Talk:Gödel's ontological proof

Cantor
Georg Cantor equated what he called the Absolute Infinite with God. He held that the Absolute Infinite had various mathematical properties, including (if I recall correctly) that every property of the Absolute Infinite is also held by some smaller object... -- The Anome


 * The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type. -- Georg Cantor, as quoted in Mind Tools by Rudy Rucker.


 * That's interesting, and belongs on the Cantor page, maybe on the God page, and on the infinity page. Goedel's ontological proof is unrelated: it uses "perfection", not "infinity" as the defining feature of God. --AxelBoldt

I agree with you that it belongs in those places. I thought it was relevant here because of the repeated theme of possession of properties by a mathematical God-like entity equated with God, and because Goedel presumably knew of Cantor's related idea.

Perhaps there should be a Mathematics and God article? -- The Anome

Proof wanted
The description of the proof seems a bit weak to me -- it spends a long time laying the groundwork and then it says, '(poof), from this we can prove that God necessarily exists'. I have no background in philosophy or Godel, but surely an entry on his ontological proof which spent so much time explaining the modal logic used in the proof should then also spend more time walking the reader through the proof? Or maybe I'm missing something obviously. I am feeling pretty feverish. -- Tlotoxl 10:06, 22 Sep 2003 (UTC)

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You might read the article on the Ontological proof, which is much more detailed. This one is pretty much the same thing, only formalized. I agree though that there should probably be more description of what the axioms mean and why they might lead to the conclusion that God exists.:Seth Mahoney 16:26, 22 Sep 2003 (UTC)

The proof is there
Hi All,

I am a mathematician and my main fields are topology and mathematical logic. In the last five years - as a hobby - I collect mathematical and semi-mathematical articles taking care the notion of God. There are a lot of - some of them seem to be very funny - but fortunately there are a lot of containing really interesting results. One of them is the so-called Gödel's ontological proof. However, in many case the interpretation of these results are misleading. The common problem is that the interpeter does not realize where the math ending and something new - philosophy, theology etc. - starts.

Gödel who was one of the most talented mathematician in history has to know the difference a mathematical model and the reality. He not just gave a proof, he built up a full mathematical theory for God, similarly as Euclides in his framework presented a mathematical theory for geometry. Now we knows that Euclides geometry is wrong, but for the beginning it was not so bad at all. In geometry using some simple axiom about the geometry we can prove much more complexed sentences, e.g. that the sum of the angle in a triangle is just 360°. Similarly Gödel proved that stated some simple properties about the notion of God a much more complex statement can be prove: the existence of God.

Modelling God
There is an old argument against the notion of God: it contains a self-contradiction. This "logical bug" in the notion of God is rooted from those properties of God which start "the most" attribute. This bug in its simplies form was formulized as the Russel's paradox. Taking care the existence of "the set of all subsets of a given set", or just thinking about Cantor diagonalization it is hardly belivable that there is a rich-enough mathematical theory within which a "the most"-type object exists.

And still, set-theory, model-theory and mathematical logic can exist only because all these theories overcame Russel's paradox.

Modelling Anselm's realm
It is amazing that Gödel's model is almost a word-by-word translation of Anselm's original argument. Quoted from Ontological argument:

"While Anselm did not propose an ontological system, he was very much concerned with the nature of being. He stated that there are necessary beings — things that cannot not exist — and contingent beings — things that may exist but whose existence is not needed"

Anselm's words "necessary beings", "contingent beings" are almost fustrating because he use the central notions of modal logic and in later in his proof he use these notions as if he have known the modal logic (of course not).

Gödel choose the second-order predicate logic S5 for modelling the above situation, I call it S²5. The logic S²5 is not a daily used logic. It's expressiveness much more then the usual first-order predicate logic. However it is a logic it's own. There is a Kripke-tzpe semantics of S²5 for which the logic is complete (i.e. it is complete in the sense of Gödel). S²5 is rich enough to model natural numbers, it means Gödel incompleteness theorem also valid within S²5. This is the logical background to define the notion of God.

For Euclide's Geometry (and many other mathematical theory) this background logic is not stated explicitely, because it use the classical first-order predicate logic (Euclide used the Aristotales's logic - idependently from that it was formilezed or not)

In the next step he start to formilaze

"Now we believe that [the Lord] is something than which nothing greater can be imagined."

Gödel can not do nothing with "nothing greater". Instead of he start to axiomatize "nothing greater in goodnes". To avoide any attack instead of "something being good" he choose "being positive". The meaning of predicate P - sometimes write as Pos - remains undefined. At first glance it is very disturbing. However all in math the situation is similar. In geometry we do no nothing about point. All our knowledge about "point" is just in axioms and their consequences. Of course we can say that point is something without any dimension, but this is only the intended meaning of the point, which help us to understand the theory and then use it in the practice.

In our case P intended meaning is that a property is good. Recently we know nothing about P only that about any property φ we can state P(φ), and this P(φ) formula can use in any other formulas as well. Next Gödel in five axiom summarize what he think about such a notion of "goodness". Let us call S²5 + Gödel's five axiom as G²5.

Gödel theorem simply states that

$$ \begin{array}{rl} \mbox{Th. 4.} & G^25 \models \bullet\; \exists x\; G(x) \end{array} $$

What Gödel has proved?
So now we reach the point where math ends. When I say that "proof is there" is means that the proof of Th.4. is in the article. The proof from mathematical point of view is not a long or compleceted one. Moreover, it is out of quenstion that the proof itself is correct (within G²5).

It is clear that not only P has an intended meaning but G as well. G is simple states about an x that x is God. Using the intended meaning of these predicates Th. 4. can be transfer into the following:

Our description of Goodness implies the existence of God (in the frame of S²5)

Summary
I tried to propose that Gödel did not prove the existence of God at all. Instead of he present a logical model within which some God-related notions became definable. He also prove some statements about these notions to point out that in his model we can examine our knowledge about God and related notions and can mathematically clarify their relations. This is why I'd like to modify the title of this article to Gödel's God Model.

It is very easy to misinterpret Th. 4. Somebody can treate Gödel's axioms as a very weak assumptions about goodness. Next step is that somebody thinks that these assumptions are so weakly that must be true in our reality as well. Moreover, these assumptions is about the notion of goodness, the notion of God. Anselm himself stated that

But certainly this same fool, when he hears this very thing that I am saying

Unfortunately this is not true. Anyway, if it is provable that these weak assumption about goodness are ture in our reality, then he or she also can prove the existence of God.

There are still another mathematical problem. Choosing a Kripke-model for S²5 we can construct different P-s for which G²5 hold. If so then instead of God we has to write God(P) stating that the notion of God depend of the initial choosing of "goodness". This latest formulazation of Gödel's results show that this model far away to give our full knowledge of God.

Gödel main achievement was to deliver whole armory of mathematical logic for those scientist who try to deep our knowledge about the entity called God.

Best Regards

Csapajev 12:56, 25 July 2007 (UTC)


 * It is incorrect, not only grammatically, to say "Now we knows that Euclides geometry is wrong&hellip;." Euclid's plane geometry referred to lines on flat surfaces. As such, it was not wrong. It was plane geometry and therefore did not refer to lines on convex or concave surfaces.Lestrade (talk) 14:08, 24 January 2009 (UTC)Lestrade


 * As much as one is serious about the premises, Gödel has validly proved God, but the critics shoot at "soundness", of course! But I agree with the above too, Gödel has as a matter of fact provided much definability, much description and put it into the logics context in the most elegant way. Cheers! 109.189.88.76 (talk) 06:44, 7 December 2012 (UTC)
 * But, naturally, the 'God' proved by Gödel's logic is not the Abrahamic deity, or any of the other deity characterized by the fatal non universality of human scripture. Gödel's is one which, if it wished to be known, would be perfectly known everywhere, and so can not w ish to be known, as the deities manufactured from human egos are made out to be. DeistCosmos (talk) 16:10, 7 December 2012 (UTC)
 * it was not the objective, though, to prove the existence of any specific Abrahamic deity. Simply to prove a God's existence. Nothing about Gödel's proof implies universal perfect knowableness. In fact, the only thing implied about the nature of this god by Gödel's proof is that it has only positive qualities and that no positive qualities exist that are not also a quality of this god. anon (talk) 10:00, 25 November 2018 (UTC)

Definition of "positive"?
You do a good job succinctly describing "modal logic", "necessary", "contingent", "possible", "property", and "entail" in preparation for your discussion, but you fail to define what you mean by "positive". Does it mean "true"? Able to be "true"? Something that can be posited?


 * I think I can get a pretty good handle on what "positive properties" must be simply by requiring that their definition be consistent with the axioms. (I'm going to use the axioms as described in the article.  They don't appear to me to be identical to the axioms described in the image, but I don't fully understand modal logic notation.)


 * Consider an arbitrary (non-empty) set of properties. For example: omniscient, omnipotent, omnipresent, benevolent, honest, life-sustaining, just, and eternal.  Or, invisible, pink, is an elephant, and is in your living room.  Whatever.  Any set of properties you want, subject to the following constraint:  It is possible that nothing with all these properties exists.  I.e., there does not necessarily exist something with all these properties.


 * Now, assume that all our chosen properties are positive. Let P be the union of these properties.  By Axiom 3, P is positive.  By our assumption, P entails possible non-existence, i.e., ~NE.  By Axiom 2, Pos(~NE).  By Axiom 4, ~Pos(NE).  This contradicts Axiom 5, so our assumption must be wrong.  I.e., if it is possible that nothing with all our properties exists, then our properties can not all be positive.


 * So, to be consistent, Pos must be defined in such a way that, for any set of positive properties, there necessarily exists something with the union of those properties. Of course, any such definition of Pos renders Axiom 5 redundant.  (Since our set of positive properties entails necessary existence, necessary existence is a positive property by Axiom 2.)  The conclusion is that a God with all positive properties necessarily exists if and only if Pos is such that it is not possible that there does not exist something with all positive properties (or, indeed, all of any arbitrary non-empty set of positive properties).


 * Unfortunately, this renders the whole argument (as presented in the article) rather uninteresting. I don't know whether other forms of the argument impose the same constraint on the definition of positive properties, but my guess would be that they do.


 * (Note: I glossed over a little in my fourth paragraph. By Gödel's incompleteness theorem, it is possible to define Pos in such a way that it entails neither NE nor ~NE.  If Pos is defined in such a manner, then Axiom 5 is neither inconsistent nor redundant, and amounts to positing as an axiom that if Pos is defined in such a way that it is not possible to determine directly from other presumed properties of God whether God necessarily exists, then necessary existence is also a property of God.  That postulate is a pretty good definition of "faith," and to some may seem perfectly intuitive, but in any case is question-begging.  Obviously, one could just as easily posit its negation.)  Capedia 02:07, 24 August 2006 (UTC)

I tried to get the implied definition from context, but it seemed too wrapped up in the arguments being made. Since quite a bit of your discussion hinges on this concept, I'd recommend that your Wikipedia entry would really benefit from a concise, explicit definition of "positive" in this context.

"Positive" is whatever you want it to be. The idea apparently was that it means "good" so it is somewhat consistent with theology, but it could be any arbitrary selection. It would be difficult to constrain it and still avoid incompatibilities and ideological strife. The absence of a "neutral" category is odd, but does not matter since "negative" does not figure into the argument.


 * Exactly, it is whatever you want it to be. I assert as an axiom that "is Capedia" is a positive property.  (My girlfriend certainly seems to think so.)  I also assert, by Descartes's reasoning, that anything with the property "is Capedia" necessarily exists.  If other positive properties are not consistent with "is Capedia," then there is no object with all positive properties; i.e., no God.  If all other positive properties are consistent with "is Capedia," then God possibly and necessarily exists, and I am He.  So either there is no God, or I am He.  Now bow down before Me and send Me all your money, you stupid shmuck. Capedia 06:04, 24 August 2006 (UTC)


 * I just thought of another way to describe "positive properties."


 * First off, realize what the term does not mean: it does not mean what we normally mean by those words. For example, humility is a positive property, but rarely attributed to God.  Ditto tall, dark, handsome, a good dancer, and not afraid to cry.  Or big tits, sexually adventurous, a good cook, knows when to shut up, and doesn't mind that you always treat her like sh!t.  Or open to new ideas, adaptable, and always improving.  Or open source.  Or concise.  There is certainly no reason to believe that all properties we call "positive properties" in general discourse are consistent with the axioms of the ontological proof, or that God is defined to have them.


 * Since these are properties that, by definition, God has, a much better translation into English is "divine qualities."

Note that correct translation of the mathematical symbols into English makes it painfully obvious what a question begger the "Pos(NE)" axiom is. Correctly translated into English, the axiom is, "Necessary existence is a divine quality." Capedia 20:17, 24 August 2006 (UTC)

Necessary/contingent vs. analytic/synthetic vs. a priori/a posteriori
The article describes necessary truths as those true by definition, and contingent truths as those inferred from observation. It should be noted that these descriptions are *not* standard in philosophy. In traditional philosophical discourse, a truth is necessary if and only if it is true in all possible worlds, and contingent if it is possible that the truth be false; the article does make these definitions later. A truth is analytic when it is true by definition, and synthetic when it makes a "real" claim about the world -- one that doesn't follow solely from definition. A truth is a priori when (in principle) it can be known absent any real-world experience, and a posteriori when it can only be known through experience.

