Ross La Haye
>Maybe this is off-topic, but I've read that Godel constructed a proof
>for God's existence in symbolic logic but I've been unable to locate it
>anywhere. Does anybody know where I can find this, hopefully on the web?
Without having an answer to your question [I'll do a webscan if some
other reader here doesn't beat me to it], please keep in mind that
when dealing with logic, one can ONLY 'prove' that any given statement
is or isn't consistent with a given logic system. But if you want to
demonstrate that a statement is consistent with observable reality,
it must be tested against reality. So, whatever you say about the
[non-]existence of one or more deities, how are you going to test and
validate your contention? Symbolically, I can 'prove' whatever I want:
1+1=3, for a large enough value of 1. Give it a whirl, eh?
Yes, Goedel's argument is a so-called 'ontological argument' for
God's existence. One fellow who's done a good deal of work on
ontological arguments in general -- and Goedel's argument in
particular -- is Graham Oppy, professor of philosophy at Monash
University. He had a paper on Godel's proof in the journal,
*Analysis*, back in 1996 (if my guess serves me right).
I do know that Oppy's work is on the web -- though I can't find
the URL, off-hand. You might also check Oppy's tome, *Ontological
Arguments and Belief in God* (1995), which has a few pages on Goedel.
Ross La Haye
Ross La Haye
To me the interesting questions [as long-time readers of this list
may recall from my earlier writings] are:
How does one count deities? That is, how can we tell if the number of
extant gods is non-zero, a negative or positive integer, or a real
number? Do demi-gods [which may or may not include angels, demons,
spirits, other such paranormal entities] count as fractional gods?
Once we enumerate god(s), how do we verify our count?
What evidence is there that one or more deities exist? How are we to
evaluate that evidence? If we even assume that deities exist and may
have some influence on observable reality, then out of intellectual
honesty, mustn't we disregard ALL alleged evidence, since ANY such
evidence could have been 'doctored' by a deity to suit their own
[unknowable to us] purposes? OJ Simpson was acquitted in large part
because physical evidence against him COULD have been tampered with,
and so was disregarded by the jury; shouldn't we hold divine 'evidence'
to as rigorous a standard? If we even THINK a deity is involved, then
ALL evidence is possibly tainted, and must be tossed out.
Since a rational theory [a workable explanation supported by the
preponderance of the data] must be falsifiable, testable, and lead
to further areas of exploration; and since invoking a deity as an
explanation leads only to the impenetrable mystery of the deity;
then isn't any deistic explanation a dead-end, irrational, a way
to block all further inquiry? Don't deities defeat curiosity?
Since a deity is necessarily of infinite complexity; and since ANY
materialistic explanation is less complex than a deistic invocation;
then, by Occam's Razor, isn't a materialistic explanation ALWAYS more
likely to be correct than a deistic explanation? And doesn't the
divine infinite complexity mean that any extant deities are unknowable
by humans, so that we can say nothing meaningful about them?
I could raise a few other points, but it's late and I'm tired. I'd
sure like to see an honest logician deal with these -- but it's not
gonna happen here, I'm sure. C'est la vie.
On 6 Jan 00, at 18:33, Tim wrote:
> Graham Oppy, professor of philosophy at Monash
> University [...] had a paper on Godel's proof in the journal,
> *Analysis*, back in 1996 (if my guess serves me right).
> I do know that Oppy's work is on the web -- though I can't find
> the URL, off-hand.
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Mark O'Leary, Manchester Computing, UK
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>No, I don't really disagree with you. That the proof came from Godel
>it all the more interesting, as compared to say a fundamentalist.
>I would say the proof has to be flawed, but given that Godel put it
>makes this position less justifiable. Beyond that, from my understanding
>was purely deductive ontological proof, meaning that it should really
>eliminate the logical contradictions and incoherencies in other
>proofs, so I'm not sure exactly how you would test it against reality.
>Either way it would be interesting to take a look at.
