Jach's personal blog

(Largely containing a mind-dump to myselves: past, present, and future)
Current favorite quote: "Supposedly smart people are weirdly ignorant of Bayes' Rule." William B Vogt, 2010

Proofs for and against God

I think I need a simple precursor to my post about proof. This post is meant to destroy the notion that there is anything we cannot prove. I have two preliminary subpoints.

There is no difference between a positive and a negative claim because one can be expressed as the other. I claim "God exists". That is a positive claim. I also claim "God is not nonexistent." This is a negative claim but says exactly the same thing as the first claim.

"Burden of proof" is an expression that signals you are suffering from diseased thinking. There is no such thing as "burden of proof" except in a legal context, where legal proof is the same thing as legal evidence. Proof in general, however, is not the same thing as evidence in general. Much confusion arises from conflating the two. In matters of Truth, there is only "burden of evidence."

Now on to the main point. First up, here is a proof for God, step by step:

1. If we humans exist, then God exists.
2. We humans do indeed exist.
3. Therefore, by the logical rule of modus ponens, God exists.

Is this proof valid? Yes. Is this proof correct? Yes. Is this proof True? As an atheist, I say no! If you're a believer, you would say "yes!" What is the difference between us? The difference is that I do not accept the premise, the assumption, the implication that is expressed in Step One as being True. The theist does.

A valid and correct proof is only as True as its premises. You cannot gain or lose truthhood along the way. In the context of proving things, "valid" and "correct" are synonyms but "True" is something very different.

Now here is a proof against God, step by step:

1. If God exists, then the earth was made in 6 days.
2. We have observed that the earth formed over billions of years, it was not made in 6 days.
3. Therefore, by the logical rule of modus tollens, God does not exist.

This is a valid proof. Is it True? I say yes, a theist would say "no".

Neither of these proofs are very convincing. Even I wouldn't have accepted the second one back when I was a kid who believed in God. The disagreement is with the premise's Truth.

It's not always disagreement with the premise, however. The disagreement is often in the conclusion's Truth. We're certainly motivated to find a disagreement in the premise if we disagree with the conclusion.

But if there is no disagreement with the premise and the proof is valid but you still don't agree with the conclusion then you are wrong and under the influence of diseased thinking.)

Note that just because you think the premise is not True does not necessarily mean you think the conclusion is not True. Perhaps someone presents to me the proof "If cows moo, then God doesn't exist. Cows moo, therefore God doesn't exist." Even though I agree with the conclusion, even though this is a valid proof and I consider it True, I still disagree with the premise and thus reject it and the proof. This doesn't mean I'm closed to proving the conclusion in a different way that I agree with. Just find a premise I agree with and it's trivial.

This obvious nonsense of rejecting True and valid proofs is why, when we decide whether to believe something as True, we use evidence and are in the realm of science and probability theory. Entering this realm, the atheist and theist disagreement can become more than just disagreement over the premise. It can become disagreement over probability and information theory, and the theist loses.

There is a subtler notion of proof as it relates to true and false. It's more complicated. It's not the everyday simple meaning. You learn it by studying rigorous logic and math. Unfortunately many people learn just enough of it to confuse themselves and not enough to realize there's a distinction. This goes in hand with the diseased thinking mentioned above.

If someone says "Prove 0.999.. = 1 is true", they better mean "I accept math as True. Please prove 0.999.. = 1 is valid by using math." If they don't mean that, they're using a diseased notion of proof. Similarly, if they say "Prove 0 = 1 is false", they better mean "I accept math as True. Please prove 0 = 1 is a contradictory statement using math." If you don't accept math as True, you have some bigger issues to worry about. (And by math I mean specifically ZFC Set Theory, but there are other mathematical frameworks one can accept as True.)

Philosophers will generalize even further complicated notions of truth, but the rule is basically the same. "Prove that this proposition is true" means, to a philosopher, "Prove that this proposition is not in violation of this set of assumptions I temporarily agree with."

Posted on 2012-03-25 by Jach

Tags: philosophy, rationality, religion


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Anonymous June 17, 2017 02:54:56 PM Both proof are valid arguments, because the premises will result the conclusion by the valid logic (although in the second case, the second statement is only saying the observation of something, and then you will assume that the observation is OK, which is a reasonable assumption to make but is not a strict proof; I do agree the Earth is form by billions of years, but is not proper proof and only the mathematical proof is the real proof of the mathematics; other than that how do you know if it is or is not all hallucination?).

I happen to disagree with the first premise of both proofs though; neither makes sense to me. (Unless by "God exist" you mean something much more including those statement of Bible, but they are just the stories, and proves nothing.)

I think your notions of proof is good though (although I am not atheist but am "panendeist", but there is not the proof this or that way).
Jach June 17, 2017 03:08:51 PM True, the second proof's second statement needs an additional assumption or clarification that the evidence from observation is true.

The whole point of the post is to show the limitations or pitfalls of "proof". I haven't written it up properly yet but the reason I'm an atheist has to do with what I consider proper notions of belief, evidence, and existence, pretty much nothing to do with proof except maybe to show that mathematically the methods of probability theory work. In logical proof, absence of proof is not the same as proof of absence. In probability theory however, absence of evidence is the same as evidence of absence. I do have a post on that one.
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