only know this because we have analyzed the chemistry of water. How would one analyze a god to determine whether it exists necessarily?

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I think it’s more usual to mistake it for epistemic impossibility - which is also incorrect. But it’s an interpretation such arguments often (misleadingly) invite. The conceivability criterion relates more easily to epistemic possibility than logical possibility, for instance.

i don’t think that changing the argument to use logical possibility and impossibility helps at all - other than rhetorically. We should not be able to define logically necessary entities into existence. A definition is a list of requirements that a thing must meet to merit the label. And if the requirements include logical necessity it is quite likely that that requirement cannot be met.

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That would only hold true if you assign necessary non-existence (roughly “if he does not exist in one possible world he must not exist in any possible world”) rather than necessary existence as one of God’s properties.

I must admit I find “metaphysical possibility” to be a very suspect concept. It would seem to be more likely to be a way for philosophers to launder their preconceptions and prejudices, than a way of discovering novel truths.

I rather suspect it is impossible. So when philosophers base arguments on that claim, they “are not interested in whether what they say is true or false, only in its suitability for their purpose” – i.e. they are bullshitting.

The utility of slinging concepts like necessity into an argument isn’t their likely truth – but rather that they are sufficiently outside the uninitiated listener’s experience that they may garner kneejerk acceptance before the listener understands their implication.

A good example of why philosophers should avoid making claims about science – the existence of the hydronium ion is a well known fact in Chemistry and H2O ⇌ OH−(aq) + H3O+(aq) is a very important equilibrium, and the basis for the pH scale.

Yes, but not only has Chemistry proved his claim false, but that analysis would only hold in a world that had fundamental constants sufficiently similar to our world.

A lovely example of a philosopher laundering their erroneous preconceptions about this world into a claim about all possible worlds.

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That’s something I find refreshing about Schmid’s approach. He limits his claims to what he has actually demonstrated and no more: The reverse ontological is valid in modal systems weaker than S5, which is not the case for the original ontological argument. That’s it. He does not insist that everyone should therefore become atheists, nor make any other claims beyond that single point. That contrasts with the wild and irresponsible claims made by WLC and other would-be philosophers who act more like apologists.

Not quite. If one accepts necessary existence as one of God’s attributes, and also the premise that it is possible for God not to exist, then the conclusion is God does not exist. And, the point of the paper, this is the case in weaker systems of logic than S5.

In that case, he chose a poor example, but that does not negate his main point. I still think the concept metaphysical possibility does capture a sense in which we often use the term “possible”. But there seems to be some disagreement on that question (Funnily enough, this article also uses the H3O example).

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Then again, some water does exist in the form H3O+, and also in the form OH-.

…and I see this has already been mentioned.

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Yes, but in that sense it is very frequently talking about (at times erroneous) preconceptions, rather than anything more profound. I think the “metaphysical impossibility of H30” is more indicative, and more impeaching, of the general concept than you perhaps do.

How does one demonstrate the metaphysical possibility or impossibility of a proposition? It would seem that philosophers will simply assert these claims.

The link states:

It concerns what could be the case given the essential nature of things – what’s possible according to the way reality itself could have been.

Babbling woolily about “essential natures” seems to be simply inviting people to smuggle in their preconceptions.

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And now I am pondering the existence of unnecessary beings. :thinking:

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I think my view of this is pretty much my view of the regular ontological argument: that no fact can be established about reality without input from reality. The distinguishing feature of the ontological argument is that there’s no there there. Logical operations upon hypothetical things, without more, cannot bear on whether some hypothetical thing exists or does not. And terms like “necessary,” though they have their applications, just muddle the thing – surely one can only say whether something existing is required in order for something else to exist if one can examine the somethings together with the “what if we get rid of something A? Does something B disappear?” sort of operation.

Pure reason, in other words, ain’t good for much, and impure reason, like the ontological argument, is worth even less.

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Quite. Such arguments start with “If this exists…,” continue on to “If this exists it must exist,” include some waffle to induce forgetfulness of the starting point, and finish with “…it must exist.”

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To put it somewhat differently: Ontological arguments deal with metaphysical reality. But, unlike physical reality, we cannot perform experiments on the metaphysical to confirm whether our intuitions are actually correct. So we are left arguing over who has the better intuitions.

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I’m not sure it’s even as worthwhile as that. It’s not so much that we cannot perform experiments – it’s that we are talking purely about the imagined logical relations between mentally-constructed hypothetical entities. Or, as Huxley would say, “matters of lunar politics.”

Difficulties arise in philosophical discussions so often because philosophy is conducted verbally and because the things people want to discuss the relations between are not simple chits one can move about on a board but are large hairy ideas with vague boundaries, freighted not only with a load of assumptions, but with a different load of assumptions depending upon who’s speaking. People try to plaster the cracks shut by way of rigorous definition, but any poor bastard who has ever had to parse or, FSM forbid, draft a statute knows that definitional rigor only imports new unexpected layers of assumption and ambiguity. There is, as XTC say, no language in our lungs for this.

I’m not sure that notions like “necessity” can have much genuine meaning, when one drills down and looks at ‘em. They are just ways we characterize our understanding of the relations between things, and so they reflect both the shortfall of our understanding and the ambiguity of language. And so when I see such things as “necessity” being referenced, I always have the sense that someone is just taking a mental shortcut, and failing to say what he actually means; he is usually trying to declare a conclusion about the logical relation between two or more things without appearing to smuggle the conclusion in, and it often has all the art and subtlety of a man trying to shoplift a canoe.

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