
Gödel's Ontological Proof - tosh
https://en.wikipedia.org/wiki/Gödel%27s_ontological_proof
======
triska
Very interesting, thank you for sharing this!

About this proof, quoting from a talk by John W. Dawson Jr., an
internationally recognized authority on the life and work of Kurt Gödel:

 _" And a final example of this sort of unfashionable pursuit is Gödel's proof
of the existence of God, which is a formalization in modal logic of an
argument — traces all the way back to Anselm — but in particular an argument
due to Leibniz. Gödel was very much interested in Leibniz's philosophy, and so
he felt that it would be possible to formalize some of Leibniz's ideas. But
because this was a theological subject he was very cautious about this. Said
very little about it during his lifetime. And although word of it sort of
leaked out, it was only after his death that the details were really made
public._

 _" In fact, when I was cataloging Gödel's papers, I realized that there was
some concern among the triumvirate of mathematicians that were in charge of my
work [...] that there might be some things in Gödel's Nachlass that needed to
be restricted, that scholars would not be allowed access to. And it quickly
became apparent that this was the primary thing they were thinking of. And it
took some persuasion on my part to convince them that while mathematicians may
think it's silly to try to prove that God exists, philosophers certainly
don't, and that this was something of real interest in philosophy. And so,
eventually, unlike Russell's papers, where — as you may know — large segments
are embargoed [...] you can see everything in Gödel's Nachlass, there aren't
any restrictions on that."_

Source:
[https://youtu.be/4vpTFZdyjKM?t=2179](https://youtu.be/4vpTFZdyjKM?t=2179)

~~~
neonate
> unlike Russell's papers, where — as you may know — large segments are
> embargoed

That's surprising. I wonder what was embargoed from Russell's papers.

~~~
_Nat_
From a quick skimming online, it sounds like there's a policy to embargo
private correspondence until all involved haven't been around for at least 5
years.

In this case, it seems that Russell took a much younger woman as his third
wife: [Patricia Russell, Countess
Russell]([https://en.wikipedia.org/wiki/Patricia_Russell,_Countess_Rus...](https://en.wikipedia.org/wiki/Patricia_Russell,_Countess_Russell)).
Wikipedia lists her as passing in 2004, so presumably there was an embargo on
their correspondence until 2009.

------
andrepd
Fun fact: the proof is formalised in TPTP (a standard benchmark library for
automated theorem provers). It is considered of average difficulty.

[http://www.tptp.org/cgi-
bin/SeeTPTP?Category=Problems&Domain...](http://www.tptp.org/cgi-
bin/SeeTPTP?Category=Problems&Domain=PHI&File=PHI003^1.p)

~~~
bcaa7f3a8bbc
Is it related to the GoedelGod project (which was an open source project on
attempting to formalize Godel's Ontological Proof, was in GSoC 2017)?

[https://github.com/FormalTheology/GoedelGod](https://github.com/FormalTheology/GoedelGod)

~~~
andrepd
I believe not. This was the citation given in the problem:
[https://arxiv.org/abs/1308.4526](https://arxiv.org/abs/1308.4526)

~~~
andrepd
Silly me, we're talking about the same thing :p

------
goto11
A lot of comments here are making counter-arguments by showing that some other
improbable entity would exist by the same logic. This is fine, but be aware
that Gödel was just formalizing a 1000 year old argument, and the first
counter-argument using this form is also 1000 years old:
[https://en.wikipedia.org/wiki/Ontological_argument#Gaunilo](https://en.wikipedia.org/wiki/Ontological_argument#Gaunilo)

The argument basically comes down to if you can define something into
existence. If the definition of X implies that X exists...then X must exist?

~~~
antisemiotic
Also, it looks like those who don't understand Kant are doomed to reinvent him
haphazardly.

~~~
jfengel
Is that such a bad thing? It's like a framework: if it's not necessary to
download a thousand pages of Kant in order to arrive at the correct
conclusion, is it really all that important to get the rigorous version
instead?

~~~
goto11
It would however save many people a lot of time if they understood that
logical reasoning cannot tell you facts about the world with are not already
implied by the premises or definitions chosen.

