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The next time someone asks you to prove that God does not exist, take him up on it. The "proof" lies in Goedel's Incompleteness Theorem. I mean, technically, with the challenge of "proving", the person has just:

(1.) accepted logic as a platform for establishing truth,

(2.) meta-mathematical logic has proven that there are propositions the truth of which are unknowable (Incompleteness Theorem), and thus

(A.) God is limited (there are things a god can't know the truth or falsehood of)

(B.) and by definition, God cannot be a god (because the definition of God is to be unlimited).

The proposition that a god exists has just been proven to be inconsistent, and therefore there is no God.

Q.E.D.

And we all know what happens next, right? The person rejects the logic, or decides he wasn't talking about logical proof, or rejects that God is bound by logic. In other words, the person will reject any bit of reason that conflicts with his pre-set beliefs, including reasons he had just asked for.

His request to disprove the existence of God was not sincere.

GlyndonD 7 Mar 3

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One more time: Goedel's Incompleteness Theorem does not state that if a system is sufficiently complex, there will exist contradiction. It only states that there exists propositions that cannot be proven to be true or untrue. They will remain indeterminate, and further, one can never tell if a proposition that falls within this class is actually a member of this class. (And this applies to gods' inquisitions, too.) Another result of this theorem is that mathematician's work will never be done -- there will be propositions that a mathematician will not know are unprovable, and thus he would not have any idea that any attempt to prove the proposition will be ultimately futile. There is no way to know that he should set the proposition aside and move on.

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push them off of a tall building so theres plenty of time to pray

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Can you explain #2 for me?

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I'd like to push back on this one a little, as well as ask for some more information and clarification. For people like me unfamiliar with this theorem, can you explain point 2 in more detail? Specifically how it relates to non-mathematical ideas? I'm not sure I'm willing to accept that everything needs to be defined by math, without some convincing. And As someone who doesn't follow math I could use a little more detail before I accept it 🙂

But also, there is one or two issues I'd like to address. Here are I think a few ways one could push back against A. One could argue that the theory (again, this is following my limited understanding) could only apply to people without omniscience. I'd like to know how the theory gets around that in particular. From what little I understand, it seems like Godel is saying things are not provable without further axioms, (not knowable by math) not that they're now and forever unknowable provided one had different means to find that information.

Furthermore, what is to stop one from saying God can be defined as one bound by logic? Or that logic is flawed? While I'm not convinced of it, part of the basic Descartes stuff is that logic itself, or at least our understanding of logic, could be flawed. I just don't think its air-tight.

It kind of seems like you're setting up the targets just to knock them down by saying something as broad as "accept logic as a platform for truth". You're right that someone can reject the logic, but is that necessarily a failure? It seems like a setup for indignation.
Similarly, I think a response would need to be had for the one rejecting God being bound by logic.
Instead of just saying "gotcha" I think a response would be needed for the rejections you mention.

I think the crux of the issue is that if A comes before B you seemingly have a contradiction entailing the falseness of B. But faced with this one needs more to convince someone of faith that the following isn't true.

God knows everything
The theorem states there are unknowable things
Therefore the theorem is wrong or not applicable

I wrote quite a bit and its a bit rambly because I just tend to write what comes to mind as I'm thinking so theres a bit of redundancy there. I tend not to clean it up until its time to write a paper haha.

I just think it's not sufficient to come to your conclusion but not write responses to the objections that you listed.

Finally (sorry haha), I wouldnt say the request is insincere based on an unwillingness to accept the argument presented without further proof. But that's just a nitpick =)

Anyway let me know more about the theorem, and how you'd get around the objections if presented!

Gödels Incompleteness Theorem (which he was able to prove, though I do not know said proof) can be stated as any sufficiently complex system can't be proven. Meaning that as we 'complete' a mathematical system (and this can be extended to any system which is built up on logic since that is the very basis of math) it eventually becomes so complex that it will have some inconsistency in it. Meaning that there will be more than one statements that are in conflict or contradiction.

When he says that the truth of systems is unknowable, he means that they are at a level of complexity such that they cannot be proven for being self contradictory, as proven must be the case by Godel.

The case he is presenting is that a god is presumed to be omniscient, but it can be proven that it is impossible to know everything as it contradicts Gödels completeness theorem, and thus god must not actually know everything (be omniscient). Either s/he is not omniscient, in which case s/he is not a god, or s/he does not exist due to being impossible (omniscient).

It actually is a reasonably tight, and endearing in my opinion, argument. 🙂

For more information on Gödelss completeness theorem:

[plato.stanford.edu]

The Incompleteness Theorem was as shocking in the mathematical world as quantum mechanics was in physics. It's very weird for the human mind to grasp, but it's logically flawless. It is a theorem about theorems. One other property of the Incompleteness Theorem is that you can never tell if a proposition (that is still undecided) falls within the domain of incompleteness (unknowable). For a while, it was speculated that Fermat's Last Theorem might be unknowable, until it was proved ten years ago or so.