The article equates necessity with analyticity, and contingency with a posterioricity. Whether these equations are justified is an issue that has been hotly debated historically, and is still far from resolved. As an example, many philosophers of mathematics hold that the statement '2+2=4' is necessarily true -- true in all possible worlds -- but not analytic -- it doesn't follow from the definitions of 2 and 4 that this equation hold.

The point is, making these claims in a definitional sense is misleading, and confusing to the unacquainted reader; moreover, there seems to be no purpose in making them, as far as the rest of the article is concerned. This sentence -- "The proof uses modal logic which distinguishes between necessary truths created by definitions and contingent truths inferred from observations of a world." -- should be changed to remove these references.

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Go for it. :Seth Mahoney 06:21, 29 Sep 2003 (UTC)

Axiomand definition debates
A lot of old stuff was deleted on 10/5/2003 because it was ridiculously long. Most was obsolete or is continued below.

Part 2
I did mention a class of things incompatible with God. "Evil" things. But of course you will say God is omnipotent -- apparently a positive property -- and could be those things if It chose to, but doesn't because (insert some lame excuse). Could if It were different. See "free will", which is an an absolute sense an oxymoron. The distinction between "possible" and "actual" invalidates modal logic as a tool for discussion of ultimate, timeless issues. If you consider all the was, is, and will be -- put it all in present tense -- then there is no distinction between possible and actual. Whatever never exists cannot exist. What exists is all then can exist. A God that does not create all possible worlds is not omnipotent. I God that does create all possible worlds is not distinguishable from Nothing, and is certainly not "good" or "positive" in any normal sense.

Of course theologians shift the definition of "God" to suit their argument, so nothing specific will work.

''I'm not asking for a precise definition of anything. I'm saying that if you assert that there are properties that are incompatible with the existence of God, list a few. Here is my list of a few positive properties: eternal, pleasant, beautiful.'' "Eternal"? God supposedly exists outside of time, thus irrelevant to us. "Pleasant"? The God of Abraham? Oh, come now. "Beautiful"? I thought It was invisible. What color is It? I hope It's blue; that's my positive color.

Now, I have to say that I think it is a fairly big waste of time to try so hard to disprove a proof when the opening section of the article says: "While Gödel was deeply religious, he never published his argument because he feared that it would be mistaken as establishing God's existence beyond doubt." If it were worthwhile, I would have found the time.

All properties that apply to God, when applied to God, are positive, and God possesses all properties that are positive for God. Where in the definitions does it say that the positiveness of a property depends on which object it is applied to?

I think this categorization is specious, but even according to you, you should use axiom - you were referring to a single axiom. I just worked with what was there. Why don't you rewrite the axioms so all the assumptions are given equal weight? That would definitely be an improvement.

What incompatible properties can axiom 2 combine? I did that. See the incompatible properties article.

I don't see in the definitions any restriction on the true/false statements abut an object that can be defined as properties. That refers to properties that you consider "actions".

"Creation" defies causality. "Formation" defies causality. "Creation" is a causal event; it assumes there is "sufficient reason why it is thus and not otherwise" (Leibniz),

''The creationist would argue, in fact, that God created causality, but that the act its self was not caused. As far as referring to the thermodynamic properties of God, I think a lot of people might suggest that He is not physical and therefore has no thermodynamic properties.'' Causality cannot be "created". See above. Anything that exists has statistical properties (of the numeric kind, not just binary), whether it is "physical" or not.

''I never intended to connect possible worlds and block time. Not sure where you got that idea. Further, there is no reason I can see to assert that block time applies to God, or that it means that He is unnecessary or worthless. Why do you think this is the case?'' You mentioned block time. If it applies to all of existence, it applies to any God that exists. There is not much point in paying attention to an invisible thing that can't change anything.

''No, it is vitally important to the argument, and the fact that you so aggressively resist accepting it is important to the validity of your proofs. In modal logic, possible worlds do not necessarily have any actual existence. It is a phrase used to describe possible states of affairs in order to talk about things that have not yet happened or may not actually exist. It is not a metaphysical reference to actual other worlds out there.''

I don't know the relevance of this unless you are trying to say Godel's argument attempts to prove uniqueness, which it does not. Fairandbalanced 21:37, 29 Sep 2003 (UTC)

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''I did mention a class of things incompatible with God. "Evil" things.''

"Evil" is synonymous with "incompatible with God" in this sense. You are therefore saying, there is a class of things, which I will call "incompatible with God" which are incompatible with God. Mention specific properties.

But of course you will say God is omnipotent

I will make no such argument here. I'm not trying to convince you of God's existence or properties.

-- apparently a positive property --

I would say that omnipotence is only a positive property when combined with benevolence and omniscience.

and could be those things if It chose to, but doesn't because (insert some lame excuse).

I think most people would say that God is not evil because it is in God's nature to be good, and the two are, oh, what's that word I don't understand again? Oh yeah, incompatible.

See "free will", which is an an absolute sense an oxymoron.

Been there. I'm not getting into this ridiculous argument again, but yes, "free will" is an oxymoron, which doesn't mean that the idea it represents doesn't exist.

The distinction between "possible" and "actual" invalidates modal logic as a tool for discussion of ultimate, timeless issues.

Then why, at the end of this article, do you try to use modal logic to disprove an ultimate, timeless issue (God)?

If you consider all the was, is, and will be -- put it all in present tense -- then there is no distinction between possible and actual. and so on...

Which is only an effective argument if one accepts determinism.

A God that does not create all possible worlds is not omnipotent.

Saying something doesn't prove it. It is certainly possible that, were God to create all possible worlds, said God would still be omnipotent. Regardless, as I was saying, the idea of possible worlds doesn't necessarily entail their actual existence.

I God that does create all possible worlds is not distinguishable from Nothing, and is certainly not "good" or "positive" in any normal sense.

A God that does not create all possible worlds is certainly distinguishable from Nothing, in that, were the creator to not exist, neither would all possible worlds, considering they are only possible provided that the creator creates. I agree that a God who would create all possible worlds is not good in any meaningful sense, though, which is a good direction to go in arguing against this proof.

''"Eternal"? God supposedly exists outside of time, thus irrelevant to us.''

"Irrelevant to you" doesn't mean the same thing as "irrelevant to us". Just because you don't find a God that exists in a different sense than you exist to be relevant doesn't mean that everyone else feels the same way, and yes, this is a matter of feeling rather than reasoning.

''"Pleasant"? The God of Abraham? Oh, come now.''

I totally agree. In all honesty though, Christians and Jews don't really worship the same God, and really, many modern Jews don't worship the same God as their ancestors. In fact, the gnostic Christians called the God of the Old Testament the demiurge and more or less thought him an ass.

''"Beautiful"? I thought It was invisible.''

Is beauty something that only exists visually? Can a song be beautiful? An idea? A theorem?

If it were worthwhile, I would have found the time [to disprove Godel's proof].

Yet that is exactly what you seem to be trying to do! So either you aren't providing counterarguments, in which case it is not worthwhile as, as I said Godel had already suggested himself that the proof didn't actually prove God's existence, or you are providing counterarguments, in which case you think it is worthwhile to disprove a proof the author didn't even think proved anything.

Where in the definitions does it say that the positiveness of a property depends on which object it is applied to?

You're taking the more restrictive view. The burden of proof is on you.

''I did that. See the incompatible properties article.''

Unless you've seriously revised the article, I (and most Christians, Theists and other interested parties, I suspect) don't find the properties listed especially incompatible without proof.

''I don't see in the definitions any restriction on the true/false statements abut an object that can be defined as properties. That refers to properties that you consider "actions".''

Don't act like you're using my definition reluctantly. When someone does something, they are said to act - it is an action. An action is something a thing does, rather than "A characteristic trait or peculiarity, especially one serving to define or describe its possessor. [American Heritage Dictionary]". This is the standard definition. If you're going to use a different set of definitions, you're going to have a harder time proving your case.

''"Formation" defies causality. "Creation" is a causal event; it assumes there is "sufficient reason why it is thus and not otherwise" (Leibniz)''

Come now, we're talking about God here, who is ineffable (apparently a positive property?). To apply our ideas of what is a "sufficient reason why it is thus and not otherwise" then necessarily doesn't work. Creation is the initial causal event, which is why I say that, according to the story, with the universe God created causation.

Anything that exists has statistical properties (of the numeric kind, not just binary), whether it is "physical" or not.

What are you talking about?

''You mentioned block time. If it applies to all of existence, it applies to any God that exists. There is not much point in paying attention to an invisible thing that can't change anything.''

First off, I don't believe in determinism, so block time doesn't actually apply - I was providing it as an argument that you're likely to encounter. Second, there is no reason to include a nonphysical being in the restrictions you place on the physical universe. Third, let's say for a moment the universe is deterministic and God created it - the universe then moves according to God's will. As to whether or not there is much point in paying attention to the reason you exist, that is up to you, but doesn't make for a sound argument.

As to the relevance of my diatribe on modal logic and possible worlds, you have for the length of this debate (and in the article its self) seemed to talk as if possible worlds must exist. There is no reason to assume they do. If you write the article in this tone, your arguments are not going to be convincing to someone who studies logic. -

Mention specific properties.

"Evil" is your game. I'm sure you can come up with something.

''I think most people would say that God is not evil because it is in God's nature to be good, and the two are, oh, what's that word I don't understand again? Oh yeah, incompatible.''

Precisely. And God cannot go against God's nature and still be God rather than the indeterminate Nothing.

''Been there. I'm not getting into this ridiculous argument again, but yes, "free will" is an oxymoron, which doesn't mean that the idea it represents doesn't exist.''

OK, it also doesn't exist, except in the compatibilist proximate sense.

Then why, at the end of this article, do you try to use modal logic to disprove an ultimate, timeless issue (God)?

I only maintain the argument for necessary existence of no god is as good as the one for gods.

If you consider all the was, is, and will be -- put it all in present tense -- then there is no distinction between possible and actual. and so on...

Which is only an effective argument if one accepts determinism.

Whatever will be, will be, but nothing else can be, whether random or deterministic.

''Saying something doesn't prove it. It is certainly possible that, were God to create all possible worlds, said God would still be omnipotent. Regardless, as I was saying, the idea of possible worlds doesn't necessarily entail their actual existence.''

You are stuck in a loop.

A God that does not create all possible worlds is certainly distinguishable from Nothing,

I think that is true, except that I should have said "distinct" rather than "distinguishable." My mistake; I interpret "distinguish" as requiring an observable.

...in that, were the creator to not exist, neither would all possible worlds, considering they are only possible provided that the creator creates.

That makes no sense at all. Worlds, with or without gods, randomly pop out of Nothing.

I agree that a God who would create all possible worlds is not good in any meaningful sense, though, which is a good direction to go in arguing against this proof.

Ah, we agree on something. Thanks, I had not thought of that.

''"Irrelevant to you" doesn't mean the same thing as "irrelevant to us". Just because you don't find a God that exists in a different sense than you exist to be relevant doesn't mean that everyone else feels the same way, and yes, this is a matter of feeling rather than reasoning.''

No, a God that is not aligned with our time cannot interact with us. You folks just make up these properties without any thought as to whether they make sense.

'''"Pleasant"? The God of Abraham? Oh, come now.'''

''I totally agree. In all honesty though, Christians and Jews don't really worship the same God, and really, many modern Jews don't worship the same God as their ancestors. In fact, the gnostic Christians called the God of the Old Testament the demiurge and more or less thought him an ass.''

The one that kills Its first-born, supposedly with real pain. That one also has a lot of issues with civilized behavior. A lot of Christians want the government to pummel everyone with their version of Ten Commandments, etc. Having your cake and eating it too?

''Is beauty something that only exists visually? Can a song be beautiful? An idea? A theorem?''

I suppose, but I still prefer blue. "X is blue" is a positive property.

Where in the definitions does it say that the positiveness of a property depends on which object it is applied to?

''You're taking the more restrictive view. The burden of proof is on you.''

No proof needed, just a something supposedly already in the article.

Unless you've seriously revised the article, I (and most Christians, Theists and other interested parties, I suspect) don't find the properties listed especially incompatible without proof.

You and most Christians, etc. are unlikely to be convinced by anything.

''Don't act like you're using my definition reluctantly. When someone does something, they are said to act - it is an action. An action is something a thing does, rather than "A characteristic trait or peculiarity, especially one serving to define or describe its possessor. [American Heritage Dictionary]". This is the standard definition. If you're going to use a different set of definitions, you're going to have a harder time proving your case.''

Fine, acting in a certain way is "A characteristic trait or peculiarity, especially one serving to define or describe its possessor." It's just a matter of rephrasing.

''Come now, we're talking about God here, who is ineffable (apparently a positive property?). To apply our ideas of what is a "sufficient reason why it is thus and not otherwise" then necessarily doesn't work. Creation is the initial causal event, which is why I say that, according to the story, with the universe God created causation.''

And that is the kind of gibberish creationists want to put in public schools! Bye, I've gotta go create something else. Fairandbalanced 01:54, 30 Sep 2003 (UTC)

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''"Evil" is your game. I'm sure you can come up with something.''

Why is "evil" my game? Regardless, you're the one asserting that specific properties are incompatible with the existence of God. You need to supply the properties.

OK, it [free will] also doesn't exist, except in the compatibilist proximate sense.

Now, see, again you've confused saying something with proving it. Just because you've decided it is so doesn't actually make it so.

I only maintain the argument for necessary existence of no god is as good as the one for gods.