You cannot prove the existence of gravity or the platypus purely by logic.
Neither can you prove the existence of "God", unless you define "God" in such
a vague way that it doesn't tell you anything about reality.

------
spectramax
Succinct form:

 _“God, by definition, is that for which no greater can be conceived. God
exists in the understanding. If God exists in the understanding, we could
imagine Him to be greater by existing in reality. Therefore, God must exist.”_

I’m having a hard time following the “modal” logic. I’d appreciate if someone
could please expand on it.

~~~
Saturn_V
Let's separate it up, with this argument, people often do follow the logic,
but do not accept the premises.

Premise 1: God is defined as the greatest thing that we can possibly concieve
("that for which no greater can be conceived")

Premise 2: real things are better than imaginary things

We can imagine God (he exists in understanding). A real God is better than an
imaginary God (2).

Then, if God does not exist, we can concieve a greater thing (a real God) this
leads to a contradiction with respect to (1). Therefore by proof of
contradiction, God must exist

~~~
justinpombrio
Premise 1: Pennywise The Dancing Clown is defined as the scariest clown that
could possibly exist ("that for which no greater horror can be conceived"
EDIT: "that clown for which no more horrifying clown could be conceived").

("Pennywise the Dancing Clown" is usually defined as "the clown from It". I'm
repurposing the name for the sake of this argument. We need a name for
"scariest possible clown"; I'm choosing "Pennywise".)

Premise 2: real things are scarier than imaginary things.

We can imagine Pennywise The Dancing Clown (he exists in understanding---
you're welcome). A real Pennywise is scarier than an imaginary Pennywise (2).

Then, if Pennywise The Dancing Clown does not exist, we can conceive a scarier
clown (a real Pennywise). This leads to a contradiction with respect to (1).
Therefore by proof of contradiction, Pennywise the Dancing Clown must exist.

Where's the flaw in this argument? Does the same flaw apply in the theological
argument?

~~~
geofft
This is the same as Anselm's argument. If the Lord of Hosts is not scarier to
you than Pennywise, you have not thought very hard about the implications of
an omnipotent, omniscient being. He isn't going to spook you like a movie
clown; no, He is far more existentially terrifying, as befits Someone beyond
Whom no greater horror can be conceived. And, after all, "The fear of the Lord
is the beginning of wisdom."

The more common formulation of your counterargument is something like
imagining the most perfect possible ice cream sandwich, to which I would also
say, is God not better than any ice cream sandwich? Are the splendors of
heaven not far beyond any earthly dessert?

~~~
justinpombrio
> If the Lord of Hosts is not scarier to you than Pennywise, [...]

I don't mean to define Pennywise as the scariest possible _being_. I mean to
define Pennywise as the scariest possible _clown_. The Lord is, I imagine you
will agree, not literally a clown.

~~~
geofft
Doesn't the fact that He's not a clown make it particularly unnerving that
He's in fact the scariest possible clown?

Or, in what sense is God not a clown when He created not only every clown but
the entire concept of clowning?

Or, being a little more serious, that constraint isn't compatible with the
problem Anselm stated. There's no reason for the scariest possible clown to
exist: there's no reason that, of the clowns both real and imaginary, the
scariest real one should be scarier than the scariest imaginary one. (I think
we could argue quite convincingly that, say, Pennywise has scared more people
than any real clown.) So the argument "A clown is scarier if it exists" isn't
obviously true.

Or put yet another way, the greatest possible mortal (existent or not) is
obviously not immortal, but you could plausibly argue that the greatest
possible being is.

If you want to maximize on one axis the most superlative _being_ , though, you
can probably get to God. I suspect Anselm's conception of God is the ultimate
realization of any axis of comparison we can think of: the supreme delight,
the supreme fear, the most resplendent, the most hidden, etc. And in
particular I think Anselm's axis of greatness is much more defensible, that
is, "A being is greater if it exists" sounds much more like a reasonable
assumption (even if I'm not sure I accept it) than "A being is scarier if it
exists."

------
ozy
Now do the same for the devil:

"The devil, by definition, is that for which no greater evil can be conceived.
The devil exists in the understanding. If the devil exists in the
understanding, we could imagine him to be greater by existing in reality.
Therefore, the devil must exist."

From which it also follows that:

"If the devil doesn't destroy god, we could imagine him to be a greater evil
by destroying god. Therefore, the devil must have destroyed god."

At which point we must conclude that it is a shame that theology has captured
the minds of so many brilliant people.

