The Modal Ontological Argument and the Possibility Premise
The ontological argument is fascinating to me, and Gödel’s modal version is no exception. Apparently, a team of AI researchers claims that “From Gödel’s premises, the computer proved: necessarily, there exists God” and that “this God-like entity is unique, i.e. monotheism is a consequence of Gödel’s theory.”
It’s noteworthy, though, that it is not the case that all of the premises of Gödel’s version are known with epistemic certainty. For example, one of Gödel’s premises is that necessary existence is a positive property. Do we know this with epistemic certainty? And is there agreement amongst the relevant experts? I suspect there are competent philosophers who would object to this premise, suggesting that we lack certainty on this matter, at least collectively.
Let’s set aside Gödel’s argument for now, and instead examine a straightforward version of the modal ontological argument.
If the existence of God is possible (i.e., God exists in some possible world), then the existence of God is necessary (i.e., God exists in every possible world).
The existence of God is possible.
Therefore, the existence of God is necessary.
If the existence of God is necessary, then God exists in the actual world (i.e., God exists).
Therefore, God exists.
Here’s a simpler version:
A. Either the existence of God is impossible or it is necessary.
B. The existence of God is not impossible.
C. Thus, the existence of God is necessary.
D. Thus, God exists.
The basic idea is that given God’s nature it follows that if the existence of God is possible, then necessarily God exists. But this raises a concern with the so-called possibility premise (PP). We don’t know with certainty that God’s existence is possible – though there are plausible arguments for this proposition.
Here are some examples of supporting arguments.
Consider first the “conceivability entails possibility” argument. Let us distinguish between subjective conceivability on one hand, and objective conceivability on the other. One might also think of this distinction as between prima facie and ideal conceivability. The former is an appearance of conceivability but not necessarily a matter of genuine conceivability. The latter is genuine conceivability, which entails possibility. Subjective conceivability inductively supports but does not entail the PP.
Think about the epistemic right to believe that which I take myself to perceive directly. Suppose I take myself to perceive that there is a tree before me. I believe this because I am appeared to treely (i.e., I have an experience of something which I take to be a tree; I am having a tree-like experience). My belief is prima facie justified even if my experience is non-veridical and there is no tree. Perhaps the best explanation of this tree-like experience is that there is in objective reality a tree and that I am experiencing it. Hence, my tree-like experience is evidence that, probably, there is a tree that I am experiencing. Am I epistemically certain that there is a tree? No. But I am justified in believing that there is one.
Similarly, one might contend, I have an epistemic right to believe that what I prima facie conceive to be possible is indeed possible. However, given human fallibility, that which seems thinkable and thus possible might in fact be incoherent. Thus, although the concept of God seems conceivable, for all we know, it might turn out to be incoherent. I am justified in believing that, upon due diligence, what seems to me possible is possible. However, intellectual honesty requires that I admit I might be wrong and thus that I am not epistemically certain.
Arguably, ideal conceivability entails possibility. If one conceives truly that x is logically consistent, then since to be true is to correspond with reality, x is logically consistent and therefore logically possible. Nevertheless, the present concern is that human beings cannot achieve ideal conceivability regarding the possible existence of God. The matter is too complicated for us, at least in our premortem condition.
Second, consider the “ought-implies-can” argument, which supports but does not demonstrate conclusively the PP. Basically, the argument is that if God ought to exist, then it is possible that God exists since whatever ought to be the case is possible. But God ought to exist, according to this argument. Therefore, God’s existence is possible. One concern with this argument is that it’s not clear what it means to say that God ought to exist. This does not appear to be a moral ought. Is it an axiological ought? Does it make sense to say that it axiologically ought to be the case that God exists? More work needs to be done on this question.
Third, Leibniz’ argument for the PP is supportive but non-entailing. Like Gödel, he held that positive attributes are logically consistent and that since God’s essential attributes are positive, they are consistent. Hence, God is possible. It does indeed appear to me that God’s essential attributes are consistent, but I’m not sure that we can be epistemically certain about this.
Lastly, I like Yujin Nagasawa’s “Maximal God” thesis, which he claims entails the PP. If he is right, then the modal ontological argument approaches the status of a definitive proof for theism. The idea is that God is, by definition, the metaphysically greatest possible being, and thus that God has the best possible, logically consistent combination of great-making attributes (whatever these attributes turn out to be). In other words, God possesses the maximally consistent set of excellent properties such as knowledge, power, and benevolence. Since this combination is and must be consistent, God is logically possible. Nagasawa (p. 204) puts it as follows: “In other words, the maximal concept of God is by definition internally coherent because its components are mutually consistent (and internally coherent). This guarantees the possibility of the existence of God.” According to Nagasawa, his thesis can be used by the perfect being theist to refute every atheistic argument that the concept of God is somehow incoherent.
Here is Nagasawa providing a good introduction to the ontological argument.
One concern with Nagasawa’s argument is that if the best possible, logically consistent combination of great-making attributes turns out not to be very great, then it’s hard to see why any being who might possess this combination would be worthy of worship. What if the best possible, logically consistent combination of great-making attributes enables the existence of a superhuman but non-divine being?
Reference
Yujin Nagasawa. Maximal God: A New Defence of Perfect Being Theism. (Oxford University Press; 1st edition, 2017).