>Ross La Haye
Agreed -- I'm a fan of Goedel's (counting roughly) three
'philosophical' endeavors, myself: to wit, Goedel's work on (1)
logic, provability, and
mathematical truth, (2) solutions to the Einstein field equations in
which time travel is possible, and (3) his ontological argument.
So, at the very least, Goedel's proof is of 'biographical' interest.
(In *The Disappearance of Time*, by the way, Palle Yourgrau attempts to
show how Goedel's diverse-seeming inquiries can be seen as instances
of a unified strategy; it's a quick -- and enlightening -- read if
you're interested in Goedel...but I digress.)
Regarding Goedel's argument for God, I'd hazard the following conjecture
about the argument's soundness.
(Conj) If you're not convinced by Descartes' ontological argument
(which essentially runs by counting existence as a 'perfection'),
then you'll have the same misgiving with Goedel's argument; because
Goedel's proof, too, essentially presupposes that we can count
existence as 'perfection'.
But by all means, give the Goedel a chance; I, for one, would be
very interested if Goedel's argument lacks the Achilles' Heel which
afflicts Descartes' ontological proof. Do let me know if my 'conjecture'
fails to appreciate the strength of Goedel's argument. (If you wish
to follow up, after reading the Goedel, the URL Mark O'Leary furnished
ought to have a bibliography of attempts to evaluate -- and, in some
cases, shore up -- Goedel's argument.)
Neither per se, I'm just an idiot who can't remember the correct name.
It's nearly a homonym, and the argument does feed on itself.
p.p.s., replies to another post:
>Without having an answer to your question [I'll do a webscan if some
>other reader here doesn't beat me to it], please keep in mind that
>when dealing with logic, one can ONLY 'prove' that any given statement
>is or isn't consistent with a given logic system. But if you want to
>demonstrate that a statement is consistent with observable reality,
>it must be tested against reality. So, whatever you say about the
>[non-]existence of one or more deities, how are you going to test and
>validate your contention? Symbolically, I can 'prove' whatever I want:
>1+1=3, for a large enough value of 1. Give it a whirl, eh?
Once got into a pissing match with someone on the skeptic list over this
point. I made this point, or more exactly that philosophy is always
exactly correct, within it's presumed parameters. As there is no rule
that the bases must be based in reality, it is possible that correct
philosophies are not valid in objective reality. For example,
communism. I still don't think that Marx was wrong, but that his basic
presumptions about human nature and social development were. Or look at
the Christian diest. Given the presumption that the Bible is the word
of God, the Bible does indeed infallibly prove his existance.
As stated above, people make the mistake of mathematical thought being
real, when indeed math can be defined to 1+1=3, albiet the size of one
doesn't need to change. The underpinning definitions must, however.
And this goes again to a point that I think I've made to death over my
years on these lists. (Years? Yikes!) Why discuss philosophical
points with theists and atheists? They are both uniquely correct. It's
when claims are made of powers given via belief, that's when rebuttal is
reasonable. For example, I recently mentioned that witch who said her
garden shears were her mightiest magic wand. (Hmmm, subject-verb
agreement?) She is absolutely correct. However, if she also said that
herbs tended by her with these shears were more potent medicinally (sp?)
because of the magic therein, then there's a claim to consider.
So let me finally close with a bit more rambling, by mentioning
mathematical induction. It is the process by which sequential formula
f(x)sub k is proven. Compute the k = 0 case and verify. Presume that
the k case is true, use this to compute and verify the k + 1 case.
Familiar yet? It is a powerful tool, used in a lot of math, yet is
itself still unproven as a valid method. The circular logic confuses
the average student. It is also wide open to abuse. For example, I
have a bag of marbles. I pull one out, it is blue. I presume that the
next marble I pull will be blue, I do so and it is (k and k + 1 cases),
therefore the bag is full of blue marbles only.
the oncological proof,
Typo or pun?
My rights may be social constructs or gift from a creator but they
did not come from some joker from Arkansas who lies on TV about
getting a blowjob.