~~~
Conjoiner
I am not aware of any claim that the devil is the largest evil that could be
imagined. Further, such a definition would not make sense in for example
traditional Christianity where evil is defined as a privation on good, not
something that exists in itself.

Having God and the devil as evenly matched but opposite powers is not
something you would find in theology. Learn the basics of it before thinking
you have created a proper critique.

~~~
goto11
> I am not aware of any claim that the devil is the largest evil that could be
> imagined.

That is completely irrelevant. The ontological proof claims to deduce the
existence of an entity from a definition of that entity. It does not matter
whether this definition happen to match some current religious dogma or not.

~~~
vinceguidry
Anselm defined God as "that which nothing greater can be thought." Introducing
a devil into this mix doesn't change this reasoning, and basically boils down
to "is evil greater than good?", which I don't think anyone can reasonably
argue.

It's not the most interesting argument for God I've encountered, but it's not
trivially invalidated by elevating evil to the same status as good. That
hasn't been a serious element of any real theology since long before the
ancient Hebrews.

Theology is the art of imagination, the same way that politics is the art of
the possible. Imagining absolute evil is only interesting when you want to
attack the idea of absolute good. Absolute good remains interesting without a
foil. So therefore people will be willing to believe in it.

~~~
goto11
The point is that if the ontological argument is valid then you can define all
kinds of things into existence also. The devil is just an example, it could
also be The Most Perfect Island, The Real Santa Claus and so on. So it is a
reductio ad absurdum.

~~~
vinceguidry
I'm not saying the ontological argument is correct, just that your reasoning
doesn't sufficiently refute it.

~~~
goto11
It doesn't refute it per se. It just shows that The Real Santa Claus also
exists by the same token. Which is not really a logical contradiction so if
you want to believe that, more power to you.

~~~
vinceguidry
The real Santa Claus did exist, the one the current myth is based on.

~~~
goto11
Fair enough, but that is totally beside the point.

~~~
vinceguidry
Maybe sibling comment is more to your liking.

------
SAI_Peregrinus
Ontological argument for the nonexistence of God.

1\. It is more great to do something with a greater handicap.

2\. Not existing is the greatest possible handicap.

3\. The greatest possible being is thus one who could create the universe
despite not existing.

~~~
ars
You have not proved step 1 or step 2. In fact I'm quite sure your step two is
false, and your step one would be quite hard to prove.

~~~
481092
Did Gödel even prove step 1?. In Gödel's argument, it's relying on very
arbitrary definitions of what many have defined as a god and that their god is
"great". OP defined what is "great" to him, it's not necessarily what's great
to you or me.

I think OP here is meaning "great" in some intellectual capacity, that you are
just as powerful or great if you can make up your lack of greatness in one
area with another form of greatness, something I don't see as greater but
equally great. Is it greater to be successful by bootstrapping off the success
of your forebearer or greater to be as successful when starting from nothing?
It's a classical argument but to me it stands on just as rational ground as
Gödel's argument.

~~~
ars
Maybe you can prove step 1, but step 2 is clearly false - a much greater
difficulty is having an adversary unmaking what you make.

------
simplesleeper
For Polish speakers, I highly recommend this book:

[https://www.ccpress.pl/produkt/Dowody_ontologiczne._W_900._r...](https://www.ccpress.pl/produkt/Dowody_ontologiczne._W_900._rocznice_smierci_sw._Anzelma_17)

It has multiple formalisations of both Anselm's and Gaunilo's arguments, and
critiques of each approach

------
coldtea
> _Hence, it must follow from Godlikeness. Moreover, Godlikeness is an essence
> of God, since it entails all positive properties, and any non-positive
> property is the negation of some positive property, so God cannot have any
> non-positive properties._

Counter argument: Of course he can.

God isn't constrained by formal logic constraints -- in fact God created logic
and can break it at will (e.g. by being two contradicting things at once).

We, as humans (or even as all of the universe), might not be able to conceive
these, but then again, why should why? We're not gods!

In other words: when one is considering a God-like figure, there's no reason
to consider one bound by the same restrictions we have, our Kantian "a
prioris", or even basic consistency. If you do give your God such restrictions
you might be able to prove this or that theorem, but only as regards to that
lesser God, not the concept of God in general.

