
Gödel's Proof of God's Existence - netrus
http://arxiv.org/abs/1308.4526
======
JonnieCache

        – The basic modal logic K is suﬃcient for proving T1, C and T2.
        – Modal logic S5 is not needed for proving T3; the logic KB is suﬃcient.
        – Without the ﬁrst conjunct φ(x) in D2 the set of axioms and deﬁnitions
          would be inconsistent.
        – For proving theorem T1, only the left to right direction of axiom A1 is needed.
          However, the backward direction of A1 is required for proving T2.
    

So, does god exist or not? Can anyone proficient in symbolic logic translate
this for us?

As someone who's read the first 2/3 of GEB at least twice, I'm planning to
reorganise my entire worldview around this.

~~~
MichaelAza
Yeah, seriously, what's the verdict? And where's the formalization itself?
Show me the code, I have a whole worldview I need to re-evaluate here.

Edit: Seems like this is the code -
[https://github.com/FormalTheology/GoedelGod](https://github.com/FormalTheology/GoedelGod)

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jamesbritt
This feels like begging the question.

Start with a selective, loaded definition of "god" that seems to amount to "A
god is a being who must exist."

God is all that is good; not existing is not good, therefore god must exist.

QED.

~~~
alanctgardner2
> selective, loaded definition of "god"

Well, you can't really win here. It's either a hand-wavey definition you could
never formally prove, or a rigid, 'loaded' definition.

That said, the basis of the proof does seem to be that 'if god exists, then he
must exist', which is not really groundbreaking.

~~~
dragonwriter
> That said, the basis of the proof does seem to be that 'if god exists, then
> he must exist', which is not really groundbreaking.

Actually, its "if god must exist, he exists".

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msluyter
This is one version of the ontological proof, which has a long history. For an
overview:

[http://en.wikipedia.org/wiki/Ontological_argument](http://en.wikipedia.org/wiki/Ontological_argument)

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chrislipa
The proof's axioms deal with what kinds of things have the property of being
'positive' (A1-A5). But lacking a separate definition of what positive means,
we really have no choice but to view these 5 axioms as an implicit description
of 'positivity' and wonder what mathematical models realize these axioms.

One thing to note from the axioms is that for every property either that
property or the negation of that property (but not both) has the label of
'positive'. This is already pretty strong, because it's making claims the
about the 'positivity' of properties that are completely unrelated to the rest
of the argument. It's almost just a labeling game: given p and -p, you must
label exactly one as 'positive'. Is the property of being red positive? Saying
no is equivalent (according to these axioms) to saying that the property of
not being red is positive.

You can pick one model for the axioms where being red is 'positive', and then
the God that's shown to exist will be red. You can pick another where being
not red is 'positive', and then the proof implies that God will not be red.
It's not a logical contradiction because they're different models, but it
certainly makes one wonder what the proof is talking about when it mentions
'positivity'. I have a suspicion that the axioms themselves generate an
inconsistency and hence they could generate proofs for any statement.

Anyways, this paper is about formal theorem provers, not theology, so hats off
to the researchers implementing higher-order logic.

------
pohl
_A God-like being possesses all positive properties

A5 Necessary existence is a positive property_

Oh, yeah, that's not circular at all...

~~~
zamalek
> He does not extensively discuss what positive properties are, but instead he
> states a few reasonable (but debatable) axioms that they should satisfy.
> Various slightly diﬀerent versions of axioms and deﬁnitions have been
> considered by Godel and by several philosophers who commented on his proof.

Such is the world of philosophy. Remember that some of the greatest scientists
and mathematicians lived when all of it was just _philosophy_. Philosophy is a
training exercise to think imaginatively and some of our best science stems
from an imaginative spark. It's like saying that people professional athletes
running around a field (philosophy) is pointless because they are not running
in a race for gold (science) at that specific point in time.

This is by all means _not_ scientific, precisely because you can't address
that specific subject matter scientifically:

1\. God exists if he makes himself/herself visibly and measurably known and is
observed and measured by a human being and the observations are confirmed by
peers within the scientific community. 2\. God does not exist if a human is
present to see the end of the universe (or variant there-of) and he has not
been yet observed (assuming he/she is tied to the existence of the universe)
and the lack of observation is confirmed by peers within the scientific
community.