You can maintain it all you want, but you haven't proven it yet.

You are stuck in a loop.

Please, if you're not actually going to address what I say, don't bother replying.

I interpret "distinguish" as requiring an observable.

Then, if you are saying that to distinguish requires observing with your senses, you interpret incorrectly. I can certainly distinguish between ideas though I can not see, taste, hear, smell or feel them.

Worlds, with or without gods, randomly pop out of Nothing.

Once again, you're saying something is true without it having been proven.

No, a God that is not aligned with our time cannot interact with us.

Why not? Again, you haven't established this.

You folks just make up these properties without any thought as to whether they make sense.

Who exactly is "you folks"?

''The one that kills Its first-born, supposedly with real pain. That one also has a lot of issues with civilized behavior. A lot of Christians want the government to pummel everyone with their version of Ten Commandments, etc. Having your cake and eating it too?''

Now, see, this paragraph isn't even coherent. "The one that kills Its first-born, supposedly with real pain." isn't even a sentence, and it doesn't actually mean anything without further reference anyway, and I'm not at all sure what you mean by "Having your cake and eating it too?"

No proof needed, just a something supposedly already in the article.

You're the one asserting that the article, or the proof its self, demands that all properties which are positive be positive across the board, when in fact this is not the case!

You and most Christians, etc. are unlikely to be convinced by anything.

I am not easily convinced, true. I have found though that most materialists are far more dogmatic than the average Christian.

''Fine, acting in a certain way is "A characteristic trait or peculiarity, especially one serving to define or describe its possessor." It's just a matter of rephrasing.''

Actually, no. Taking a particular action is usually not a characteristic trait. Tending to act in a certain way may be.

And that is the kind of gibberish creationists want to put in public schools!

Just because you don't agree doesn't make it gibberish. I mean really, this kind of pedantic, expressionless stereotyping is exactly the sort of thing one would expect from someone who adheres to a particular dogma without giving it much thought, something you present yourself as opposed to while characterizing all your opposition as.

Bye, I've gotta go create something else.

Please let that mean you've grown bored with this article.

Yes, you have been able to raise no valid objections, so I think it is in pretty good shape. You obviously don't understand some fundamental concepts, so there is nothing to gain from further discussion. Oh yes, my free will and first cause articles will be published eventually, and then can be incorporated into their respective articles. Fairandbalanced 00:40, 1 Oct 2003 (UTC)

Continuation
If you're not even going to bother to respond to objections I guess you don't mind if I edit your edits.
 * Seth Mahoney 05:50, 1 Oct 2003 (UTC)

Any improvements are welcome, but I don't recall you raising any valid objections lately. Fairandbalanced 22:20, 2 Oct 2003 (UTC)

Okay, if you're actually interested, here are my objections to your portion of the article as it exists today:

It may be impossible to satisfy condition 2.

The second axiom, as I stated earlier, essentially says that if x, y, and z are all positive properties then when considered as a whole, x + y + z must be positive as well. It seems to me to be a reasonable statement. For example, for a pencil, the ability to write is a good thing, as is having an eraser attached to one end. I would also say that it is good when the pencil is nice and new and not yet all chewed up. Therefore, when a pencil can write and has an eraser and is not all chewed up, this is a good thing too. Now, it may be impossible to satisfy the definition of God as "a being that possesses all positive properties (and presumably only positive properties)", but right in this paragraph I satisfied the second axiom for three positive properties of pencils. Therefore, it is not impossible to satisfy the second axiom.
 * Read your links. They point out that later revision replace that axiom because it could not be proved.  I showed counterexamples.
 * Which link says that? Where?  What counterexamples have you shown (I can't seem to recall any, but it is possible I have just forgotten)?

A property that is positive for one object is positive for all, and conversely.

Nowhere, nowhere in this proof does it say that a property that is positive for one object must be positive for all, and if it did the argument would be seriously flawed right there! Extremely high acidity is, for example, a positive property in solvents but a negative property in hand lotion, as I don't want horrible acid burns every time I try to moisten my skin.
 * Glad you agree it is flawed. Positiveness is an attribute of a property, not of an object.
 * Positiveness can only be an attribute of a property when it is applied to an object, as I illustrated for acidity.
 * Only Godel's axioms and definitions matter here.
 * That's true, and Godel's axioms and definitions don't require a property that is positive for one object be positive for all objects!

Does God believe in a higher power?

A very easy and reasonable retort is that God is infinite. God's higher power would be God, so if God believes in a higher power, he believes in himself and this is, indeed, a positive property for himself.
 * Fine, all infinite things are equal. Assuming infinite things are possible, they are all God.  Do you like that better?
 * I'm fine with that, actually. All infinite things are God or, maybe even better, God is all infinite things.  Sure.
 * Now you only need to prove the existence of infinite things and you have your God, probably infinite gods.
 * I'm not trying to prove the existence of the Theistic God or any other God. I'm saying that your argument is flawed to anyone who has this perception of God.  If it is actually your intent to disprove Godel's argument or to construct a viable counterargument, it would be worthwhile to take this into account.

A second retort is that nowhere in the proof does it say that for a property to be positive it has to be positive for all things. Since this idea of positive properties is introduced in this proof (it is not a part of modal logic), any definitions as to the way it works would have to be included in the proof its self. If positive properties don't have to be positive across the board, then it is perfectly reasonable to say that belief in a higher power is perfectly fine for humans and perfectly okay for God not to have.

A third easy and reasonable response would be to say that it is not just belief in a higher power that is a positive property, but belief in the higher power that actually exists, and that, even if it is required that positive properties be positive for all things, all this means to God is that He believe in the higher power that exists, namely himself.

A fourth argument, similar to the third, would be to say that belief in a higher power is not what is positive, but belief in a power higher than humans or a power higher than nature or a power higher than the physical world. For example, I could have believed in Hitler as a power higher than myself. This would not be a positive belief. God is a power higher than humans, nature and the physical world and therefore if God were to believe in Himself he would satisfy the property.
 * You are being silly and repetitive.
 * Now, see, saying "you are being silly and repetitive" isn't the same thing as actually countering an argument. What such a statement does suggest is that you aren't even taking your own writing seriously and aren't willing to either admit that you could have been mistaken or to actually address other people's arguments when they disagree with your own.  How can you expect everyone else to accept your arguments and take them seriously (as I have done here) when you aren't willing to address the arguments of others (as you have not done here)?
 * You are being silly and repetitive again.
 * Look, I know I've not been the friendliest person to argue with at times throughout this conversation, but my goal here isn't to make you look like an ass. I think that wikipedia is a great idea, and I want it to be a success.  Because of that, I want this article to be a good one, and just constructing counterarguments all pell mell with no regard for whether or not they are convincing or even sound isn't a good way to do that.  All three of the arguments I have presented here are valid counter-counterarguments, and if you actually want to present your ideas in a manner that contributes to the overall quality of the article, it is worth your time to consider them and respond.

If the null world is possible, it must have its God.

First off, I would recommend explaining what you mean by the "null world". I am reading "the world that was never and never will be created" or "the world that, for whatever reason, doesn't exist and will never exist". My initial response would be: do you have any reason for believing that the null world is possible?
 * No more or less than for believing a God is possible.
 * That doesn't actually address the question. Further, you don't seem to think that God is possible.  Therefore, if you have no more or less reason for believing that a null world is possible, you do not, in fact think such a world is possible, and your argument fails because of your own beliefs.
 * Only Godel's axioms and definitions matter here, not beliefs.
 * I agree, and if Godel is trying to prove the existence of God, his definitions and axioms likely approach God as something that, while present in the universe, isn't contained in it. If the "null world" is a possible world then God must be a part of it, in a sense.  However, again, possible worlds do not actually have to exist - they are just logically possible.  Therefore, if for any reason the "null world" is not logically possible, it is not a possible world.  Now, you have indicated you have no reason for believing that the "null world" is a possible world.  If this is the case, then you must think it is not logically possible and, thus, you must think that this particular argument fails.  If you're not even convinced that an argument is sound, you can't expect others to be either.

''A null world would exist, but contain nothing. (This is based only on the Wikipedia article.)''

Again, what wikipedia article are you referring to? The language here in parentheses is also a little awkward. Why does a world that contains nothing preclude God?
 * Godel's ontological proof. It would be a null God.
 * Please, complete sentences. I have shown you the courtesy of actually examining your arguments and responding with complete ideas.  You should return the favor.  Now, to address what I think you're saying here, the world is not the same thing as the Theistic God, nor does the world contain the Theistic God.  Therefore, an empty world does not necessitate a "null God", whatever that means.
 * Thet is all nonsense. A world is the top level, a null world does not contain a non-null God.  Pretty simple stuff.
 * It doesn't matter if you think it is nonsense. Only Godel's beliefs, definitions and axioms matter here.  I'm saying that Godel's proof addresses a God that is one throughout all possible worlds, so God here is the top level object, in a sense.

''God is not shown to correspond to the God of the Bible. Here is one example: x is "visiting the iniquity of the fathers upon the children, and upon the children's children, unto the third and to the fourth generation." (KJV, Exodus 34:7) Is that a positive property? Remember, if the property is positive for God, it is positive for each of us too. ''

This sounds like it should be two separate statements, with "God is not shown to correspond to the God of the Bible." on one line and maybe the rest with your positive properties statement, as an example? They don't really seem to be related as they are now.
 * Maybe I should improve it someday.
 * Okay, I'm fairly convinced now that you aren't even taking your own reasoning seriously and are just responding to a personal bias against religious belief.
 * First, after doing a quick search, the only articles I have found that you have contributed toward, with one possible exception, have been articles concerning religious belief. Second, your goals in each article are generally the same (suggesting your user name "Fairandbalanced" is a misnomer).  Third, you don't seem interested in actually backing up any of your arguments.  Fourth, you are unwilling to provide definitions you are using.  Fifth, when you either are unable to or don't feel like responding to an objection, you often resort to insulting language (suggesting that the former situation is the more likely).  I therefore conclude that you aren't interested in writing a really good article and are just interested in making counterarguments that you don't even take seriously enough to back up.
 * First, after doing a quick search, the only articles I have found that you have contributed toward, with one possible exception, have been articles concerning religious belief. Second, your goals in each article are generally the same (suggesting your user name "Fairandbalanced" is a misnomer).  Third, you don't seem interested in actually backing up any of your arguments.  Fourth, you are unwilling to provide definitions you are using.  Fifth, when you either are unable to or don't feel like responding to an objection, you often resort to insulting language (suggesting that the former situation is the more likely).  I therefore conclude that you aren't interested in writing a really good article and are just interested in making counterarguments that you don't even take seriously enough to back up.

Now, as far as that being a positive property or not, there are indeed some who would say that it is, or at least that it may be. Anyone who, for example, values justice over compassion, anyone who believes that humans are strongly shaped by familial bonds and that such visitations of iniquity may be necessary for the children to learn proper behavior, etc.

Condition 2 is so dubious that Anderson's version substitutes for it the condition that being God-like is positive

I am really not sure what you read the second axiom as saying. Perhaps you would care to share?
 * It's explained by one of your links.
 * I didn't ask for a reference to "one of my links", nor do I wish to waste my time rereading pages of material in hopes of gleaning out what you may think axiom two says. Why don't you just tell me?
 * Does daddy still read you stories?
 * Please. I asked a genuine, nonoffensive question about what you are thinking.  If you haven't actually given much thought to what you read the second axiom as saying, just say so.  I'm certainly willing to show you why I think my translation works.  If you do have a working definition, share it.  It can only make the article better.

Substitute "incompatible with God" for "positive" as the attribute of an acceptable property.

Where are you having us make this substitution? Where in the article has the idea of an "acceptable property" been introduced?
 * I should have omitted "acceptable".
 * That doesn't address the first question.
 * The first question: "Where are you having us make this substitution?" You addressed the second question.  Therefore I replied that you still haven't addressed the first.
 * The first question: "Where are you having us make this substitution?" You addressed the second question.  Therefore I replied that you still haven't addressed the first.

Theologians argue that God is incompatible with some absolute negative moral principles, so such properties must exist.

Do you really mean to say that everything Theologians argue about must exist? Or are you saying that because Theologians say that certain properties which are incompatible with God would preclude His existence, they must exist? The sentence seems to be intended to make one of these two statements.
 * If theologians know about an actual existing God that created this universe, then yes. See, with the right axioms, anything can be proven.
 * First, I don't think it is proper to say that theologians "know" about an actual, existing God that created this universe. I believe the term is faith.  Second, once again you haven't proven anything.  Third, I'm not even sure which statement you are suggesting you have proven.  Fourth, both of the statements I presented were nonsense.  Fifth, perhaps with the right axioms anything can be proven, but the catch is that the axioms have to be accepted: "Axiom: A self-evident principle or one that is accepted as true without proof as the basis for argument; a postulate." (American Heritage Dictionary)  That everything Theologians argue about must exist is not a self-evident truth.
 * It is a postulate, but not mine. I've lost the relevance of this.  Oh yes, theologians and Godel don't think God could create all possible worlds, just the good ones.  Thus some things are incompatible with God.  You are free to assume otherwise.  With the right axioms....
 * Actually, this world must be a possible world. This world is not entirely good, or we don't understand the nature of good.  Therefore theologians and Godel, unless they are completely insane, obviously do think that God could create *all* possible worlds.  There is a fairly famous bit of speculation in theodicy that goes something like this: God can do anything that is logically possible.  An entirely good world wherein there are free agents who can choose between good and evil is impossible.  Therefore God cannot create an entirely good world.  Another (in my opinion weaker) older argument is simply that we do not understand what "good" means, or that our idea of good is rooted in our finiteness.