~~~
goto11
The ontological argument is about a specific definition of "God" as having
certain properties. You cannot counter that argument by assuming a different
definition of "God".

Your "God" can be two contradictory things at once which seems fundamentally
different than the "God" defined in the ontological proof. So basically you
are talking about two different things. (But OK, if logic doesn't exist then
who cares?)

~~~
coldtea
> _The ontological argument is about a specific definition of "God" as having
> certain properties. You cannot counter that argument by assuming a different
> definition of "God"._

Of course you can.

The ontological argument arrived at the "specific definition" (of axioms about
God) under the assumption that those are required and true attributes of any
entity that can be called God.

If those are just a random selection of attributes merely thought necessary by
Anselm (or Godel here), and not inherently necessarily tied to the notion of
God in general, then the whole argument is moot, nothing more than a logical
deduction based on some arbitrary axioms that tells us nothing about God
existing or not.

The purpose of Anselm and Godel is not to show that (a) "a specific definition
of God having [those] certain properties exists".

It is to assert that "those certain properties" are necessary properties of a
God entity, and (b) "a God having those properties must exist", (c) "God
exists".

> _Your "God" can be two contradictory things at once which seems
> fundamentally different than the "God" defined in the ontological proof. So
> basically you are talking about two different things._

No, we're just talking about two different assertions of what properties God
can and cannot have. God as a notion pre-exists any attributes assigned to it
in a specific logical argument (for example, Godel and Anselm have both heard
about the notion of God before they've picked their axioms).

When trying to match an existing notion it's not enough that one picks axioms:
they should also make sure those axioms are the proper ones to capture the
notion properly.

Else it's just a new arbitrary definition of an entity, which they called
"God" but could just as easily have called "Bob" or "Jane".

~~~
jhanschoo
You are talking past the comment you are replying to, and Goedel's argument
altogether. That is, you are referring to an entity that may have
contradictory properties in the way you mentioned, but Goedel's philosophical
God isn't such an entity.

> Else it's just a new arbitrary definition of an entity, which they called
> "God" but could just as easily have called "Bob" or "Jane".

It exactly is arbitrary. The argument works for every referent that satisfies
the properties.

~~~
coldtea
> _You are talking past the comment you are replying to, and Goedel 's
> argument altogether. That is, you are referring to an entity that may have
> contradictory properties in the way you mentioned, but Goedel's
> philosophical God isn't such an entity._

Which is the point exactly. Even if Goedel's argument didn't have logical
jumps based on non-essential assumptions, it still doesn't prove the existence
of God per se, only the existence of something Goedel calls God, which
satisfies Goedel's axioms ("every referent that satisfies the properties").

But the problem is that Goedel doesn't say he tries to prove the existence of
"any referent that satisfies the properties" but of God.

Well, who (apart from Goedel himself) said that those are the properties of
God, and not others?

~~~
jhanschoo
> it still doesn't prove the existence of God

You mean the God of your religion. If Goedel believed his argument that would
make him a kind of deist.

> Even if Goedel's argument didn't have logical jumps based on non-essential
> assumptions

Goedel's argument is tight given the axioms, though. It's been formally
verified.

The God that you mention that may have contradictory properties isn't that
interesting for logical analysis, since it's likely that logicians only want
to consider "Gods" whose existence do not render useless their logical system
(contradiction leads to the principle of explosion). Hence you won't find
primarily logical works discussing such a God.

> which satisfies Goedel's axioms

to be pedantic, his "God" doesn't satisfy Goedel's axioms, his "God" satisfies
his definition of "God". Then the argument has that you accept its existence
once you accept the axioms of the argument.