I doubt that. Oncology is the medical study of tumours, so unless you are
a very nice tumour, I suspect you mean ontological. OTOH, the study of E
Robert's contributions might well fall under oncology.
the Skeptic of Oz
The argument discussed at that URL is as follows:
>Definition 1: x is God-like iff x has as essential properties those and
>only those properties which are positive.
>Definition 2: A is an essence of x iff for every property B, x has B
>necessarily iff A entails B
>Definition 3: x necessarily exists iff every essence of x is
>Axiom 1: If a property is positive, then its negation is not positive.
>Axiom 2: Any property entailed by [= strictly implied by] a positive
>property is positive.
>Axiom 3: The property of being God-like is positive.
>Axiom 4: If a property is positive, then it is necessarily positive.
>Axiom 5: Necessary existence is positive.
>Theorem 1: If a property is positive, then it is consistent [=possibly
>Corollary 1: The property of being God-like is consistent.
>Theorem 2: If something is God-like, then the property of being God-
>like is an essence of that thing.
>Theorem 3: Necessarily, the property of being God-like is exemplified.
If we were simply to substitute Minotaur or Unicorn for God in this
argument does it mean they would exist?! Of course not, no more than
this argument is proof for the existence of God.
It has always seemed to me that there are two fundamental problems with
the ontological argument:
1. Asserting that necessary existence is a property of God as a premise
doesn't actually make it so.
2. By having a premise that necessary existence is a property of God
amounts to a circular argument - the premises assume what is being
argued as a conclusion.
Logical "proofs" for the existence of God such as the ontological
argument are really nothing more than fatuous.
Anselm of Canterbury lived from 1033 to 1109.
> The term "God" is defined as the greatest conceivable being.
> Real existence (existence in reality) is greater than mere existence in
> understanding. Therefore, God must exist in reality, not just in the
If Graham Oppy is going to write books called "Ontological arguments
and belief in God", he needs to go back a bit further than Goedel for his
research. It isn't Goedel's idea, he just used a lot more words to say it.
God used to play dice with his partner Goedel, and ended up owing Goedel a
lot of money. When God's attorney pulled a habeas corpus, Goedel had to
prove that God existed. Goedel assembled a suitable proof, which was
correct and perfect, but only assuming the consistency of non-trivial
axiomatic systems, whereupon God pulled a coup by implanting in Goedel's
mind the seeds of doubt. Goedel subsequently decided that non-trivial
axiomatic systems were not universally consistent, and hence we have
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Share what you know. Learn what you don't.
Can it be mere coincidence that Goedel is "God" with the addition of
"eel"? One would expect a slippery argument from such a source.
Ross La Haye
Ross La Haye
You raise a good point: if Oppy were to maintain that "Goedel's
argument" as synonymous with "the [sic!] ontological argument," then
Oppy could definitely be charged with not having done his -- let's say
-- "historical homework."
Happily, though, Oppy's book doesn't have such a historical
blindspot. In the text in question, Oppy systematically considers
attempts by all the ontological argument's historic friends (Anselm,
Descartes, Hegel...) and enemies (Aquinas, Kant, etc....).
Sorry if I'd left the impression that the scope of Oppy's research
is restricted to Goedel -- 't ain't. In fact, if there's any
contemporary philosopher who's soundly and carefully diagnosed
why the ontological argument(s) -- in all their historical
incarnations -- are *really* dead, I'd have to say that there's
no better coroner (ghostbuster? :)) than Oppy. :)
Yes, it seems your quite right on this. I personally think definition 3
fatal to the argument in that in order for definition 3 to be true you
first establish that every essence of x is necessarily exemplified and
Ric's point even more relevant that in the end the argument needs to be
tested against reality.
Ross La Haye
It's kind of sad that after all this time people are still having to
produce works debunking the ontological argument, I still can't
understand why anyone could have taken it seriously in the first place.
> Happily, though, Oppy's book doesn't have such a historical
> blindspot. In the text in question, Oppy systematically considers
> attempts by all the ontological argument's historic friends (Anselm,
> Descartes, Hegel...) and enemies (Aquinas, Kant, etc....).
