A Refutation of Wollen's Spurious "Proof" of the Existence of God

Ever since I decisively proved God doesn’t exist, theists have been quiet. Even the courageous Amos Wollen is afraid to respond to it:

Hilarious, I know, but the argument was actually quite clever. It’s one of those philosophical tricks where the proof is plainly bogus but it’s hard to articulate the mistake.

In Wollen’s defense, however, he does respond to my proof with a counter-proof. If his counter-proof succeeds, then that implies the disjunction of dialetheism and my proof being inadequate. Thus, we may consider him as having indirectly addressed my challenge.

Wollen’s counter-proof goes as follows:

1. If an omniscient being would believe something, you should believe it too.

2. An omniscient being would believe that an omniscient being exists.

3. So, you should believe that an omniscient being exists.

I agree with Wollen that, if an omniscient being exists, then it’s probably God. But as is typical of the Incorrect, Wollen spends his effort defending the wrong premise; he puts considerable effort into defending (1), which is indubitable, and not where the heart of the issue lies. What Wollen fails to realize is that (2) is false: an omniscient would not believe an omniscient being exists. Given that (2) is false, the argument is unsound, and so its conclusion is false.

I have three proofs that an omniscient being would not believe that an omniscient being exists.

First, suppose a man named Bob flips a coin a countably infinite number of times. Bob tells Alice that, shockingly, the coin only landed heads a finite number of times. What should Alice’s credence be that flip #1 landed heads? The answer must be 1/2, for it is arbitrary to consider flip #1 as part of the series, and flip #1 is irrelevant to the matter of whether there were only finitely many heads. If Alice has a different credence that flip #1 was heads than 1/2, then she would have to believe the same about every coin flip she ever encounters again, as that could be considered as part of the series of infinite coin flips. But her credence also cannot be 1/2, for as I have shown, that implies the existence of a uniform distribution on the natural numbers, which is impossible according to Math. Thus, we have a paradox, and the only solution is that it is impossible for Alice to learn a probability-zero event. But then God would be incapable of flipping a coin infinitely many times and telling an angel in the event that only finitely many flips landed heads, an absurdity. Thus, God, and therefore no omniscient being, exists. An omniscient being would be entirely aware of the correctness of my reasoning here, and therefore, an omniscient being would conclude that no omniscient being exists.

The second proof that an omniscient being wouldn’t believe an omniscient being exists is inspired by the argument from “Grounding and Omniscience” by Yuval Avnur. For those who don’t know, “grounding” is just metaphysical determination: e.g. this substance is in a certain chemical state because it is in a certain physical state, which is to say, the former is grounded in the latter. Now, from the perspective of our omniscient being, let P = “I am omniscient” and Q = “I know I am omniscient.” Because “Bob knows that p” is partly grounded in p (i.e. someone knows something, in part, because the thing is true), we have that Q is partly grounded in P. Now, P just means “For all true propositions p, I know p,” which is partly grounded in “I know p” for any true p (universal generalizations are partly grounded in their instances). But assuming it is true the omniscient being exists, his omniscience would then be partly grounded in his knowing he is omniscient, which is to say, P is partly grounded in Q. But recall that Q is also partly grounded in P; we therefore have a circle of ground, which is impossible, and so no omniscient being exists. An omniscient being would recognize this reasoning to be correct, and so conclude that there is no omniscient being.

The third proof that an omniscient being wouldn’t believe in an omniscient being follows from the observation that an omniscient being wouldn’t believe he exists, since there is no self (Gautama c. 500 BC). We can easily establish this conclusion on the basis of Hume’s proof of the nonexistence of the self:

1. If I can’t see something, then it doesn’t exist.

2. I can’t see the self.

3. Therefore, the self doesn’t exist.

(2) is indubitable. I can see my body, my brain, my thoughts, etc., but I cannot see this self that supposedly lies behind all of them; all I see are a sequence of ideas and impressions, not the glue that supposedly holds them all together. Some may doubt (1); I challenge such a person to show me one thing which I cannot see, but which nevertheless exists.

An omniscient being would, therefore, conclude that he does not exist, removing his only basis for the belief in an omniscient being. He would thenceforth not believe an omniscient being exists.

Wollen’s argument for his premise (2) was as follows:

Premise (2) is beyond doubt [sic], and extremely modest to boot. Of course an omnicient being would believe in an omniscient being. Belief is essential to knowledge, and since an omniscient being would know He exists, He would believe he exists as well.

Wollen’s argument relies on controversial assumptions about the semantics of counterpossibles. His argument assumes that If an omniscient being existed, then he would believe an omniscient being exists, which in turn relies on the truth of If an omniscient being existed, then an omniscient being would exist. But my three proofs above made no appeal to any assumption about the existence of an omniscient being, and therefore, they establish that If an omniscient being existed, then an omniscient being would not exist.

To tally up the score, I now have four proofs (one from my previous post, and three from here), while Wollen only has one. Therefore, the balance of reasons speak in favor of my conclusion, and so Wollen’s conclusion is incorrect.