Godel's Incompleteness theorem and god
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03-01-2017, 11:43 AM
Godel's Incompleteness theorem and god
I found this site while googling, evidence for god, and found a logical argument for god. Heard of this one before, I know I haven't. https://www.perrymarshall.com/articles/r...s-theorem/

Also, first time being on this blog and am eager.
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03-01-2017, 05:32 PM (This post was last modified: 03-01-2017 05:38 PM by GirlyMan.)
RE: Godel's Incompleteness theorem and god
Sure. It's a comment on the intrinsic limitations of formal systems. Never seen it used as a proof for God before other than the tongue-in-cheek "God exists since mathematics is consistent, and the Devil exists since its consistency cannot be proved." (Weyl) The comments are entertaining at least.

There is only one really serious philosophical question, and that is suicide. -Camus
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03-01-2017, 05:54 PM
RE: Godel's Incompleteness theorem and god
(03-01-2017 11:43 AM)Anti-stupidity Wrote:  I found this site while googling, evidence for god, and found a logical argument for god. Heard of this one before, I know I haven't. https://www.perrymarshall.com/articles/r...s-theorem/

Also, first time being on this blog and am eager.

If there was any indication of a god's existence, it'd be headline news.

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03-01-2017, 05:57 PM
RE: Godel's Incompleteness theorem and god
Hello, welcome to the forum.

So... some one is dressing up William Craig's arguments in a new coat, then?

Or... did I miss something?

Consider
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03-01-2017, 05:57 PM
RE: Godel's Incompleteness theorem and god
At best it is an argument against gnostic atheism. Even if it applies to the question, it only means that there are statements of fact that can not be proven within the system. It does not mean that any specific claim is actually a statement of fact. What they are saying is that it is rational to believe in god because it can't be proven and that's ridiculous.

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03-01-2017, 05:59 PM
RE: Godel's Incompleteness theorem and god
(03-01-2017 05:57 PM)unfogged Wrote:  At best it is an argument against gnostic atheism. Even if it applies to the question, it only means that there are statements of fact that can not be proven within the system. It does not mean that any specific claim is actually a statement of fact. What they are saying is that it is rational to believe in god because it can't be proven and that's ridiculous.

Um... an 'Ultimate' god of the gap?

Consider
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03-01-2017, 06:14 PM
RE: Godel's Incompleteness theorem and god
(03-01-2017 05:59 PM)Peebothuhul Wrote:  
(03-01-2017 05:57 PM)unfogged Wrote:  At best it is an argument against gnostic atheism. Even if it applies to the question, it only means that there are statements of fact that can not be proven within the system. It does not mean that any specific claim is actually a statement of fact. What they are saying is that it is rational to believe in god because it can't be proven and that's ridiculous.

Um... an 'Ultimate' god of the gap?

Consider

More just a convoluted "you can't prove he doesn't exist" dressed up in science-sounding language.

Atheism: it's not just for communists any more!
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03-01-2017, 06:28 PM
RE: Godel's Incompleteness theorem and god
In the distant past I have seen it used as a "proof" God cannot exist.

Godel proves in any non-trivial formal system, there are statements that cannot be proven true or false. God cannot know if these statements are true or false. God is defined as omniscient. God is not omniscient. God does not exist.

Weak stuff.

When I shake my ignore file, I can hear them buzzing!

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03-01-2017, 07:52 PM (This post was last modified: 03-01-2017 08:02 PM by Reltzik.)
RE: Godel's Incompleteness theorem and god
I've encountered this before.

It's (very poorly) rendered into that "circle representing everything we know and can't there be something outside of it" argument, if we can even call it an argument. Which the incompleteness theorem does not actually say.

What the theorem DOES say is that, given even a moderately robust (complete) means of generating propositions, there will always be SOME propositions that we can generate that will be unknowable to us. Alternatively, you can describe it as showing that some axioms or premises must be assumed to engage in deductive logic, and that given a limited number of axioms/premises, there will always be open questions that cannot be conclusively answered without additional axioms/premises.

The liar's paradox isn't really part of the proof, but it's related. It's a class of paradox that's self-referential, and they were indeed bedeviling many mathematical logicians in the earlier half of the first 20th century (and the end of the 19th), with Russel's Paradox being the initial catalyst. This exposed flaws in what is now called naive set theory, which mathematicians were reformulating most of their fields to be described in terms of.

After Russel exposed the flaws (much to his own dismay), several attempts were made to salvage naive set theory to eliminate the flaws while still preserving its power. Even when they eliminated the known paradoxes, each ran afoul of a new but similar paradox.

Finally, Godel demonstrated that for ANY set of propositions, and given some decent mathematical tools (what was required for a "complete" system) he could formulate something akin to this. He simplified the discovery of these paradoxes to little more than a fill-in-the-blank game no matter where the people trying to get around them started, thus proving that the paradoxes would ALWAYS be there.