Now, which theologians are saying this? It doesn't seem reasonable for a theologian, a person whose life is devoted to exploring God's existence, to try to prove the nonexistence of God. It seems in fact more likely that, rather than try to prove that the existence of, say, Evil, precludes God's existence, a theologian would try to prove in some way that both Evil and God can coexist.


 * Again, no response.
 * Not relevant.
 * It isn't relevant that you are claiming that theologians are making certain arguments and I want to know which theologians are supposedly making said arguments? It also isn't relevant that the argument you claim theologians are making has actually never been made by any theologian ever?  I disagree.  It is entirely relevant because it speaks to your understanding of the subject matter.

G is the "no-God" property and an object x that has any no-God property prevents the existence of a God, since incompatibility means the two cannot coexist.

So for example, say that Evil is incompatible with God, that is, that God cannot be evil. The presence, then, of one evil thing prevents God from existing?
 * By George, I think you've got it!
 * If you're going to argue about theology, I think you might benefit from studying it more. There is a whole branch of philosophy or theology (depending on how you want to look at it) that deals with precisely this problem: Theodicy, and the simple fact is that many people are able to reconcile the existence of a perfectly good creator God with the existence of evil.  That you seem to be unwilling or unable to do so doesn't mean that it can't be done.
 * People can reconcile anything with anything, but it often doesn't make any sense at all. The relevance to Godel's argument escapes me.
 * The relevance is to your counterargument. Most people would not agree that the existence of one evil thing means that God cannot exist (if your first premise is untrue, the argument is not sound).  Some would not even agree that the existence of evil in God is a paradox (though Godel probably would.  See mysticism for more on this, if you're actually interested in theology, even from a negative POV.

The nonexistence of God follows.

The nonexistence of God does not follow, not necessarily because this argument is seriously and fundamentally flawed in some way - it sounds to me like a version of the argument from evil. The reason the nonexistence of God does not follow is because you haven't actually carried it to its conclusion.
 * It is similar, not identical. You have not explained all the steps in the proof either.  If you do, I'll point out any steps that vary slightly.
 * Right, it is similar, hence "a version of the argument from evil". What steps in what proof have I not explained?  Why should I be required to explain anything in order for you to explain your thinking?  This isn't a contest, it is an encyclopedia, for Christ's sake.
 * If the logical derivation of no-god differs from Godel's, show where.
 * I obviously do not understand how your argument even mirrors Godel's, much less how it leads to its conclusion. You need to spell it out - remember, this is supposed to be an encyclopedia, a reference source.  If you are unable or unwilling to actually demonstrate your proof, you need to remove it.

As I said earlier, it is becoming clear that you aren't actually taking this debate, this article, or even your own arguments seriously, and it seems that you are only intent on using wikipedia as a vehicle for your own distaste for religion. As I also said earlier, this isn't an article about whether or not God exists but about a particular formalization of a particular "proof" that is particularly famous throughout philosophical history. As such, it is not the proper forum for you to air what seems to be purely your frustration with religion. If you want to seriously point out flaws in the argument or actually research the proof and present common retorts, that is fine, but if you aren't going to take your arguments seriously there is no reason for me to do so either.
 * On the contrary, the flaws in an argument are more significant than the argument. If you think it improper to criticize religion, then change it to a proof of the existence of unicorns and change "positive" to some neutral term like "clockwise".
 * I don't necessarily think it is improper to criticize religion. I do, however, think that this is not the place for it.  Perhaps you can start an article at religious criticism or something.  You can present valid counters to Godel's argument (and I have been willing to accept some of yours as valid throughout this discussion), but if all you are doing is using this forum as a way to express your anti-religious POV, this is not the place for it, and Fairandbalanced is not an appropriate name to use.  Now, as I said (and you seem to think I said the opposite of what I said for some reason), if you are really, seriously interested in pointing out reasonable flaws in the argument or actually research the proof and present common retorts, that is fine, but if you aren't going to take your arguments seriously there is no reason for me to do so either.


 * Seth Mahoney 17:33, 3 Oct 2003 (UTC)

More nested arguments
Only Godel's axioms and definitions matter here. That's true, and Godel's axioms and definitions don't require a property that is positive for one object be positive for all objects!
 * Nonsense. Oh well, then I'll just define all the properies of me to be positive.  I'm God.  Worship me and send money or else!  Unfortunately, positiveness is an attribute of properties, not of objects.  But I could still use the money.
 * Now, I'm not saying that you can define the properties any way you like, but that properties only have positiveness or negativeness when applied to things. Godel may have been referring only to universally positive properties though the idea seems to me to be ridiculous.
 * Positiveness is entirely arbitrary. That is a standard theological objection to Godel's proof.  Since you find Godel's definition ridiculous, we agree.

A third easy and reasonable response would be to say that it is not just belief in a higher power that is a positive property, but belief in the higher power that actually exists, and that, even if it is required that positive properties be positive for all things, all this means to God is that He believe in the higher power that exists, namely himself.

All infinite things are God or, maybe even better, God is all infinite things. Sure.
 * All infinities are not equal, see Georg Cantor (if I have the first name right), and God is not a higher infinity than Itself. It would be interesting
 * I'm familiar with Cantor, and we've been over this before. Cantor also defined uncountabily infinite sets, which are all, for all intents and purposes, the same size.  The whole point is that, by definition, the only thing higher than God is God (in Anselm's argument, "that which none is greater").  The fact is, though, that belief in a power higher than one's self isn't considered a positive property by religious people, but the belief in a power higher than  humans, or higher than nature is.  Either property as a universally positive property presents no paradox when applied to God.
 * Insufferably silly. Read about sets of all subsets.  Cantor never showed that there was an actual utlimate limit, he just liked the idea.
 * Oh good! Now we've degenerated from such name-calling as "silly" to "insufferably silly"!  Fabulous.  Perhaps you should read the article you linked to.

Look, I know I've not been the friendliest person to argue with at times throughout this conversation, but my goal here isn't to make you look like an ass. I think that wikipedia is a great idea, and I want it to be a success. Because of that, I want this article to be a good one, and just constructing counterarguments all pell mell with no regard for whether or not they are convincing or even sound isn't a good way to do that. All three of the arguments I have presented here are valid counter-counterarguments, and if you actually want to present your ideas in a manner that contributes to the overall quality of the article, it is worth your time to consider them and respond.
 * and long-winded. They were silly arguments.
 * See? Again, you don't bother to actually respond.  I assume, reasonably, that you are incapable, and rather than actually admit that you could possibly be mistaken or could have not considered all posibilities when constructing your criticisms, you resort to characterizing my arguments as silly.

I agree, and if Godel is trying to prove the existence of God, his definitions and axioms likely approach God as something that, while present in the universe, isn't contained in it. If the "null world" is a possible world then God must be a part of it, in a sense. However, again, possible worlds do not actually have to exist - they are just logically possible. Therefore, if for any reason the "null world" is not logically possible, it is not a possible world. Now, you have indicated you have no reason for believing that the "null world" is a possible world. If this is the case, then you must think it is not logically possible and, thus, you must think that this particular argument fails. If you're not even convinced that an argument is sound, you can't expect others to be either.
 * No, he asserts his God is the object in a world that satisfies G(x).
 * That is certainly what the article seems to suggest. In that case, you might take as an additional criticism of Godel's argument the fact that Godel's God, as an object in the world, doesn't correspond to many notions of God as a transcendent being.  Regardless, though, you haven't established that a "null world" is logically possible.
 * I maintain that a null world is consistent with the definitions and axioms. If you can show otherwise, I'll withdraw it.

It doesn't matter if you think it is nonsense. Only Godel's beliefs, definitions and axioms matter here. I'm saying that Godel's proof addresses a God that is one throughout all possible worlds, so God here is the top level object, in a sense.
 * Nonsense. If you can't read, go watch Fox News.
 * Again! What the hell?  Is your position really so weak that you have to resort to insults?  Does criticism of your POV really hurt so much that you can't respond with reasoning?
 * According to Godel, each world has a God. He said all worlds were identical, but the revised Anderson version does not.  If you don't like it, you can watch Fox News instead.
 * I would rather pull out my eyes and serve them up on skewers than watch that especially vacuous news network. Regardless, according to Godel, each world should have *the same* God, not just a God.

First, after doing a quick search, the only articles I have found that you have contributed toward, with one possible exception, have been articles concerning religious belief. Second, your goals in each article are generally the same (suggesting your user name "Fairandbalanced" is a misnomer). Third, you don't seem interested in actually backing up any of your arguments. Fourth, you are unwilling to provide definitions you are using. Fifth, when you either are unable to or don't feel like responding to an objection, you often resort to insulting language (suggesting that the former situation is the more likely). I therefore conclude that you aren't interested in writing a really good article and are just interested in making counterarguments that you don't even take seriously enough to back up.
 * Perhaps I have a purpose-driven life. I helped clean up some articles full of religious propaganda, made them more fair and balanced.  Religion is, after all, the greatest threat to human civilization, rather important to counteract.  Maybe you should spend your time understanding the subject matter.
 * If you were truly fair and balanced, you would also go into aggressively anti-religious articles and make sure that they presented both sides of the article with equal respect. Sigh.  As far as religion being the greatest threat to human civilization, now you're the one making silly statements.
 * I have not rean such an article, but I have corrected some overstatements. I don't think they are helpful. If you discover a greater threat, let me know.  And be sure to tell the usurper President too.
 * First, religion is not a threat to human civilization, much less the greatest threat. Dogmatic beliefs and the abuse of religion are threats though.  Basing all religion on wonderful examples like Jerry Falwell, the inquisition and the crusades is an unfair and unrealistic characterization.  Second, I would suggest that such non-religious items as nuclear weapons and industrial pollution are far more dangerous to all human life, and therefore human civilization, than religion could ever be.  Finally, I'll let you know if I see any articles that are unfairly critical of religious views, so you can have a shot at living up to your user name.
 * Name an Abrahamic religion that does not breed fundamentalist extremists who want to seize control and impose their views on everyone else. The danger of weapons depends on who controls the United States, and religious zealots are the only real threat.  You apparently don't know the source of my user name, and I'm not telling.
 * It doesn't matter how many "fundamentalist extremists" a religion or set of religions "breeds". It is still not reasonable to characterize all practitioners in a certain way.  Further, your statement said "religion is, after all, the greatest threat to human civilization", thereby characterizing ALL religion in the same way, not just the Abrahamic religions.  Further, the danger of nuclear weapons is inherent.  They are simply not safe.  They are not safe to make, they are not safe to store, they are not safe to use.  The danger to civilization is there no matter who is in control, although yes, the danger does increase when someone like GW gets into a position of control.  You're right, I haven't figured out the source of your user name, and if you want to act like a six year old and "not tell", I don't really care.
 * Yes, it might be more precise to say Abrahamic religion is the most serious threat to civilization, although Hindu fundamentalism could become one if India produces more nukes and a long-range delivery system. Buddhism has a pretty good record overall, I guess.  Communism is no longer a threat.  Anyway no non-Abrahamic religions are a serious threat, so I don't really care about them.  Without religion, there would be no fundies, so my statement was correct.
 * Without humans there would be no wars resulting in the destruction of civilizations. Therefore I conclude that humans are the greatest threat to human civilization.
 * I thought we agreed that we could be more specific, like "Abrahamic religions". I agree that humans are a threat, but at this point also the only solution.

Condition 2 is so dubious that Anderson's version substitutes for it the condition that being God-like is positive I am really not sure what you read the second axiom as saying. Perhaps you would care to share?
 * Follow the links at the end of the article. Maybe they weren't yours.  The axiom is pretty simple, but does not make it valid in a non-null real world.
 * Seriously! Why don't you just tell me what you think the second axiom says?
 * OK. If P1, P2, P3, ... are positive properties, then the property (P1 AND P2 AND P3 ...) is positive as well.
 * So how is it dubious that a set of positive properties is also positive?
 * As I have shown, and because it cannot be proven.
 * You have neither shown that such a statement is dubious, nor have you shown that it cannot be proven. It seems absolutely self-evident to me.
 * Self-evident truths are often false. As to your first claim, I have, and professional mathematicians have.
 * That's true, but they have to be proven false. You have not done so.  Professionaly mathematicians may have, but such proofs are not present in this article.
 * It is mentioned in at least one of the linked outside articles. The incompatible properties of God or sufficient disproof for theistic purposes.  Things that are false are false even if not proven false.  Dubiosity is sufficient for me.

Substitute "incompatible with God" for "positive" as the attribute of an acceptable property. The first question: "Where are you having us make this substitution?" You addressed the second question. Therefore I replied that you still haven't addressed the first.
 * So you can prove the nonexistence of God.
 * That doesn't address the question!
 * That is why you would make the substitution.
 * Okay, what I'm asking is, where would you make this substitution, not why would you make this substitution.
 * Look for "positive", make substitution.
 * In which case it is no longer anything like Godel's proof, and no longer carries even the level of certainty Godel's proof carries, because there is no evidence that the property "exists" is necessary for a thing that is incompatible with God to possess, while in Godel's proof, if you accept that "exists" is a positive property and that God definitionally possesses all positive properties, God must possess the property "exists".
 * It is exactly Godel's proof with only one essential substitution, and it carries exactly as much certainty as Godel's original (zero). I could also start with Gasking's assumptions (in the Anselm article) since they are superior to Anselm's, but that would be too far off topic.
 * If Godel's axioms are true (this is really the big question), his conclusion is true. If your axioms are true, your conclusions may be true.  There is clearly a difference in the level of certainty here.  Yours is not exactly Godel's proof with one modification, because the modification you made undermines the proofness of the proof, as I outlined above.
 * Since the same logical derivation applies to both, there is no difference.