> Well, who (apart from Goedel himself) said that those are the properties of
> God, and not others?

Well, in most cultures, you call a kind of sufficiently magical or spiritual
or ineffable entity a god. Nobody has a monopoly on the word "God", and many
cultures use the word to refer to entities unrecognizable as the one you call
God.

------
dvt
Whenever this makes top of HN, it remains one of the most contentiously
misunderstood pieces of formal logic -- much like some of Gödel's other famous
results. The proof is basically a formalizing of Anselm's Ontological
Argument[1]. The proof doesn't "prove" there is a God, it just shows that the
argument, written in S5[2] (a type of modal logic), is correct -- more
specifically, that if the premises are true, then the conclusion follows.

Alvin Plantinga also did a lot of work refining these kinds of modal
ontological arguments in the 70s and 80s; of note is his famous "victorious"
ontological argument[3] -- still hotly cited to this day. Modal logic, for the
uninitiated, essentially adds two new operators to the "usual" logical
operators we might have seen in college (negation, implication, conjunction,
disjunction, quantifiers):

    
    
        Necessity: ◻P -- P is true in all worlds
        Possibility: ◇Q -- Q is true in some (or no) worlds
    

It's a very fun and surprising type of logic! A very intuitive result (and one
of the first you'd learn) is what happens when you negate a necessary
proposition.

    
    
        ~◻P -- P cannot be true in any world!
    

What Gödel's proof shows is that God -- as defined by the premises (basically,
as maximally "everything positive") -- is necessary; which is why his last
line includes a ◻. I don't want to get too bogged down, so this was
purposefully a very surface-level comment. If I piqued your interest, I
strongly suggest you check out some of the linked resources!

The historical context is also very interesting. It was somewhat unknown how
valid Anselm's argument was, and it took almost a millennium before we could
satisfactorily formalize the ontological argument (although many non-modal and
Aristotelian proofs had been written).

What does it mean for non-logicians? Well, if you buy the premises (which is
key!), it shows that it's not _irrational_ to believe in God (as defined by
the argument). Again, it doesn't _prove_ the existence of God, but it does
show that the logic of the argument makes _sense_.

[1] [https://plato.stanford.edu/entries/ontological-
arguments/#St...](https://plato.stanford.edu/entries/ontological-
arguments/#StAnsOntArg)

[2] [https://plato.stanford.edu/entries/logic-modal-
origins/](https://plato.stanford.edu/entries/logic-modal-origins/)

[3] [https://plato.stanford.edu/entries/ontological-
arguments/#Pl...](https://plato.stanford.edu/entries/ontological-
arguments/#PlaOntArg)

~~~
shkkmo
> What does it mean for non-logicians? Well, if you buy the premises (which is
> key!), it shows that it's not irrational to believe in God (as defined by
> the argument). Again, it doesn't prove the existence of God, but it does
> show that the logic of the argument makes sense.

This understates what the proof shows. It shows that if you buy the premises
it's not rational to believe God doesn't exist (as defined by the argument).

~~~
dvt
"Rationality" is not a (meta-)logical property. You're right that the proof
shows that, logically speaking, if one buys the premises, God _must_ exist.
But more colloquially, it shows that by accepting some premises that are
reasonable, one reaches the conclusion that God exists. Ergo, there's an
argument a rational person would accept whose conclusion is the necessity of
God.

~~~
shkkmo
> But more colloquially, it shows that by accepting some premises that are
> reasonable, one reaches the conclusion that God exists. Ergo, there's an
> argument a rational person would accept whose conclusion is the necessity of
> God.

I think that is a very weak conclusion, there are an infinite number of proofs
for god that are valid so long as you accept their particular premises. It is
the specific plausibility of the premises and definitions implied in St.
Anselm’s Ontological Argument that make it of interest.

What this shows colloquially is that if you are arguing against god, you must
either reject this definition of god or one of the other premises. If you
don't your argument is self-contradictory.

~~~
dvt
> I think that is a very weak conclusion ...

That's kind of my point. It's not some knock-down argument, but it's a very
nuanced result that achieved a few very neat things:

1) Formalized Anselm's "greatest of which can be conceived of" notion.