We simply don't know until either (1) or (2) is satisfied, therefore this is
_exactly_ the type of stuff philosophy is good at. It's not saying "can we
prove it" it's saying "let's think about creative ways to prove it if we can
get a little lax about the scientific method." Were "getting lax about the
scientific method" means that "proof" can be derived from either common sense
or logical arguments.

~~~
lutusp
> Remember that some of the greatest scientists and mathematicians lived when
> all of it was just philosophy.

Not really. Galileo and Newton turned philosophy into science by doing
experiments, and scientists never looked back. Science differs from philosophy
by being steered -- defined -- by empirical evidence, and by falsifiability,
the idea that any idea must be testable against reality and must be discarded
if the test fails.

That's certainly not philosophy.

> It's not saying "can we prove it" it's saying "let's think about creative
> ways to prove it if we can get a little lax about the scientific method."

There's no middle ground such as you're suggesting here. There's no overlap
between science and philosophy. They are distinct ways of processing ideas.
One of them must be compared to reality at every turn.

------
cliveowen
I didn't know there was software to verify mathematical proofs. Heck, I didn't
even know there was a formal syntax for writing them.

~~~
netrus
A prominent example for proofs by computer algorithms is the 4 color theorem:

[http://en.wikipedia.org/wiki/Four_color_theorem](http://en.wikipedia.org/wiki/Four_color_theorem)

~~~
aardvark179
That's not quite the same thing. The 4 colour theorem was proved by boiling it
down to several thousand test cases and using a computer program to test those
by colouring them. This paper is about using theorem provers to check axioms
for consistency and proofs derived from those.

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mej10
[http://en.wikipedia.org/wiki/Ontological_argument](http://en.wikipedia.org/wiki/Ontological_argument)

There are obvious (and not so obvious) problems with such an argument even
when formalized, some of which are discussed on the Wikipedia page.

------
samatman
This would appear to be a more formal version of Thomas Aquinas' Argument from
Gradation of Being, borrowing some elements of the Argument from Possibility
and Necessity.

Logically proving the existence of God is a very old game. Modern atheists
tend to ignore these proofs in favor of attacking superstition and the more
obvious theological nonsense.

Which is a shame, because they can be refuted, with interesting consequences
for one's worldview. The stance that most powerfully refutes any Ultimate
argument for God (of which there are a few good ones) is, imho, Madhyamaka
Buddhism, which holds that everything is empty because all phenomena
dependently co-arise.

------
joshdance
If there were a God and he was all powerful, and he wanted you to believe
before you knew He existed, it makes sense that you would be unable to prove
or disprove His existence.

~~~
benjohnson
Indeed! if God mad His existence easily knowable, it would take away your free
will to have faith.

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mbubb
How cool.

Made me think of a Uni course on Thomas Aquinas from eons ago. I'll have to go
back and check but I think:

"An essence of an individual is a property possessed by it and necessarily
implying any of its properties"

could have come from Aquinas' "Being and Essence".

And - forgive me it has been eons - didn't Wittgenstein deal with this time of
formulation showing you could in parallel construct its opposite.

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agentultra
This was paid for by tax-payer money? Wow Germany. Awesome.

I've only just begun studying Gödel's proof of incompleteness and so I'm not
qualified in any way to verify this paper. However it seems to me, as a
layman, to be a very large stretch and mostly a tongue-in-cheek exercise of
various logic proof verification software.

Or possibly a troll. Hard to tell. :)

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netrus
As an atheist, I have mixed feelings about it. I like it as a training in
logic, yet I feel it is of no theological value...

~~~
bsullivan01
"God" doesn't necessarily mean one that cares what you ate on Friday.....or if
you pushed the elevator buttons on Shabbat.

~~~
astrodust
Replace "God" with "burrito" and it's the same thing.

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jballanc
Now what would be really interesting is some form of comparison between this
proof and the conjecture by Brian Greene (and others) that it is highly likely
that we are all bit players in a massive computer simulation of a Universe...

~~~
lutusp
Yes, but those ideas aren't comparable -- proof or disproof of one doesn't
influence the other. They're orthogonal ideas.

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icpmacdo
Everything in this thread is going way over my head. Would someone be kind
enough to explain it to me like I'm 5?

~~~
lutusp
It's an argument that, if certain logical conditions are met, then the
principle of the existence of God is inescapable. Note that I said the
_principle_ , not the fact -- the fact was not the matter under discussion.

It's like discussing the concept of an honest politician -- such a thing can
obviously be proven to exist in principle, but that doesn't require that it
exist in fact, in everyday reality. A good thing, too.

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bachback
Gödel is so overrated. How is this actually science? "This work has been
supported by the German Research Foundation under grant BE2501/9-1."

~~~
pmelendez
I believe that a "Formalization, Mechanization and Automation" of any logic
proof would enter in the definition of science

------
lutusp
People who read these tracts need to understand that the goal is not to
literally prove that God exists (all superficial appearances to the contrary),
only to show that the argument can be made and is logically consistent. The
same argument can be made with equal justification about Bigfoot, the Loch
Ness monster, or an honest politician.

All other issues aside, the Holocaust proves that either (a) God doesn't
exist, or (b) he's Spinoza's God, the one who can't be bothered about humans
and their problems.