Actually, this world must be a possible world. This world is not entirely good, or we don't understand the nature of good. Therefore theologians and Godel, unless they are completely insane, obviously do think that God could create *all* possible worlds. There is a fairly famous bit of speculation in theodicy that goes something like this: God can do anything that is logically possible. An entirely good world wherein there are free agents who can choose between good and evil is impossible. Therefore God cannot create an entirely good world. Another (in my opinion weaker) older argument is simply that we do not understand what "good" means, or that our idea of good is rooted in our finiteness.
 * Do you actually believe this rubbish or are you merely attempting to debate? Yes, I have read the problem of evil article.  I believe it points out that a God that creates all possible worlds cannot be "good."  Anyway, no entity can do otherwise than what it does, period.  Try it sometime, do what you don't do.
 * I actualy believe that this world must be a possible world, that either this world isn't entirely good or that we don't understand good, that the fact that this world isn't entirely good or that we don't understand good when combined with the fact that this world is a possible world and with belief in God necessarily renders that conclusion that God could create all (logically) possible worlds. I also believe that there is a famous bit of speculation in theodicy that has to do with God being able to do all things that are logically possible.  As far as being able to do other than what it does, what does that have to do with anything?  I mean, seriously, that is the biggest piece of tautological nonsense I have heard in a while.
 * You should read what you write. You are saying that what you said is nonsense.  I agree.
 * I don't recall saying that a being is unable to do what it does, and as this is what I referred to as "tautological nonsense", I don't see the point you're trying to make here.
 * Neither did I.
 * You don't recall my saying that a being is unable to do what it does, or you don't see the point you're trying to make here?
 * Neither of us recall you saying that.
 * Then where have I supposedly said that what I was saying is nonsense?
 * I replaced a "could" with a "would", or something like that,

G is the "no-God" property and an object x that has any no-God property prevents the existence of a God, since incompatibility means the two cannot coexist.

I obviously do not understand how your argument even mirrors Godel's, much less how it leads to its conclusion. You need to spell it out - remember, this is supposed to be an encyclopedia, a reference source. If you are unable or unwilling to actually demonstrate your proof, you need to remove it.
 * Apparently you don't understand Godel's argument, so no surprise. I aim for brevity.  If Godel's argument is expanded in the article, I'll tie mine more closely to it.
 * It doesn't matter whether or not I understand Godel's argument. In fact, with the hope of making this a better article, let's assume I, like the average person stumbling on this article don't understand the proof.  You, as the author of the so-called proof of God's non-existence, need to actually establish God's non-existence!  If you can't, or for some insane reason wont, then it is not a proof and no one should be expected to accept it, and if no one should be expected to accept it, it doesn't belong in an encyclopedia, as you are neither a historical figure nor a celebrity and thus your opinions and half-truths are not significant.  If you can construct a full proof, go for it.  Include it.  If you can't, or wont, don't bother doing it halfway.
 * It is Godel's proof with a couple of substitutions. It is available elsewhere.  Someone should put more of it in this article, but between the Wikipedia server, a buggy computer here, and your comments, I can't get to higher priorities.
 * Yeah, the server issues are pretty obnoxious. If you don't want to respond to my comments, don't.  I thought this would be a good way to prevent an all-out edit war and maybe get to a point where we're starting with some of the same ideas.  Anyway, it is not Godel's proof with a couple substitutions.  Godel attempted to rigorously set up a system wherein God must possess all positive properties, and these properties include existence.  You seem to be trying to set up a system wherein you prove God can't exist because negative properties (like evil) don't exist - in other words, formalizing the argument from evil.  Its a fine argument (though your formalization isn't especially rigorous), but it is not "Godel's proof with a couple of substitutions".

I don't necessarily think it is improper to criticize religion. I do, however, think that this is not the place for it. Perhaps you can start an article at religious criticism or something. You can present valid counters to Godel's argument (and I have been willing to accept some of yours as valid throughout this discussion), but if all you are doing is using this forum as a way to express your anti-religious POV, this is not the place for it, and Fairandbalanced is not an appropriate name to use. Now, as I said (and you seem to think I said the opposite of what I said for some reason), if you are really, seriously interested in pointing out reasonable flaws in the argument or actually research the proof and present common retorts, that is fine, but if you aren't going to take your arguments seriously there is no reason for me to do so either.
 * Showing that Godel's "God" does not conform to standard doctrines and has not been shown to exist is not a criticism of religion.
 * You haven't yet shown that you even understand standard concepts of God, much less Godel's personal concept of God or anyone else's. You can't construct a very valid criticism if you aren't even willing to explore what people mean when they say "God".
 * This belongs in Talk:God, not here.
 * Considering you are writing here, and that this is an article about a proof of God's existence, I'm sure this is a fine place for it. Normally I'm fine with putting things where they belong, but this is a cop-out.

Seth Mahoney 17:33, 3 Oct 2003 (UTC)
 * Fairandbalanced 18:52, 6 Oct 2003 (UTC)
 * Fairandbalanced 00:56, 8 Oct 2003 (UTC)

Ohms
Why, out of curiosity, are you so resistant to adding an actual detailed description of your version of Godel's proof? As this is an encyclopedia article, it really needs an explanation if it is going to appear in here, and as you seem to be the only one at the moment who understands what it is you're trying to say, it makes sense to put one in.

Last try
Here is your "proof": One can slightly modify the definitions to prove the nonexistence of any God. This requires only two changes:


 * 1) Substitute "incompatible with God" for "positive". Since God is supposed to be "good" and therefore would never allow existence of all possible worlds, such properties must exist. (See the the problem of evil.)
 * 2) G is the "no-God" property and an object x that has any no-God property prevents the existence of a God, for "incompatibility" means the two cannot coexist.

The nonexistence of God follows by the logic of the original proof.

Proposition 1 states that we can substitute "incompatible with God" for "positive". If we make this replacement in the original proof, we are looking for a being that possesses all of the properties which we have deemed incompatible with Godel's God. It would seem to be reasonable to suggest that such properties would stand in opposition to Godel's concept of God. One of the properties Godel defines as positive (and that is therefore possessed by God) is existence. Therefore the object we are searching for, the one that possesses all "no-God" properties, must possess the property of non-existence, and our search is in vain.

Proposition 1 also doesn't make sense. "Substitute 'incompatible with God' for 'positive'" doesn't actually relate to the next sentence "Since God is supposed to be good..." I think I know where you're trying to go here, but again, you seem to refuse to explain your thinking, so there is a good chance that if I edit it you aren't going to like the result.

Proposition 1 also states that a good God wouldn't allow the existence of all possible worlds, but there is no reason to assume that just because something is logically possible it actually exists, so the mere logical possibility of a world's existence doesn't actually say anything about God. Now, there is a catch here. If God exists and is active in the world, the number of logically possible worlds drops dramatically.

Proposition 1 also seems to say that because God wouldn't allow something to exist, such things must exist: "therefore would never allow existence of all possible worlds, such properties must exist". This is ridiculous.

Proposition 2 makes absolutely no sense, especially in conjunction with proposition 1. You seem to be saying that the existence of any object with a property that is incompatible with the existence of the Theistic God prevents such a God from existing, and that God's nonexistence follows by the logic of the original proof, but the original proof states that God must exist because God possesses all positive properties and one of those properties is existing. Now, according to your version no incompatible objects must exist because existence is not a required property for any of your objects. Further, it does not follow the logic of the original proof because the original proof requires God to possess ALL positive properties and if we replace "positive" with "incompatible with God" we have to require our object to possess all incompatible properties, which, as I suggested above, may include non-existence. Now, as stated, and as I have said before, your argument seems to be a version of the problem of evil, but it has nothing whatsoever to do with Godel's proof. If you aren't willing to modify it to make its relationship clearer, I will.


 * I realized that I had not proved such a property exists in every world, so I removed the nonexistence proof. The arbitrariness of positiveness shows the exisence "proof" is nonsense anyway, so using it is pointless.


 * I wish you would stop trying to insist the proof applies only to your concept of God because it is a waste of time to continually correct that.
 * Fairandbalanced 21:17, 20 Oct 2003 (UTC)


 * I never said the proof only applies to my concept of God - I have no concept of God. I said that Godel wrote it regarding his concept of God.  Regardless, your objections are a lot clearer now and pretty good.  Thanks for putting the time into it!  I still have one issue, which would probably be pretty easy to resolve: in critique 3 you say, "If 'positive' is given some standard moral or utilitarian meaning when applicable, it is not difficult to find counterexamples."  If I'm reading it correctly, I appreciate where you're going, but it isn't clear what you mean by counterexamples.  Do you mean that once "positive" is clearly defined there are instances where either some positive attributes do not apply to the Biblical God, or that such attributes may be inconsistent or contradictory?
 * Seth Mahoney 06:52, 22 Oct 2003 (UTC)


 * I hope this article get some rest soon.

I said the definitions provided apply to any object x with property G(x). There is no uniqueness proof nor any assertion that one is superior to any other. Godel's own concept of a deity is relevant only as a historical note. I meant that one can find properties that would be positive for some objects and negative for others. It is not necessary that they be important for the godlike object. I lost interest in looking for specifics. Has anyone else noticed the problem with the arbitrariness of positiveness? It took me awhile to notice it, but it is hard to believe that it was never noticed before. I just kept looking because I knew there must be some simple absurdity about this proof of a counterfactual.


 * Ugh. Not again.  Okay, here goes.
 * 1. Just because you don't like or agree with a proposition doesn't make it counterfactual.
 * Recognizing that it is counterfactual reveals that the proof must be flawed. Apparently you are saying that you agree with propositions you know to be counterfactual.
 * No, I'm saying that I'm not willing to throw out an argument because I disagree with its conclusion.


 * 2. I agree that there are properties that are positive for some objects and not for others, but I have not seen any place where Godel asserts that a property that is positive for one is positive for all.
 * Point out where he says a property is positive for some objects and negative for others. He doesn't because your version would make a mockery of the proof.
 * It doesn't have to. That is the commonsense way of looking at positive.  If Godel wanted to say that he was using a nonstandard definition, it would be up to him to explicately state that.


 * 3. I have no idea why you bring up importance.  I haven't, Godel hasn't, the article hasn't.  Where did this come from?
 * You like to claim that your God is more important than all the others derived from the proof, so it is necessary to emphasize that it is not.
 * Okay, for like the twentieth time, I'm not a Christian, I'm not a Theist, I'm not a Jew or a Muslim or a Hindu or a Zoroastrian or a Buddhist or anything of the sort. There is no "my God".  Next, this article isn't a response to me.  You should be writing it for anyone who comes across the page, not just for me and people you think are like me.  Next, there is one God necessarily derived from the proof, and any other Gods so derived would be identical to Him.


 * 4. Yeah, I've noticed the problem of the arbitrariness of positiveness.  I think it is the proof's biggest weakness.
 * I didn't see you mentioning that it invalidated the "proof", which I put in quotes because it obviously does not prove all such objects exist and are gods.
 * I realize that is why you put it in quotes, but it looks snotty and its not up to you as an author of this article to decide whether or not the proof proves anything. It is a logical and mathematical proof, as defined in the American Heritage Dictionary thusly: "The validation of a proposition by application of specified rules, as of induction or deduction, to assumptions, axioms, and sequentially derived conclusions."


 * 5. Regarding your constant rewrite, Godel is saying that only an object that possesses all positive properties, that is, all properties that are positive for God, is God.  The conditions of the proof cannot be satisfied by allowing for everyone's arbitrarily chosen set of positive properties for God and then saying that each set defines a God that must necessarily exist - there is one set of properties (presumably Godel's) that defines God, and no other.  The reason the proof supposedly works is that God is defined (by Godel) as the being that possesses all positive properties (for a God) and one of these properties is existence, which suggests that, by definition, God must exist.
 * Go back to school and learn to read. Then read the definitions again.
 * Once again, rather than actually respond by reasoning you respond with a personal attack. Bleh.
 * You are resorting to the usual circular Christian reasoning: "Good exists", "God is good", "Good is what God is", "Therefore there is a God."
 * No, I am saying that the proof works thusly:
 * a. God is defined as the being that possesses all positive properties (for a God - in the same way that a tasty apple can be defined as the thing that possesses all the positive properties for an apple).
 * b. One of these properties is that the being exists.
 * Therefore, God exists.
 * I'm not saying that this proves God exists. I'm saying that this is, succinctly, Godel's proof.  I'm not interested in whether or not Godel has proved God exists.  I'm interested in accurately describing Godel's proof and reasonable objections to the proof based on the proof its self, not some ridiculous misreading of it.