2) The concept of "accidental" (contingent) and "non-accidental" (necessary)
properties had existed since antiquity, but modal logic essentially formalized
the idea.

3) Showed that Anselm's argument _was_ indeed valid. Again, this project took
around 1000 years.

Plantinga did a lot of work in trying to make the premises more palatable, but
of course, the argument for the existence of God still rages on. (As I'm sure
it will far after we're gone.)

------
danharaj
This sort of thing casts doubt on the formal logic in question more than it
makes a case for God.

~~~
goto11
It it not really the formal logic that is at fault. In logic you are basically
allowed to make any assumption or definition you want.

The problem is thinking a proof can tell you anything about reality which
isn't already implicit in those premises.

If we define that X exists, then it is logically true X exists. But this
doesn't prove that X exist in the real world.

------
throw0101a
I'll take the First Way of Aristotle/Aquinas:

* [http://tofspot.blogspot.com/2014/07/first-way-some-backgroun...](http://tofspot.blogspot.com/2014/07/first-way-some-background.html)

* [http://tofspot.blogspot.com/2014/08/first-way-moving-tale.ht...](http://tofspot.blogspot.com/2014/08/first-way-moving-tale.html)

* [http://tofspot.blogspot.com/2014/09/first-way-part-ii-two-le...](http://tofspot.blogspot.com/2014/09/first-way-part-ii-two-lemmas-make-lemma.html)

> _Some things in the world are changing. (Observation)_

> _Whatever is changing is being changed by another. (Lemma 1)_ See Part I.

> _There cannot be an infinite regress of instrumental changers. (Lemma 2)_
> See Part II.

> _Therefore, there must be a changer that is not itself being changed by
> another._

* [http://tofspot.blogspot.com/2014/10/first-way-part-iii-big-k...](http://tofspot.blogspot.com/2014/10/first-way-part-iii-big-kahuna.html)

~~~
hota_mazi
> Whatever is changing is being changed by another

> Therefore, there must be a changer that is not itself being changed by
> another.

A proof that contains its own refutation :-)

~~~
state_less
> Whatever is changing is being changed by another

It started off good :)

Makes me wonder about the technical details of what hardware God runs on and
how that was created?

I got interested in Sethianism, since Seth is my given name, and it has a fun
creation mythos. You get a little backstory leading up to the garden of eden.

[https://en.wikipedia.org/wiki/Sethianism](https://en.wikipedia.org/wiki/Sethianism)

~~~
throw0101a
> _Makes me wonder about the technical details of what hardware God runs on
> and how that was created?_

If it is created, then it cannot be God by definition. If we are talking about
creation and existence (and not change), then we are getting into the Second
Way:

> _1\. Everything which has come to exist has been caused to come to exist._

> _2\. Nothing which has come to exist can be the cause of its own existence._

> _3\. Everything which has come to exist is caused to exist by something
> other than itself. (follows from 1,2)_

> _4\. It is impossible for a chain of causes of this kind to go on to
> infinity._

> _C. There must be a first cause, which causes other things to come into
> existence but did not itself come into existence. (follows from 3,4)_

* [https://www3.nd.edu/~jspeaks/courses/mcgill/201/aquinas-cosm...](https://www3.nd.edu/~jspeaks/courses/mcgill/201/aquinas-cosmological-argument.html)

NB: the argument is _not_ "everything has a cause", which, if it is your
starting proposition, tends to leads to problems:

* [https://en.wikipedia.org/wiki/Kalam_cosmological_argument](https://en.wikipedia.org/wiki/Kalam_cosmological_argument)

------
username90
> God, by definition, is that for which no greater can be conceived.

This axiom is very questionable to people who don't already believe in God, so
the proof is worthless. For example, I'd define God as a social construct
created to cope with existential dread. By that definition God doesn't exist.

~~~
contravariant
By your definition God does exist.

------
dang
Thread from 2014:
[https://news.ycombinator.com/item?id=8806293](https://news.ycombinator.com/item?id=8806293)

2009:
[https://news.ycombinator.com/item?id=417917](https://news.ycombinator.com/item?id=417917)

Others?