The Incompleteness Theorem doesn't relate to anything outside logic. I use it only because it says that there are propositions that aren't knowable -- cannot be proved to be true or untrue. Mathematical logic is based on 5 axioms (if I remember correctly). One of the axioms, The Axiom of Choice, has been debated, and some mathematicians do not completely accept it. Another technique of determining the truth of a proposition -- to assume the proposition to be true, but if it produces a logical inconsistency, the proposition must be false -- is also debated. But I'm pretty sure all mathematicians regard the Incompleteness Theorem as being valid.

Logic is all about determining consistency and contradiction. It is hard for me to imagine that a contradiction can exist. For example, it will have rained yesterday or it will not have rained. You can't have both be true. They are inconsistent. Can God make 1 + 1 not equal 2? I can't imagine it. I can't imagine God being able to beat me in a game of Tic Tac Toe, either, no matter his omniscience or all-powerful self. Similarly, trained and skilled mathematicians cannot imagine how the Incompleteness Theorem cannot be true. And it says that there are (not might be) propositions where the truth of it can't be determined. Only if God could create contradiction could the Incompleteness Theorem not be true, but this would be a whole different thing than simply parting the Red Sea. How can you imagine that 1 + 1 does not equal 2? What kind of powers would it take to ensure this? I can't imagine it. I might be able to imagine that a god has weird unlimited powers to do fantastic things in the real world, but not powers to make contradiction true. Nope. Nada.

I'm not trying to say everything is mathematical. I'm just pointing to a place where God having unlimited powers is a contradiction. And if God has limited powers here, he has limited powers, period.

You're saying that logic doesn't apply to those that are omniscient, and therefore you can't use logic to prove that something is not omniscient. This is circular reasoning. You're making a statement, and defining it as being true. Kinda like the statement "God exists and knows everything" must be true and can't be debunked. I can't argue with someone who will not accept argument.

Goedel says that within the framework of logic, there are statements that can't be determined. That's it. Yes, one could say God can exist outside logic, but I don't think there's a human alive that can fathom that. If you think logic is flawed, please point out to me the flaw. If it's not air-tight, show me the leaks.

When one says "Prove it", it implies a requirement to use a logical argument. I'm not the one who says "Prove it". I merely supply the proof. If one does not accept the proof that he asks for, he should point out where the proof is incorrect. If he can't or won't, then he's rejecting logic, he doesn't accept proofs, and thus his call to "Prove it" was insincere. I just wasted my time. It's similar to trying to convince a flat-earther that the world is oblate -- he says "Prove it", but then rejects any evidence or reasoning that contradicts his insistence of a flat earth. His request to prove that the earth is not flat was insincere because he had no intention to accept a proof of any kind.

The indignity is when someone wants to argue that logic is flawed, but that his argument is also assumed to be logical and not flawed, or when someone wants to introduce his statement that "logic is flawed" as some kind of axiom that cannot be challenged. Only omniscient gods are allowed to do that!

My penultimate activity in getting my math degree was taking a course entitled "Mathematical Logic", where the whole course was devoted to understanding Goedel's Completeness and Incompleteness Theorems. One textbook. The final was to regurgitate the Incompleteness Theorem. Sorry, I won't do that again here.

You'll just have to do the math.

While that's a clever way to end the essay, that feels just a bit too snarky to be honest. I feel like it means that this thread is for math majors only. (maybe it is?) I'm stuck on not understanding how
the theorem explaining the unknowability (or unprovability?) of math, and how it relates to things outside of math. Mostly because math is a construct, defined in such a way that is has to be true.

Oh, the logic thing is just some basic cartesian silliness. I'm not sure how much stock I put into it, but its an idea he gave up on because he didn't know how to move forward without logic.

Finally, as for the god existing outside of logic, that's an objection I can definitely see coming from a religious person. I think because faith isn't built around things being knowable or provable, and I think that's an issue that has to be dealt with. I was once told that its hard to argue with a religious person because they are working on a completely different playing field than us. I think that's why its hard for me to argue the "god outside of logic" thing because it's not something I believe. But it is something I hear quite often. But again you got me on the circular logic thing, which is true. It's just something one would expect to hear in response. Even though you're right, that does equal insincerity as you described.

On that note I do like how you used the flat earther as an example, because they are definitely ones who claim evidence but refuse to admit evidence

While I understand its a complex theory and you've obviously taken great lengths to understand it in detail (far more than I ever could have), I'm not sure it works to say that others should use what you've learned to argue if they don't understand how it applies. At this point I would have to take it on faith and wouldn't be able to argue it further, because I simply don't understand the application of the theorem in complete detail.

@Gnarloc That does help me understand it, at least a little better. While I'm still not sure entirely certain how it makes the jump from math to not-math, that does help quite a bit, and I appreciate it! Thank you 🙂

Any argument is built upon some assumptions. As here the assumption that god (should he exist) is omniscient. That is your 'given.' Well, you apply the same rules to build an argument that you do to build a proof (if you are good at arguing, which I would say I am not).