 * 6. Whether or not you agree with Godel's proof or think that it actually proves God exists (Godel didn't seem to) doesn't matter.  When you make a great mathematical discovery you can have your own set of articles in encyclopedias that talk about your beliefs.
 * I assume Godel has a Wikipedia article.
 * He has more than one. Like you could have if you made a major mathematical discovery, he has several - a bio page, pages about his other proofs, and a page about his version of Anselm's proof.  I assume it was put on a separate page because its a big enough topic to warrant this.


 * 7. If you're not interested in an article, don't contribute!  Focus on the ones you're actually interested in.
 * So you can turn it into a religious tract?
 * Once again, I have no interest in turning anything into a "religious tract", though your dogmatic stance is showing again (disappointing, after you had been making some real progress on the article, weeding out the weaker counterarguments and strengthening the good ones). I am not religious in any way.  I don't want this article to be anything more than it should be, which is a description of an interesting thing an interesting guy did and possibly some commonly used and really good counterarguments.  If you keep insisting that the proof is saying something other than what it is saying, your counterarguments aren't going to be very good and if you keep insisting that God (that is, the Theistic God) is something other than He is defined to be, your arguments aren't going to be very convincing.  Like I said before, if you're not interested in an article, or not actually interested in making it better rather than distinctly POV, walk away.  I've read some of your other contributions and they're usually pretty good, which makes the half-assed ones here that much more frustrating.
 * Fairandbalanced 14:29, 24 Oct 2003 (UTC)

Another edit war?
If you continue to reinsert your ridiculous interpretation instead of using the definitions initiated by Godel, I'm just going to revert. This is a waste of time. The links referred to in the article use "God-like" rather than "God" consistently. Did Godel actually specify that a God-like object was a God within his proof, or is that your work? Fairandbalanced 07:13, 25 Oct 2003 (UTC)


 * Godel only uses the word God in his proof, not god, not a god, not a God, and not God-like. He is defining a single thing, God.  You can go to your library and check out 'Collected Works: Unpublished Essays & Lectures, Volume III' to confirm this.  The proof appears on page 403.  Whether or not a lesser god may be defined as an object that has some positive properties is not a subject he brings up, and is therefore not appropriate for this article.  However, it would seem to me that an object that possesses a subset of the God properties is not God, as follows:


 * 1. A god can be defined as any being that possesses a subset of all positive properties.
 * 2. Intelligence is a positive property.
 * 3. I am intelligent.
 * I am a god.
 * I am a god.


 * Since I am not a god, but a human being, this proof fails. Since no one would consider the inference invalid and propositions 2 and 3 are both true and the conclusion is false, I must conclude that proposition 1 is also false.


 * Now, Godel also has a specific conception of God in mind (the fact that he chose to define God as the being that possesses all positive properties tells us as much), so the 'meaning' of the proof is not that each interpretation of what is and is not positive constitutes a God that necessarily exists, but that there is one conception of God that relates to the (presumed) reality of God and this conception of God's properties is the set of all positive properties.


 * Next, as far as conflicting properties goes, Godel at least thought he had taken care of this with $$M(\exists x)G(x)$$, which he backs up in the proof. Generally, the argument that the properties often ascribed to God not only conflict between conceptions of God but even within a single conception is a good counter, but probably not in this case.


 * Last, Godel doesn't clearly define the positiveness of properties as inedependent of properties or anything else, because he doesn't clearly define what he means by "positive property". Further, even if he had done so it doesn't seem that (after a reexamination of the proof) a comparison to real-world properties is an effective counterargument because he (vaguely) defines positive properties as being positive "in the moral aesthetic sense" - meaning that God is good, beautiful, intelligent, etc.  The vagueness with which he defines positive is probably your best counterargument (maybe tied with the fact that Godel's conception of God isn't necessarily that of any particular religion, though Godel may not have been interested in describing the standard Christian God but rather something more akin to the Platonic or Neoplatonic conception of God).


 * In general, once you put effort into them your arguments have been good, but you can't hold on to what seems to be your frustration with and preconceptions about religion when you examine this proof - you have to take it for what it is and what it says.
 * Seth Mahoney 19:20, 27 Oct 2003 (UTC)

I removed the argument about subsets because it did not seem correct, so I have no idea why you bring it up again. The positiveness definition is quite clear, so I reverted to erase your ridiculous interpretation. If Godel asserted that properties are positive "in the moral aesthetic sense", the proof is invalid because:
 * 1) Properties that are not positive must be negative.
 * 2) Valid predicates about some objects have no "moral aesthetic sense" whatsoever, and thus can be neither positive nor negative in that sense.

There may be no two people who find all the same properties "positive" "in the moral aesthetic sense", so there can be no God according to that interpretation. Anyway, it is apparently his commentary, not part of the proof.

Until you start making sense, I'm not going to bother editing.


 * Okay, here goes, one more time:
 * 1. Godel NEVER uses the phrase "God-like".  He EXCLUSIVELY uses the term "God".
 * 2. Your first argument seems to be saying:
 * a. The selection of positive properties is arbitrary because what is positive (in the moral-aesthetic sense) to one person is not necessarily positive to all.
 * b. Since the argument requires necessary existence to be positive, all conceptions of God that include all positive properties (as defined by an individual) must equally necessarily exist.
 * c. This is absurd.
 * This is fine, but Godel doesn't seem to think that the positiveness of a property is something that can be reasonably assigned by an individual - the positiveness is inherent in either the property or the property-object combination (he isn't clear about which). The last sentence also seems to bring up the idea that Gods in logically possible worlds must actually exist, which rests on the premise that the worlds associated with these Gods must also exist.  If this is not what you mean to say, you need to be more clear.
 * 3. The positiveness definition is not at all clear.  There is nowhere in the proof that he says that what is positive for one object is also positive for all, though as I said above, even if he has this in mind, it doesn't matter what attributes are ascribed to any specific conception of the Theistic God - the only definition that matters for the proof is Godel's, and according to Godel God must possess every moral-aesthetically positive property, including existence.  Unless you can think of a combination of moral-aesthetic properties that are contradictory, your third argument isn't appropriate for this article.
 * 4. You need to quit using "a god" - the correct term here is "God", "conceptions of God", etc.
 * 5. Again, there is no reason to believe that logically possible worlds (and therefore the versions of God associated with them) actually exist - a logically possible world is a world that exists in a thought experiment, not in reality.  You seem to rely on this idea in your second and fifth arguments.
 * 6. Have you actually read the proof?  Again, it seems that you are more venting your frustration with general religious contradictions and abuses than actually examining Godel's proof its self.
 * 7. You still need to explain (in the article) what you mean by "it is not difficult to find counterexamples".
 * 8. Godel defines positive as being positive in the moral-aesthetic sense, or as pure attribution, in the proof its self, not in a footnote or commentary.  It doesn't matter anyway.  The point is that Godel, however vaguely, defined positive.  Even if he defined it in a footnote, he still defined it.
 * 9. Your objection stated above is virtually identical to Andersons, and is a good one.


 * 10. Claiming that you will wait until I start making sense (though you seem to equate "disagreeing with you" to "making sense") before editing an article suggests that you aren't really concerned with the quality of your output. This is disappointing.
 * 162.119.64.114 18:36, 31 Oct 2003 (UTC)

If Godel used the term "God" in his version of the proof, then I have no objection to it in reference to the same entity. It is odd that the obviously Christian site linked from the article does not use it.

As to positiveness being relative to objects, your version is degrading to Godel because it trivializes his proof.

Most of your comments are no longer intelligible. I had thought we finally achieved a detente, but apparently you are on some sort of crusade here.

I could add a comment about the "m-a sense," although it makes the section even longer. I had tried to keep it short in order to let the logic dominate.

When you figure out exactly how positiveness can be assigned to make "God" unique, consistent and complete, describe your solution. Fairandbalanced 02:13, 1 Nov 2003 (UTC)


 * Come on, seriously. You find it unintelligible when I say, "logically possible worlds don't actually have to exist", "you need to explain what you mean by 'it is not difficult to find counterexamples'", "your objection is good and resembles Andersons" and "you shouldn't wait until I make sense (to you) to start improving your article"?  You seem to have more than enough intelligence to understand those ideas.  As far as the others, they aren't especially complicated either.
 * Seth Mahoney 02:34, 1 Nov 2003 (UTC)

I don't see why the possible vs. actual stuff is important now, so why bother with it again?

If you want to argue about positiveness in the article, I can counter your stuff easily, so it would just make the objections much longer than the proof. Or I can just revert. Don't you have anything better to do? Fairandbalanced 21:02, 5 Nov 2003 (UTC)


 * Your text: "Since the proof is equally valid for all such selections, it proves that in every world, for almost every set of properties, there necessarily exists exactly one object with that set of properties, and every one is God." I am saying that if something in or part of a world necessarily exists, that world also necessarily exists, and this existence of logically possible worlds is not the case.  My objection is that you still seem to be holding on to this idea that logically possible worlds must exist, when they in fact don't have to, when in fact there is no reason that any world except our own exists (and possibly not even that one).  Modal logic, thought experiments, and all other tools that make use of the idea of logically possible worlds don't demand that such worlds exist, they are just ways of saying "what if?"  It seems to me that you are saying that there are worlds that are logically possible where the definition of God varies because what is or is not positive varies in those worlds.  This is a fine argument, though I think it values the words (or symbols) Godel uses over the meaning he intends, and thus does not actually address the argument.  It does not need to be extended to say that these versions of God necessarily exist, because for all intents and purposes the worlds these Gods would inhabit or would have created do not exist.
 * As far as the positiveness issue, I am trying to point out that your method for determining positiveness doesn't seem to be Godel's, so you are making an argument that doesn't address what he is saying. Whether or not you can counter my objections easily isn't what is important - you do not counter or even take into account very valid objections in the article.  I also bring this up because in the article you say "Gödel clearly defines positiveness is an attribute of properties, independent from objects" (incidentally, you should change that "is" to an "as") when in fact Godel makes no such definition.  Look at the proof for yourself if you don't believe me.  In fact, look at it either way if you are going to write about it.
 * Are you actually saying that if you can't counter my objections you will just revert the article?
 * You still need to explain what you mean by "it is not difficult to find counterexamples". I am not saying that this argument in general is necessarily flawed, but that sentence's meaning is not at all clear.
 * There is still a further issue in that Godel is describing a Theistic God, not necessarily the one you are raising objections to with your rant about contradictory properties.
 * Seth Mahoney 05:55, 7 Nov 2003 (UTC)

Your arguments are so convoluted I can't make sense of them. Perhaps you are a philosopher? The proof asserts existence in an actual world. The definitions and axioms essential to the proof render all other assumptions irrelevant. I think you are denying those facts.

Reason rather than instigation
Yeah, yeah, for any counterexample you can find some objection. I'm not going to bother endlessly discussing this crap in the article. For the same reason, I'll revert your changes that just add more layers of complexity with no value.

But I see you are still ranting onward. Must be a boring life. Fairandbalanced 22:54, 13 Nov 2003 (UTC)


 * Urgh! Again, rather than actually respond to objections you toss them aside - saying, essentially, "it is what I think that matters, not what is reasonable."  You embark in a cooperative venture (Wikipedia) then refuse to actually approach it cooperatively when you come across someone who objects to your lame-brained concepts.  You parade words like "facts" when, in fact, you mean "my misunderstandings of the topic".  Then!  You present arguments that don't even address the issue and sugget mine are convoluted!  Sigh.  Look, I'll put it to you in the plainest english I can:


 * 1) Logically possible worlds do not necessarily have any existence.  It is part of modal logic that we pretend they might exist.  Your arguments still take this pretending for reality.
 * 2) Godel does NOT clearly define positiveness, other than to say that it is positive in the moral-aesthetic sense, whatever that really means.  Your statement that Godel clearly defines positiveness is just wrong.
 * 3) You clearly are saying that if you can't actually address my objections you will simply revert the article.  And you talk about how my life must be boring!  At least I write, instead of feverishly clicking, hoping that no one has changed my inane linguistic flatulence.
 * 4) You say, "it is not difficult to find counterexamples", yet you don't say what you are finding counterexamples to, or even what you are talking about.  Just say it!  Say it in the talk page if you're too shy to write it out in the article!
 * 5) You might check out neoplatonism, theism, deism, panentheism, zoroastrianism, Mithraism, the form of the good, gnosticism, etc. if you are actually interested in religious proofs, even if only to refute them - at least with some study you might actually know what you are talking about.  I mean really, get over this "I'm sixteen" nonsense and start addressing the world through reason rather than blind assertion.
 * Seth Mahoney 06:12, 15 Nov 2003 (UTC)

Since you are attributing your own arguments to me, you are obviously delusional. I no longer bother to read your version. Go away, get a life. Fairandbalanced 22:26, 5 Dec 2003 (UTC)

When have I said that logically possible worlds must exist, or based an argument on that premise, that Godel clearly defines positiveness as an attribute of properties, or based an argument on that premise, that, rather than addressing your arguments I will simply revert the article? How could I possibly be attributing the statement "'it is not difficult to find counterexamples' doesn't make any sense" to you? And if you no longer bother to read "my version", how could you possibly know whether or not I am attributing my own arguments to you? Seth Mahoney 19:47, 6 Dec 2003 (UTC)

Go find where Gödel says positiveness is an attribute of objects rather than properties. Then find the properties universally agreed to be "positive" in a "moral aesthetic sense." Then you will have a point to make. Fairandbalanced 22:20, 9 Dec 2003 (UTC)

Go find where Gödel "clearly defines positiveness is an attribute of properties, independent from objects" (might want to correct your grammar, btw). I totally agree that it is nigh-on impossible to find two people who agree which properties might be positive in the moral-aesthetic sense, let alone two people who agree on what it might mean to say that something is positive in the moral-aesthetic sense. I'm not saying that there are no valid objections to this particular argument, just that many of the ones you have been raising are either questionable or don't make sense as written - and since you refuse to rewrite them so that they DO make sense...
 * Seth Mahoney 18:21, 12 Dec 2003 (UTC)

Fair warning - this page is liable to get protected if the edit war doesn't stop. Pakaran 18:26, 5 Jan 2004 (UTC)

Here's hoping it stops then. ::Seth Mahoney 18:46, 5 Jan 2004 (UTC)

Fairandbalanced: 1. Your page is not consistent with Godel's writing. 2. You still haven't shown where Godel (not someone else who wrote about Godel, and not just your arbitrary opinion of what Godel meant) "clearly defines positiveness is an attribute of properties, independent of objects" (incidentally, you STILL need to change that "is" to an "as")  and, 3, since my last revert changes have been made that should be left in the article - if you choose to revert again (discussion might be more appropriate, given the warning someone left above), you should incorporate them (also, you should change that "is" to an "as" - there's no need to keep restoring your typos).

