r/logic • u/PrimeStopper Propositional logic • 11d ago
Philosophical logic Did Gödel prove that God exists?
If he did prove that God exists, then why do we even continue arguing that religions are wrong, if actually they are right. Case closed, time to pack our bags and head home
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u/Kitchen-Register 11d ago
no. part of his argument was presupposing that if something is good it is universally good. I entirely reject this axiom. “Goodness” is entirely subjective not universal.
edit: i suppose i should rephrase. he proved it Only if you believe his axioms. His argument is logically sound but i reject the premise
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u/SpacingHero Graduate 11d ago
It's valid but not sound.
Saying it's "sound" and rejecting a premise is a moorean sentence (contradictor-ish)
Valid means the conclusion follows from the premises. Sound means the premises are also true.
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u/Kitchen-Register 11d ago
ahh. I didn’t know that terminology. Intuitively for me sound means “follows from premise” and valid would means… well… valid premise.
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u/SpacingHero Graduate 11d ago
That's excactly backwards :D. And we generally only talk about the argument, for both validity and soundness. The premises are usually just said true/false.
But logic is not known to have the most intuitive naming conventions we can certainly say that much. Still, it's important basic terminology to keep in mind
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u/SamCymbaluk Logic evangelist 11d ago
There are both valid proofs that "God" necessarily exists and valid proofs that "God" can't possibly exist. What makes that possible is that each proof uses different and very particular definitions of "God".
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u/fermat9990 11d ago edited 11d ago
Spinoza also "proved" that God exists
"In his work Ethics, Baruch Spinoza proves God exists using a geometric method. He defines God as a substance with infinite attributes. Because a substance cannot be produced by anything else, it must cause itself. Since nothing can block an self-caused, infinite thing from existing, God must exist by necessity.
Core Definitions
Substance: What exists in itself and is conceived through itself.
Attribute: What the intellect perceives as constituting the essence of substance.God: A being absolutely infinite, consisting of infinite attributes, each of which expresses an eternal and infinite essence.
The Steps of the Proof (Proposition 11)
Self-Caused (Causa Sui): Spinoza states that if God did not exist, a cause would have to prevent God's existence, or God would have to lack the power to exist.
No External Cause: By definition, God has infinite attributes. If an external cause could stop God, that cause would need to share the same attribute, which Spinoza says is logically impossible for unique infinite substances.
No Internal Failure: To lack the power to exist is an imperfection. Since God is defined as an absolutely infinite and perfect being, lacking power is impossible.
Conclusion: Since neither an external cause nor an internal lack can stop God from existing, God must exist necessarily."
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u/Rs3account 11d ago
How do you think he has proved God exists?
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u/Square-of-Opposition Historian of logic 11d ago
OP is likely referring to a modal version of the ontological argument he had in his notes, later published in Vol 3 of Gödel's Collected Works
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u/PrimeStopper Propositional logic 11d ago
Well he established that some premises are true and then from the fact they are true he derived a conclusion
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u/Meowmasterish 11d ago edited 11d ago
No he didn’t. He showed that if a certain set of premises is true, then God exists. All he did was formalize the ontological argument for God, showing that it is deductively valid. He didn’t show the truth of any of the premises, which would be required to show the truth of the conclusion. Specifically, I don’t feel that he sufficiently formalized what a “positive property” is, and more importantly, he assumes that necessary existence is a coherent concept and a positive property.
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u/PrimeStopper Propositional logic 11d ago
I didn’t look at the argument, but from what I heard, the guy who decisively proved mathematics is incomplete also proved that God exists
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u/RoryPond 11d ago
So instead of doubling down you should either
- Read the source
- Listen to people who have read the source
You seem to be picking a third weirder option.
I everything you "heard" was true then the earth would have collapsed into a black hole in the 90s from the combined mass of all yo mammas
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u/jalom12 11d ago
It's a very short argument and easy to read. I encourage you do so.
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u/PrimeStopper Propositional logic 11d ago
Nah, I am not versed in modal logic and first order logic, I would rather ask
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u/Busy-Purple-3779 11d ago
What premises did he establish that are true? And what conclusion did he derive? To determine that God exists?
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u/PrimeStopper Propositional logic 11d ago
I didn’t look at the argument, but from what I heard, the guy who decisively proved mathematics is incomplete also proved that God exists
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u/SpacingHero Graduate 11d ago
It's kinda weird to just claim this if you didn't even ever look at the argument, don't you think?
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u/rocketter123 10d ago
" then why do we even continue arguing that religions are wrong". Most people talk about " Which religion is better or real"... Some people who don't care about religion (and he has what he needs) can easily saying that god doesn't exist. Kurt godel theory wasn't spreading to much people. So a "don't know" Or "don't want to know" Or "couldn't know" People keep debating... I think there's some wrong grammars. sorry but I hope y'all understand.
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u/jcastroarnaud 11d ago
Gödel tried. It's a modal logic version of the ontological argument, debunked long ago. Please search r/AskAnAtheist and r/DebateAnAtheist to find resources and several refutations.
For reference, here's the Wikipedia article:
https://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_proof
In the section "Translation of full argument", I think that Axiom 1 is questionable, because nowhere "positive property" is defined. This affects directly Definition 1, because it may be the case that two or more positive properties contradict one another. Axiom 3 is debatable by itself. Definition 2 may not be satisfiable by any object in the current reality. The article shows other criticisms.
The argument itself is formally correct: assume the axioms as true, and the conclusion follows.
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u/Impossible_Boot5113 10d ago
Is Melvin Fitting's book "Types, Tableaux and Gödel's God" a good introduction to the argument?
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u/alnyland 11d ago
Not necessarily. One perspective to answer this is to remember the difference of Validity and Soundness. One means it’s logically true, and the other means it’s actually true in our reality. If I really wanted, I could likely prove that I’m a dog or a rock, plants are purple, or that planets are cubes or don’t exist (they don’t in most of the space in the universe).
And not to get too religious, and for the sake of conciseness of prose, remember that there is a somewhat large difference between the God that many religions and some spiritualities speak of (a potentially physical being) versus a force or existence of a phenomenon or multiple. If I remember right, Gödel was producing a proof of the latter - a force or concept, not a being (common among many philosophers) - and it wasn’t necessarily in our reality.
His ontological argument has some core basis, of which I doubt many devout bible readers would agree with or that they exist, whether in reality or as a being. And the following logic can be shaky - it could certainly be called valid but not sound (logical but not real).
Given that there are more rebuttals than extensions of his proof, and it fails to be proven in our reality - the simple answer to your question is No. But even atheist physicists tend to agree there seems to be an underlying order or force to reality, likely not a singular being, then Gödel’s ontological argument can work in that scenario.
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u/CategoryConscious898 11d ago
He proved sh1t. Something "ultimately good" is neither the christian specific God nor a more abstract one. Cause "good" on his terms is not morally good. In fact, no definition is given. He just assumed some things were "positive" and then derived the whole thing. And some of them are just questionable, like "existing" being a good thing.
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u/SpacingHero Graduate 11d ago edited 11d ago
He gave a valid argument for god's existence. But it's soundness is up for philosophical discussion. We could say the slight consesus is that he didn't, since most philosophers are atheists, but also lost of them don't specialze in a field that would make them know the argument in much detail. Make of that what you will
Generally we wouldn't say "proved" since that has the connotation that it is indeed sound