For the record: my degrees are in applied mathematics (Electrical Engineering) and Education (teaching math). I am a rube compared to @GlyndonD and freely admit it. Though I did pay more attention to the theoretical side of the house than most of my heretical applied compatriots.

My attempt was to bring the language of Gödels theorem down to laymens terms. I freely admit that means that I left out a heckuva lot of information. In fact, in reading Glyndons response, I missed a lot of nuance that he obviously understands better than I. I think, in fact, that my introduction and reading of the theorem lead me to understand it in a way that is not perfectly in keeping with his and thus may be in error. BUT, good theorems can be dusted off and reread to find new goodies in to ponder. If that were not true, there would be no reason to go to school and pursue a degree and attempt to improve the art. It would be simply learning what we already knew with no chance at exploration. Thankfully, we keep finding more to explore, which leads to yet more. 🙂

@gnarloc What I left out of the conversation was that I got lost in that Mathematical Logic class, and failed in my attempt to regurgitate the theorem. So, I have to introduce some faith in my my argument of using the Incompleteness Theorem, too. It helps to know that Goedel and the followup mathematicians had no hidden agenda behind the proving of the theorem (i.e. some kind of argument that God doesn't exist), but think and believe (yes, the faith that the initial axioms the theorem is based on are indeed true) that the theorem is consistent (true). I have faith in the logic, theorem, and mathematicians, because I failed in my mathematical abilities to 100 % reason that it is true.

I believe you need to have faith when your reason does not fill the vacuum. I strive to fill the vacuum as much as I can with knowledge and reason, and to limit my default reliance on faith. For example, I have used science and reason to think that the Big Bang, evolution, and brain science to describe our universe and "souls", but I still can't conceptualize why there is a universe in the first place, why the Big Bang happened (what caused it to suddenly happen), or why there is a continuum of Big Bangs (and why this continuum exists). I get the "what", but I can't figure out the "why". I don't even have a faith-based idea for the "why". God? OK, then why did God suddenly appear, or how is it that there was always a God? Belief in a Creator of the universe still does not answer my fundamental question of "why". I'm not sure if the human brain has the capacity to ever understand the reason of "why", maybe much like humans can't really comprehend infinity and quantum mechanics and unknowable propositions, except in the form of equations.

I guess the answer I have to accept as to the "why" of the universe is, "Because."

@GlyndonD sounds like a pretty good answer to me! I dig cosmological argument discussion and I find it very interesting how we can conceive of the notion of infinity but not conceive (clearly and distinctly) an actual infinite thing. It does end up either being turtles all the way down or something defined by its existence. I've always liked the comparison of God to matter. Which usually is described as something that had always existed. But that could probably fill up its own thread 🙂

When talking about sentience, the question "why" is correct. Because 'why' asks after motive and reasoning.

When talking about inanimate objects, substances and chemical or energy based processes, the question is 'how' or 'what', not why. Again, because there is no brain here, no sentience to have a reason driving the action.

Once you realize that, you stop asking questions that ask for a reason behind a chemical reaction or one of particle physics. It happens because the right elements happened to be in the right configuration and proximity. It's a "how did this come about."

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I just tell them that if the big bang is real, and it is, then a creator diety couldn't have created the universe 6,000 years ago. We can prove the big bang happened through the detection of gravitational waves over 14 billion years ago. We can measure the rate of expansion through thermodynamics, specifically entropy.

This just argues against Genesis - it doesn't disprove the existence of God.

@GlyndonD it disproves the Abrahamic God, and all other claims of creator dieties as no creation myth includes a big bang.

@Cassandra nothing disproves God to a believer. All you can do is eliminate the possibility of God. Also believers have faith, that is the problem, they will keep believing or they won't. It's only they who can make their choices.

So, you don't like my "proof"?

@GlyndonD it's a good system for determining what isn't real, but you can't prove a negative by definition.

The "good system" determined that some propositions aren't knowable, and thus the positive claim that "God knows everything" is false. And you can prove a negative: you assume the positive, and if it fails to be consistent, then the positive is false. If the positive is false, then the negative is true.

@GlyndonD not so. If you claim that turnips are awesome for your health there are many other options in the negative. Such as they are poison, ok for you, average, or bad for you.

Well, either turnips are awesome for your health, or they aren't. The statement you are testing has to be worded halfway decently in order to be determined true or false. If you were to say, "Turnips are pretty nice.", I don't know how to put that through a proof.

I think the whole point, from the beginning, is to let the believer see how Reason can work, how you choose to use if over Faith, and that, after you state the proof, the believer rejects it, not because of anything about the proof, but because he has decided to choose Faith over Reason. He will reflect Reason, period. It's a choice. It's a choice for him, and it's a choice for you.

@GlyndonD the Christian God exists, or he doesn't. What about if he's dead?

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