All that said, since there hadn't been any reverts in what, 20 days(?), I was starting to worry - glad to know you're still alive.
 * Seth Mahoney 18:36, 29 Jan 2004 (UTC)

--

Very good article, I also like how you explain the basics first (necessary vs. contingent) and build a comprehensive article.

Please everyone take a look at some of the mathematical articles starting with Atiyah-Singer_index_theorem (and the links coming out of there including Laplacian). These articles give no back ground, and look like proofs ripped out of a graduate mathematics text book. There is nothing wrong with having very very complex things in an article, but you have to build somesort of foundation or this isnt an encyclopedia, its some text book then.--ShaunMacPherson 10:44, 28 Mar 2004 (UTC)

Reasoning behind revert
-Seth Mahoney 06:29, 26 May 2004 (UTC)
 * 1) I believe it is more important to explain some of Godel's reasoning for not attempting to prove God's uniqueness rather than criticize the proof, which I would remind editors, Godel didn't even believe absolutely proved God's existence, and is a part of this encyclopedia for historical and biographical reasons, as well as for those who have an interest in formal logic, not as an article saying, "see! I have proven God's existence!  Bow down and worship him!"
 * 2) The goal of any logical or mathematical proof is essentially a tautology, to demonstrate that x = x (more specifically, that the left hand term equals the right hand term).
 * 3) Nowhere does Godel define positiveness to be either an attribute of properties alone or to properties only when applied to specific objects, though common sense would suggest that many of the properties Godel had in mind only have meaning when applied to objects.
 * 4) God's color, or lack thereof, is irrelevant to the article, and irrelevant to the proof. Godel doesn't assert that positiveness, in the sense that he means here, can be meaningfully applied to all properties.
 * 5) * Eh? From the article:  "Axiom 4: If P is a property, then either P or its negation is positive, but not both." Capedia 06:52, 24 August 2006 (UTC)
 * 6) To say that different sets of positive properties results in different Gods in different worlds is irrelevant unless we assume that logically possible worlds have to exist (and therefore their logically possible Gods), which is not the case. The idea of logically possible worlds, in this case, amounts to little more than a thought experiment.
 * 7) Even if we are proving the existence of multiple Gods rather than a single, distinct God, God is the appropriate word to use, rather than gods, as each God is purportedly the monotheistic God of each world.

one world
very nice article. The result of the existence of only a single world may be seen as an unintended, but all the more satisfying by-product, doing away with parallel universes dab 11:42, 2 Nov 2004 (UTC)

Another criticism
Here's something I thought of while reading this article. If a property P is positive and P entails Q, then by axiom 2, Q is positive. However, let Q be the (trivial) property that is always true (let's call it 1): for all x, Q(x) holds. Assuming that there is any positive property at all, then Q must be positive. But isn't that a contradiction to axiom 1? Of course, axiom 1 is more of a philosophical axiom than a mathematical one, so I'm not necessarily talking about contradictions in the strict mathematical sense, but can the trivially true property be considered "positive" in a moral sense? (This is probably similar to asking whether 0 is a positive integer or not - something I'd also say is not the case, since if 0 was positive, then -0 must be negative, which is a contradiction because no number should be both positive and negative at the same time. The analogy is not good, of course, since the negation of 1 is not 1, but I still think it's a similar philosophical issue.)

I'm pretty sure someone else must've wondered about that already - does anyone know anything about that? If a reference can be found, it should probably be added to the "Critique" section. -- Schnee (cheeks clone) 14:58, 23 Mar 2005 (UTC)

I came to this talk page to post an objection to axiom 2, and here I find that Schnee already posted a very similar argument. My hat off to Schnee. I was going to suggest that a property can be positive if the majority of other properties it entails are positive; it is not obviously required that all properties it entails be positive. For instance, the property P="being able to turn a single living rabbit into an infinite supply of a wonderdrug that cures all human disease forever" is quite arguably positive, but clearly entails the property Q="being able to kill a rabbit" which is not obviously positive by itself. (Rabbit lovers who don't believe that any amount of healing is worth a single rabbit please substitute other equivalent properties...) Like Schnee, I presume some philosopher must have pointed out this obvious problem. Does anybody know a reference for it, so we can mention it without OR? - Mglg 01:14, 14 June 2006 (UTC)

Mistake in 'derivation' section
It says that the god property is the infinite conjunction of all the positive properties, but it's only defined as being coextensive with this infinite conjunction. More importantly, it only follows from axiom 3 that a finite conjunction of positive properties is itself positive. The positivity of the god property doesn't follow from axioms 2 and 4 either, unless there are a finite number of atomic positive properties, in which case the god property would follow from the finite conjunction of those, which would be positive by axiom 3. Michael Keats 18:39, 15 January 2007 (UTC)

"religious"
I think we should be careful about claiming that Gödel was or was not "religious", a fairly ambiguous word. There is no question that Gödel believed in the existence of something beyond the material world. Religion, however, is (at least in my usage of the term) more a matter of social observance than personal belief (there are lots of religious people who don't believe in God, and non-religious people who do). I am not aware that he was a church-goer (or synagogue- or mosque- or temple-goer), so in that sense he was probably not religious. --Trovatore 21:51, 11 April 2007 (UTC)

See the discussion on his talk page. "I went home with Einstein almost every day and talked about philosophy, politics, and the conditions of America. Einstein was democratically inclined. His religion is much more abstract, like that of Spinoza and Indian philosophy. Mine is more similar to church religion. Spinoza's God is less than a person. Mine is more than a person, because God can't be less than a person. He can play the role of a person." was a quote. 98.198.83.12 (talk) 16:16, 28 January 2010 (UTC)

My Edits to the Biographical/Historical data about the Ontological Proof
I plan to add citations for the biographical/historical data about the proof, correcting what I don't think can be verified as I go. I've recently studied the sources on this proof and Gödel's life and they are fresh in my mind. If I change something which can be verified, I hope Wikipedians will revert with citation.

Guidelines for Evidence: Mathematicians are notoriously lousy biographers, and they don't get any better when talking about Gödel. When I was in grad school in CS (~1977) Gödel was alive and there was much talk about him. I can't prove that everything I was told was wrong, but I do know that none of it is verified in first-hand or careful scholarly sources.

It's therefore necessary to be careful in evaluating evidence. I use these rules:

1.) Nothing second-hand is considered evidence unless from a source carefully edited for biographical accuracy.  The only secondary sources I know of that meet this criterion are the authoritative biography of Gödel by John Dawson, and the apparatus in Gödel's Collected Works.

2.) Other math books, even when scholarly, and even when punctilious about math, when they veer into biography usually report stories which if they can be traced to a source at all, have changed in the telling.  I've learned to discount anything in them not fully confirmed by another source.

3.) While lousy biographers, mathematicians are good witnesses.  They are usually accurate about what they observe first-hand.  I treat all first-hand accounts as evidence.

My rewritings will obey the above criteria and always be accompanied with a citation.

Jeffreykegler (talk) 23:10, 23 February 2008 (UTC)

Explaining my edit of the historical material
I included material about Gödel's beliefs, to the extent they are relevant to the subject matter of the proof. It can be useful in trying to understand what Gödel intended to know if he intended the proof to be convincing, or merely as a logical exercise. To this extent, it's relevant whether he was a believer or not.

Some scholars have also seen Gödel's assumptions as opening the way to proving the existence of ghosts. In evaluating such claims it's useful to know that Gödel believed in a very wide variety of supernatural entities, ghosts among them (see Dawson 1997, p 165).

In keeping the neutral point of view, I was presented with a real problem of evidence. With regard to Gödel's intent, we have Morgenstern's diary entry, contemporaneous, from a usually reliable source in a good position to know, specifically addressing that question and quoting Gödel. Ordinarily, you'd just quote a source like that and that would end the question, and a few commentators do exactly that.

The problem is that Morgenstern's report that Gödel did not believe in God is contradicted by just about every other piece of evidence there is. Dawson, his definitive biographer states outright that Gödel (p. 6) was a believer. Hao Wang who recorded more of Gödel's philosophy then anyone shows a man who many would call not just religious, but superstitious.

The solution I adopted was to quote Morgenstern (I didn't think there was a fair way to ignore him), then cite some of the overwhelming evidence that conflicts with his account of Gödel's motives for doing the proof.

Some material I eliminated because I simply could not find any backing for it in the sources. In particular I regret replacing this:

"Although Gödel was religious, he never published his proof because he feared that it would be mistaken as establishing God's existence beyond doubt."

I thought this was a very intriguing idea. It hints at a Gödelian inconsistency result -- that God may exist, but if proof beyond doubt of his existence came out, some kind of harm might result. I like to think Gödel would have been intrigued by this idea. The problem is that nothing in the record indicates that Gödel had any objection to establishing God's existence beyond doubt. As I say, I like this idea, and I'd been pleased if someone finds I've overlooked evidence in support of it.

Jeffreykegler (talk) 01:57, 25 February 2008 (UTC)

A old transcription of the proof
The annotated proof in this transcript is somewhat more traceable than the proof in the article.

http://img253.imageshack.us/my.php?image=goedelsontologicalproofzh0.jpg

Maybe one will add annotations to the proof in the article, too. Perhaps maybe one will even upload this transcription to Wikipedia.

Two remarks: 1. I've never seen the original of Gödel's proof. So I do not know whether the annotations are from Gödel himself or whether they have been added later by someone else. 2. I guess the initials J.R.B. in this transcript stand for 'Julius Richard Büchi'.

--87.78.160.96 (talk) 21:26, 25 May 2008 (UTC)

"disavowal of belief"
The article currently says
 * Morgenstern's diary is an important and usually reliable source for Gödel's later years, but Gödel's disavowal of belief in the August 1970 diary entry is strongly at odds with extensive evidence in rest of the record.

But the thing is, it's not clear, even taking Morgenstern's diary at face value, that there was any disavowal of belief. What the diary says is that Goedel wouldn't publish for fear that people would think that he believed in God. This does not license the inference that he didn't believe in God, but only the inference that he didn't want people to infer that he did believe in God, on the basis of having published the argument.

Needs to be rephrased, but at the moment I don't have a suggested wording.

--Trovatore (talk) 07:14, 3 September 2008 (UTC)


 * I've reworded that passage. In ordinary idiomatic English, there's a clear implication that when saying "I don't want people thinking I believe in God", that I do not.  To say that I do, but don't want people to find that out, I would say "I don't want people to know I believe in God".


 * On the other hand, Morgenstern's original is in German, which I do not read well enough to pick up this kind of nuance, and the implication, very strong in the English translation, may be weaker or absent in the original German.


 * On another matter in similar circumstances, Morgenstern's diary would be accepted as conclusive evidence. In those days Morgenstern knew Gödel better than anybody except Adele, Gödel's wife.  In this case, Morgenstern's the only contemporary account of Gödel's motivations for the ontological proof, and it's from from a reliable, well-informed witness.


 * My conviction is that the evidence clearly shows that Gödel did believe in God, and the article to be accurate and complete must say so. That makes all the more important to be fair to important evidence which does not fit the conclusion.  There is some controversy about Gödel's belief in God, and most of the those who think he was an atheist draw that conclusion from the Morgenstern diary entry.  It is hard to explain why Morgenstern wrote what he did, other than to try to conclude that he wrote the entry hastily and his wording didn't come out right.

Jeffreykegler (talk) 17:08, 3 September 2008 (UTC)


 * I agree that there's strong evidence Goedel believed in God, but I still don't see the diary entry as necessarily indicating otherwise. If he had said, à propos of nothing, "I don't want people thinking I believe in God", then sure, that would be a strong implication. But in context it seems to me that it could easily be read that he didn't want people inferring, from the publication of the proof, that he believed in God, because that would be an invalid inference, and he doesn't want people making invalid inferences about his personal beliefs, which are not part of the discussion. For as precise a thinker as Goedel this is not an especially subtle distinction. --Trovatore (talk) 20:22, 3 September 2008 (UTC)


 * Ok I see your point.  And your reading does make more sense of the Morgenstern diary entry than any other I've heard.  Morgenstern, knowing this was a sensitive matter, might have been more or less quoting Gödel exactly.  For just about anybody but Kurt Gödel, I'd say this was an over-labored reading, but this is Kurt Gödel, and it strikes me as entirely possible your reading of his words is correct.  In fact, I can't think of a better way to explain the evidence.