This was not, and never was meant to be, about the Theory of Everything, which is limited to physics and is about explaining observations inductively rather than producing fields of mathematics deductively. But it is true that there will always be more questions that we have not answered.

The metaphor applying this to Euclid's Postulates is accurate. The metaphors applying it to a bicycle, and to the universe, are not. Neither the universe nor the bicycle are deductively-constructed logical systems, they way Euclidean geometry or set theory are.

It should be noted, by the way, that mathematics has been revised so that this is not a problem. Naive set theory is only taught as an introductory "let's not bother them with the details yet" subject, and set theory proper has those problematic "complete" elements neutered so that they're no longer problems. It's not as robust as we'd like it to be, but if we made it that robust it would also break, so this is the best we'll do. Similarly for the other fields of mathematics, the axioms are recognized as the gateways to applicability. Everything in Euclidean Geometry holds true in any application where Euclid's axioms (postulates) hold true, but figuring out whether you're dealing with an application where they hold true is the user's responsibility. Two points might define a unique line here on Earth, but might not define a straight line near the gravitational distortion of a black hole, and certainly not in the realm of psychology. Geometry isn't "true" in any more sense than a truism. It and every other field of mathematics are valid if-then statements. Deductively powerful, but still subject to garbage-in, garbage-out.

That was the site's summary of the Incompleteness Theorem, which was moderately accurate in depiction but seriously flawed in its examples. Things go downhill from there.

Faith and Reason are not enemies: Depends how you define faith, and this is something that people LOVE to equivocate on. In that faith involves just having made a few assumptions, which is how exactly zero people ever describe faith save when they're trying to pull a bait and switch? No they're not. In that faith involves making assumptions, and then defending them against all evidence and all reason and refusing to examine them with a skeptical eye? Yes they are. Godel's proof may show that our understanding will always be incomplete, but that doesn't prevent that understanding from EXPANDING. Religious faith is all about blocking, denying, or ignoring that expansion wherever that expansion threatens its assumptions, and that IS the enemy of reason. Nor should it be thought that the faithful regard the objects of their faith as unknowable, the way this argument implies. Far from it.

All closed systems depend on something outside of the system: In the sense of logically-constructed systems? Yes. In other senses of the word system, such as the closed systems of thermodynamics? Not necessarily. This is going far beyond the axioms of Godel's Incompleteness Theorem which, obviously, would be self-contradictory if it applied to everything. (And remember that it was never meant to apply to everything. It was focused entirely on systems of pure logic.)

Moving on a bit more rapidly... technically-correct but very-deceptively-worded description of the absence of absolute knowledge in science that sets up later equivocations and special pleadings, check. Misapplying concepts again in similar ways to before, check. Oooh, that's a new one to me. They've gone and equivocated "can be described in mathematical terms" with "is mathematical". Not often I see new bullshit mixed in with the old stale stuff. Moving on... designation of something as immaterial without even defining the term, check. Failure to ask what happens if you "draw the circle" around THAT thing, check. Huh, I guess they're also failing to say "let's draw a circle around everything both material and immaterial" and so prove that there's a third category. Misapplying the term "information" in a way that shows that not only they don't know what they're talking about, but they lack the humility to recognize that they don't know what they're talking about, check.

Eeeyup, they're plopping down all the normal bullshit patties. And yes, it is suspicious that this sounds like how theologians describe gods. Specifically, it makes me suspicious that pretty much this entire fallacious misadventure was directed with that predetermined-conclusion in mind.

(03-01-2017 06:28 PM)Cheerful Charlie Wrote:  In the distant past I have seen it used as a "proof" God cannot exist.

Godel proves in any non-trivial formal system, there are statements that cannot be proven true or false. God cannot know if these statements are true or false. God is defined as omniscient. God is not omniscient. God does not exist.

Weak stuff.

I've used it before.

"An omniscient being cannot know that this sentence is true." But I can. It's not even unknowable, it's just unknowable to something that knows everything. Checkmate, theists.

... well, checkmate theists-that-believe-in-omniscient-gods. Man, that's a mouthful.
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03-01-2017, 11:20 PM
RE: Godel's Incompleteness theorem and god
(03-01-2017 11:43 AM)Anti-stupidity Wrote:  I found this site while googling, evidence for god, and found a logical argument for god. Heard of this one before, I know I haven't. https://www.perrymarshall.com/articles/r...s-theorem/

Also, first time being on this blog and am eager.

I think people conflate Gödel's brilliant work on the foundations of mathematics with his misguided ontological proof.

The Incompleteness Theorems are a work of genius. His 'ontological proof', not so much.

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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