~~~
ARandomerDude
Seems like it's made the rounds a few times. Still, 2014 was 5 years ago and
2009 was 10 years ago. It's likely that many of us either weren't on HN at the
time or several years is sufficient for us to have forgotten.

~~~
dang
Oh yes, reposts are fine after about a year—this is in the FAQ:
[https://news.ycombinator.com/newsfaq.html](https://news.ycombinator.com/newsfaq.html).
The reason for linking to past discussions is just that some readers find them
interesting.

------
zzo38computer
I think that it is difficult to define what is meant by "God"; and maybe even
by "exists" in such a context, too. So, many people will disagree. Also, even
if a proof may be mathematically valid, it may be misapplied, or have invalid
premises, or misuse of words (which can be a kind of misapplication, I
suppose).

------
b_tterc_p
Something I like about this is that whatever number you imagine as the
greatest number signifying god, your conception is still much lower than
Graham’s number. Graham’s number is the terrifying giant that reminds you that
the limits of your conception are that of a weak human mind.

No I don’t care to debate technicalities :)

~~~
shkkmo
If you are postulating that "greatness" is infinitely conceivable, then
defining "God is the greatest thing that can be conceived" would mean that
god, like the largest number, does not exist.

~~~
b_tterc_p
No actually the opposite. I’m saying we have a finite capacity to imagine
magnitude, though it’s not readily apparent. Infinite is easy conceptually,
but most people’s pragmatic place holder for “basically infinite” is going to
be a really big number. Very big to be sure. But Graham’s number is so large
it’s beyond the scope of numbers you’re likely to have conceived could exist.
It’s not something you can quite fit in your head even reading about it, like
something out of Lovecraft.

Whatever you imagined in imagining God as the greatest thing, Graham’s number
is inconceivably larger still.

And that is why Cthulhu wins.

~~~
shkkmo
> Whatever you imagined in imagining God as the greatest thing, Graham’s
> number is inconceivably larger still.

And despite that, there are still more numbers between 0 and 1 than increments
required to reach Graham's number.

It seems to me like you are assuming that conceptions of god and integers
share the same cardinality when I'm not so sure that is clearly the case.

------
a1369209993
> I think God is the greatest jelly donut in existence.

Mmm, applied theology.

0:
[http://machall.com/view.php?date=2003-04-21](http://machall.com/view.php?date=2003-04-21)

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elwell
If God wanted to be 'provable', we wouldn't we have anything left to prove (it
would already be proved...). The option to doubt (or to believe) the existence
of God, leaves an opportunity for love. Choice is essential to love. If we saw
God, we would lose that choice. Though it's interesting to attempt to prove
God; I'm currently reading "The Physics of Christianity" [0]. I can't say I
stand behind it completely, but it's a fascinating effort.

[0] - [https://www.amazon.com/Physics-Christianity-Frank-J-
Tipler/d...](https://www.amazon.com/Physics-Christianity-Frank-J-
Tipler/dp/0385514255)

------
ukj
This proof exploits an edge case in dualistic human reasoning which occurs at
the intersection of ontology and epistemology.

Lets do some term re-writing, so we can move away from the emotional trigger
that is the God-word.

1\. God, by definition, is that for which no greater can be conceived.

This conception of God is equivalent to what we call 'The Universe'.

Rewritten: The Universe, by definition, is that for which no greater can be
conceived.

2\. God exists in the understanding.

The Universe itself doesn't exist in the same way a planet, or a galaxy
exists. The Universe is ALL things that exist. Conceptually it's the set of
all sets.

Planets, stars and galaxies exist ontologically as members of the set. The
Universe exists only epistemologically as a category in your head.

Rewritten: The Universe exists in the understanding.

3\. If God exists in the understanding, we could imagine Him to be greater by
existing in reality.

Rewritten: If The Universe exists in the understanding, we could imagine The
Universe to be greater by existing in reality.

Uh what? We could imagine The Universe to exist within The Universe?

From a contradiction anything follows.

It's simply a case of Equivocation fallacy. Godel uses the word 'exists' in
multiple senses throughout the argument.

The premises could have been about anything.

