There have been several recent discussion of the modal ontological argument for theism on this forum, 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
This is 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 summarized the article with Phil Halper (skydivephil) in the video below:
I’ll try summarize the video;
First of all, let’s review the original modal ontological argument. It exists in several forms, and in the video Schmid gives two examples. First, the simplified “airplane” version:
- God possibly exists.
- God’s existence is either impossible or necessary.
- Therefore, God necessarily exists.
A more rigorous version of the argument is:
- If God exists, then it is necessary that God exists.
- Possibly, God exists.
- Therefore, God exists.
The argument is valid in the form 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).
- God possibly does not exist.
- God’s existence is either impossible or necessary.
- Therefore, God does not exist.
or, more the more rigorous version:
- If God exists, then it is necessary that God exists.
- Possibly, God does not exist.
- Therefore, God exists.
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 or 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 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:
