On Formal Proofs For/Against God

[Updated 2/28/2021]

Over on Ed Feser's
blog, is another attempt, in a never-ending series of attempts, to formally prove the existence of God. [1] I was playing devil's advocate by taking the position that the answer to Feser's question is a resounding "no" by providing counter-arguments to their arguments. [2] [3]

"Talmid" made
the statement:

You can defend that the arguments fail...

This is where the light came on.

Nobody would say of the proof of the Pythagorean theorem, or of the non-existence of a largest prime number, that "the arguments fail." That isn't how proofs work. If a proof fails, it's because of one of two reasons. Either a premise is denied, or there is a mistake in the mechanical procedure of constructing the proof. When you read these proofs of God's existence (or non-existence), at some point you come to a step in the proof where it looks like the next logical step was taken by coin-flip, instead of logical necessity. This is evidence of the presence of an unstated premise.

Find the unstated premises. Don't let your common sense get in the way. [4] If the argument assumes that things have a beginning, question it. Why must history be linear and not, say, circular? Why can't something come from nothing? That may defy common sense, but it's still an assumption.

Now, suppose that in an argument for or against God that there are five premises. If the premises are independent of each other (and they should be, otherwise one of them isn't a premise), and each premise has a 50-50 chance of being correct, then the proof has a one in thirty-two chance of being correct. Those aren't great odds.

An immediate response to this would be, "but Euclidean geometry has five premises, and it's correct! So why not an argument for/against God with the same number of premises?" The answer is simple. We can measure the results of Euclidean geometry with a ruler and a protractor. While it's against the rules to construct something in Euclidean geometry with anything other than a straightedge and a compass, it isn't against the rules to check the result with measuring devices. And for non-Euclidean geometry, which is used in Relativity, we can measure it against the curvature of light around stars and the gravitational waves produced by merging black holes.

But we can't measure God, at least the non-physical God as God is normally conceived.

If that's the case, then it doesn't make sense to argue for/against the existence of God by any means other than "assume God does/does not exist". That gives a one in two chance of being right, as opposed to one in four, one in eight, ... one in 2^(number of premises).

If the premise "God does/does not exist" leads to a contradiction then, assuming the principle of (non)contradiction, the premise is falsified. I suspect, but cannot prove, that both systems are logically consistent. If this is so, then the search for God by formal argument is futile.

[Update:]

It seems to me that if the search for God by formal argument is futile, then the choice of axiom - God does/does not exist - is a logically free choice. And if it's a choice that you are not logically compelled to make, then it comes down to desire. [5]



[1]
Can a Thomist Reason to God a priori?
[2] Commenting as "wrf3".
[3] I've informally taken this position
here, here, here, and here.
[4] One unstated premise is ususally, "common sense is a reliable guide to true explanations." It isn't. Relativity, and Quantum Mechanics, defy "common sense". Quantum Mechanics, for example, uses
negative probabilities in the equations of quantum behavior. What's a negative probability? What's a "-20% chance of rain"? Yet we are forced by experiment to describe Nature this way.
[5] For the desire to be fulfilled, God must then fulfill it. You can't tickle yourself. If you want to experience tickling, you must be tickled by someone else. If you want to experience God, then God must reveal Himself.

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Electric Charge and the Laws of Thought

In one of the interminable discussions on whether or not we can prove the existence of God through reason (we can't), I made the claim that the behavior of electric charge is identical to the laws of thought. This table summarizes the relationship:

ThoughtCharge
1IdentityLike charges repel, opposite charges attract
2Non-contradictionPositive charge is not negative charge
3Excluded MiddleCharge is either positive or negative

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