> Sorry if I'd left the impression that the scope of Oppy's research
> is restricted to Goedel -- 't ain't.
Thanks for that, Tim. My real problem was the use of the words
"Goedel's Ontological Argument" rather than "Goedel's case for the
I am a little sensitive to this sort of thing just now because I opened a
national newspaper last Thursday to find an article by an academic
containing a lot of points about the Y2K nonsense that bore a
remarkable similarity to the contents of a speech which I gave in
November and which has been published since both on the 'net and in a
magazine. Investigations are continuing.
Dene Bebbington says:
> It's kind of sad that after all this time people are still having to
> produce works debunking the ontological argument, I still can't
> understand why anyone could have taken it seriously in the first place.
It's still being talked about because it's a good thing to talk about. It
really has nothing to do with religion but with epistemology (and, dare I
say it, classical skepticism). In it's original form it looks like a
circular argument or paradox, but the fact that it has occupied minds
like Descartes, Hegel, Goedel, Kant, Aquinas etc (some of whom have
better minds than us) suggests that it might be worth taking seriously
for other than its face value.
I certainly understand -- especially in the present context.
One thing I've found, again and again, was that the Medievals
were a lot more clever and perceptive than they're often given
credit for. More on this below.
>I am a little sensitive to this sort of thing just now because I opened a
>national newspaper last Thursday to find an article by an academic
>containing a lot of points about the Y2K nonsense that bore a
>remarkable similarity to the contents of a speech which I gave in
>November and which has been published since both on the 'net and in a
>magazine. Investigations are continuing.
Now I certainly *doubly* understand. I'm sorry to hear about
that. I've often read about this sort of thing -- I remember
about a year back, some romance novelist or other had lifted
*entire scenes* from a rival's novels. Good luck with getting
a fair investigation.
>Dene Bebbington says:
> > It's kind of sad that after all this time people are still having to
> > produce works debunking the ontological argument, I still can't
> > understand why anyone could have taken it seriously in the first
>It's still being talked about because it's a good thing to talk about. It
>really has nothing to do with religion but with epistemology (and, dare I
>say it, classical skepticism). In it's original form it looks like a
>circular argument or paradox, but the fact that it has occupied minds
>like Descartes, Hegel, Goedel, Kant, Aquinas etc (some of whom have
>better minds than us) suggests that it might be worth taking seriously
>for other than its face value.
Well said. I'm reminded of something Dan ("Consciousness Explained")
Dennett used to say when he'd teach his undergraduates about Descartes.
Maybe I'm digressing a bit...but bear with me, please. :)
"Folks," he'd say, holding up a copy of the *Meditations*, "this
book has a mistake on every page. The book is *full* of mistakes.
So why read it? Because Descartes' mistakes are *interesting*
mistakes: we learn a great deal by teasing out precisely *why*
Descartes' arguments are wrong." (paraphrase)
Another, clearer, example in this spirit might be Zeno's Paradox.
Richard Cartwright at MIT once wrote that: "It won't do to reply to
Zeno as my mother-in-law once did. 'There!' she said, taking
a firm step. No, what is called for is explanation, not refutation."
Explanation, that is, as to which of Zeno's premises is/are in error,
and what the error is -- no small feat! Zeno's paradox, that is,
is another example of what I'd call an interesting mistake.
And I guess I'd tow the same line about the Ontological Argument.
Almost *no one*, that is, buys that Anselm's argument has both
(a) true premises and (b) is deductively valid. (Otherwise,
we'd have to agree that the 'greatest conceivable being' exists
-- Eek! :)) But an argument isn't worthless just because the
conclusion is false -- even *obviously* false. (And conversely:
there are a lot of bogus arguments for true conclusions...) For
in the course of *spelling out* which of Anselm's premises is
false, and why it's false, we end up learning a good deal about
central features of language. ("Is existence a predicate?" for
And this, I'd hazard, is why so many have found the Ontological
Argument an alluring topic: Anselm made a mistake -- a whopper
of a mistake! -- but darned if his mistake(s) don't prove to be
-- Tim :)