 * What to do about it is another question. Every source I know of that discusses the Morgenstern diary entry (as opposed to merely quoting it, then changing the subject) takes the implication that Gödel was an atheist, whether they argue with that implication or agree with it.  Your reading AFAIK is original, which is a no-no in Wikipedia, so it can't go in the article (unless you publish it somewhere in which case I'll be happy to refer to it in a footnote).


 * Best thing with the current sources available is just go neutral, saying that most (and in fact AFAIK all) sources take the implication that Gödel was an atheist, include one or two sources (Sobel is the most important on this), then proceed to give the evidence that Gödel was a believer.--Jeffreykegler (talk) 01:09, 4 September 2008 (UTC)


 * Don't you mean "Most sources indicate that Morgenstern's interpretation of Godel's beliefs was that he was an atheist." Because I'm pretty sure, from reading his article here on Wikipedia, that most sources indicate that he was a theist. 98.198.83.12 (talk) 16:24, 28 January 2010 (UTC)

Novel based on Gödel's Ontological Argument
I've added The God Proof, my novel based on Gödel's Ontological Argument to the External References. As it happens, it is the only full length book of any sort, fiction or non-fiction, scholarly or non-scholarly, entirely devoted to Gödel's Ontological Argument. It's freely available as an electronic download.

I hope this edit is useful, and believe it is appropriate, and consistent with WP:COS. But in the interests of full disclosure, I also thought it appropriate to alert other editors with this note.

--Jeffreykegler (talk) 20:07, 4 January 2009 (UTC)


 * It doesn't seem too bad a novel; certainly I'd prefer if it was even a little bit notable in a book sense, but I at least at not going to object to it. --Gwern (contribs) 05:24 10 January 2009 (GMT)

Axiom 3 and the compactness theorem
Someone at IP address 195.189.104.34 left a note here saying simply: "The compactness theorm [sic] proves axiom 3". I'm not sure "axiom 3" here means the one that says that any conjunction of positive properties is positive ("Axiom 3" in the article) or the one that says that "having all positive properties" is itself a positive property ("Ax. 3" in the initial formal presentation in the article). Neither of these seems to me to follow from the compactness theorem, and indeed I don't see how they could. Perhaps one can use the compactness theorem to show that certain properties that the proof requires positivity to have are consistent -- e.g., that if you can have something with all finite combinations of positive properties then you can have something with all positive properties, or something like that -- but (1) that doesn't seem to have much to do with proving axiom 3, and (2) I think we need to see more details :-). 195.189.104.34, if you're reading this, would you care to elaborate? Gareth McCaughan (talk) 14:17, 23 February 2009 (UTC)

Wrong description?
Hi, The description of the axioms seems not to fit to the symbolical proof! Is this on purpose? 62.178.21.227 (talk) 14:50, 16 June 2009 (UTC)

Optimal Leberwurst Ontological Proof
I just applied a version of the ontological proof to try to demonstrate that there must be an optimal cut of leberwurst in my lunchbox, but still had to go hungry.

Poor Gödel. He must have been far gone at this point to have forgotten of philosophers as early as Kant who made us aware that existence preceeds essence, i.e., the existence is not an attribute, so that it would be nonsense to say that an optimal form of some thing (dragons, leberwurst in my lunchbox, etc.) must possess the attribute of existence. Gödel also forgets the many philosophers of language (Wittgenstein, the Vienna Circle...) who systematically studied the conundrums following from such misuse of language..

I still greatly respect Mr. Gödel, and tend to look upon attempts to direct attention to his manias on the deathbed in the same way as I regard people who, say, focus on Bobby Fisher's late deteriorated state instead of giving recognition to him for his accomplishments. Could it be, in the case of Mr. Gödel, that such people are driven by an external motive and hope to appropriate Mr. Gödel as their instrument?

--Philopedia (talk) 12:49, 15 January 2010 (UTC)


 * Sooo... you just posted to say that you don't like his theism. Okay. Philosophers always find contradictions and conundrums with other philosophers. Or are you claiming that theists are trying to make use of his arguments for an "external motive?" Aren't we, as editors, supposed to assume good faith on Wikipedia, you know, assume that editors are trying to do their best to fix and edit articles? Hmmm. Well, darn, I guess when someone disagrees with me I can call out bias too. 98.198.83.12 (talk) 16:35, 28 January 2010 (UTC)

"This article is about the existentialist catch-phrase coined by Jean Paul Sartre. For the transcendent theosophy founder, see Mulla Sadra. The proposition that existence precedes essence (French: l'existence précède l'essence) is a central claim of existentialism, which reverses the traditional philosophical view that the essence or nature of a thing is more fundamental and immutable than its existence." --Wikipedia article on Existence Precedes Essence (my emphasis) Hmm, so Kant was a follower of Sartre?71.185.255.17 (talk) 04:19, 24 January 2012 (UTC)

Did Gödel "formalize" Anselm?
The pre-edit sentence stated that Gödel's proof is a "formalization" of Anselm's. I had no particular objection to that statement, but there is a small literature devoted to trying to formalize Anselm's proof. Gödel's ontological proof is not a "formalization" of Anselm's, when the word "formalization" is taken in the sense it is used in that literature -- to mean a formal analysis attempting to elucidate the direct meaning of Anselm's words. At least one serious scholar I know of felt that the original lead sentence of this Wikipedia article was simply wrong, and that it greatly diminished the quality of the Wikipedia article.

My edit attempts to preserve readability, and to make the same point intended when the word "formalization" was used. It tries to steer clear of any charges that Wikipedia is making unsupportable claims about the usefulness of Gödel's proof as an method for a careful word-by-word analysis of what the original text by Anselm of Canterbury really meant.

--Jeffreykegler (talk) 17:22, 10 April 2010 (UTC)

Critique: infinity not an issue in Drange's criticism
I removed a discussion on infinite collections because it was tangential to the point, which is the claim that axiom 3 is false: the positiveness of a property can alter depending on what other properties are present, and positivity can be mutually exclusive. The existence of infinite collections of positive properties is irrelevant. The claim is that there exist finite examples of contradictory positive properties, and hence axiom 3 is false. —Preceding unsigned comment added by Winterstein (talk • contribs) 08:59, 27 May 2010 (UTC)

Axiom numbering
I lost the thread of the prose description of the proof in part because it looks like the axioms are numbered in a way that doesn't match the way they are numbered in the formalized proof itself. It's also not clear to me where to fit in the axiom that any property that is positive is necessarily positive. Can someone who has a more confident sense of this than I do please clarify it? MJM74 (talk) 00:24, 16 August 2010 (UTC)

Criticism Section
The criticism section for this article aren't really appropriate because they are for the ontological proof in general and not specific to Gödel's proof. Are there any published criticisms of Gödel's proof? Tweisbach (talk) 11:02, 6 January 2011 (UTC)


 * I agree that, as it stands, the criticism section does not belong here, because it applies to the ontological argument in general rather than Gödel's more sophisticated formalization. In particular, the C. Anthony Anderson quote does not refer to Gödel's proof, but rather to Anderson's own restatement of it, making its relevance here questionable.  In the paper from which the Anderson quote is extracted, Christopher Small says:


 * "I should remind the reader again that the version of Gödel's argument that I have presented is not Gödel's original argument. When I first read Gödel's notes on his ontological argument, I, like many others, found the axioms confusing and difficult to accept. So I turned to the emended version of the argument due to Anderson. This version has now been widely discussed. But the more I fuss around with this version the more uncomfortable I become with it. I went back to Gödel's original version and found that it was far better than I had originally understood. If you are interested in studying this argument, and the reasons why I prefer it to Anderson's emendation, you can click to obtain a PDF file entitled Reflections on Gödel's Ontological Argument."4granite (talk) 23:19, 8 April 2011 (UTC)

THE DAMN PROOF
What's the damn proof in plain language? Sn't Anselm's ontological argument was stupid but Gödel is an intelligent man, here the article is abotu his proof but we are nto given his proof only a logical representation of it, he has to have made it in words, where is it?Undead Herle King (talk) 22:22, 7 January 2011 (UTC)


 * Why would he have made it in words? He was a logician. --Gwern (contribs) 18:04 17 January 2011 (GMT)

As an example of Gödel's logic, he starved himself to death because he thought that someone was trying to poison him.Lestrade (talk) 16:22, 19 January 2011 (UTC)Lestrade

Can someone *translate* the proof into plain language, then? Or is this against some rule of Wikipedia?72.213.177.26 (talk) 04:21, 1 May 2011 (UTC)

I'll look at doing this at some point. I don't know when I'll get round to it; if someone else wants to do it, I recommend using this source, which outlines the argument in plain English. ItsZippy (talk • contributions) 20:18, 9 December 2011 (UTC)

It just prove that very smart people can be also very dumb when it comes to religion. It's basically the same dumb Anselm argument disguised with math — Preceding unsigned comment added by 201.150.158.34 (talk) 19:56, 27 September 2020 (UTC)

Seems to me the Wiki Wangs are belling the cat
I have a real problem with nonsense such as this discussion page, and with reference [sic] works where no authorship is attributed. How do I know anyone posting here knows their own ass from a hole in the ground? Certainly, based on the stunningly inept commentary here, I can only conclude that this encyclopedia [sic] is the result of some centralized planning committee's anointed vision of the "People's Encyclopedia," in which all knowledge must be rendered to the lowest common denominator of humanity. Thus, attempting to explain any of Kurt Gödel's work by showcasing it through the distorted and defective lens that is the ignorance of a bunch of nearsighted Wiki Wangs strikes me as just trying to bell the cat. I'm sure Kurt Gödel and God have shared a laugh more than once while pondering this dreck. Just something to think about. — Preceding unsigned comment added by 209.169.203.158 (talk) 03:52, 2 November 2011 (UTC)

Lead rewrite
I've placed a lead rewrite tag on the article because it does not comply with WP:LEAD. The lead should summarise the entire article - nothing should be in the lead that is not in the article. At the moment, it is being used as an extra section. I recommend the current lead (copyedited) is moved into its own section and a new lead is written, summarising the entire article. I'll do this at some point; if someone gets to it first, that is what I'd recommend. ItsZippy (talk • contributions) 20:21, 9 December 2011 (UTC)
 * You mean you recommend it be moved into its own section? --Trovatore (talk) 21:22, 9 December 2011 (UTC)

Godel's definition of necessary existence seems absurd
Let's say the essence of venomous dogs are the propositions is_a_venomous-animal(y) and dog(y). Let's assume necessary existence of venomous animals and dogs. $$ \begin{array}{l} E(\text{venomous dog}) \iff [ \operatorname{\text{venomous}} \text{ ess } \text{venomous dog} \to \square \; \exists y \operatorname{\text{venomous}}(y) ] \text { and } [ \operatorname{\text{dog}} \text{ ess } \text{venomous dog} \to \square \; \exists y \operatorname{\text{dog}} (y) ] \\

\square \; \exists y \operatorname{\text{dog}} (y) \\

\square \; \exists y \operatorname{\text{venomous}}(y) \\

E(\text{venomous dog})

\end{array} $$

I suppose it's not true that there is necessary existence of venomous animals, and necessary existence of dogs. But I think it brings up a flaw in Godel's definition. Why should necessary existence be defined as having all its essences manifested in at least one thing, when the assertion of the manifestations makes no logical connection to them all being connected together? — Preceding unsigned comment added by 149.144.132.180 (talk) 05:04, 6 February 2015 (UTC)

Edit: Ahhh, my tex screwed up. I'll fix it later. — Preceding unsigned comment added by 149.144.132.180 (talk) 05:11, 6 February 2015 (UTC) Edit: Fixed now — Preceding unsigned comment added by 149.144.132.180 (talk) 04:04, 13 February 2015 (UTC)
 * Hi 149. Per the talk page guidelines, this page is supposed to be used for discussing what should appear in the article.  It is not for discussing the subject matter of the article per se, except insofar as it relates to how the article should or should not change.
 * You might ask this question on one of the Wikipedia reference desks, perhaps WP:RD/Humanities. --Trovatore (talk) 05:31, 13 February 2015 (UTC)

"Few other axioms"
If the article goes into detail of what the proof supposedly proves, given that the subject matter is modal logic, the article really should specifically state the "few other axioms from modal logic", since they have a very significant effect on proofs. Modal logic isn't a single thing but essentially a framework of separate logics that behave very differently depending on the axioms used. -- 88.192.19.110 (talk) 16:35, 19 May 2015 (UTC)

Criticism
Oops, I seem to have stumbled into a wasps nest of argument here.

I added a criticism section. Nobody seems to have pointed out the main flaw in this "proof": it depends on its axioms and we don't know whether the axioms are "true" or not.

The article as it was was misleading: It presents axioms and conclusions based on them. However, unlike for other logical systems, these axioms are questionable: it's basically disguised assumptions as axioms, and it needs to be clear that philosophers acknowledge that they're not necessarily true, and in fact attempts have been made to show that they are actively false, rather than just unknown. H123b wiki (talk) 12:14, 8 November 2015 (UTC)

Results by automatic theorem provers
What about these results:
 * http://page.mi.fu-berlin.de/cbenzmueller/papers/C55.pdf
 * http://page.mi.fu-berlin.de/cbenzmueller/papers/C40.pdf

Should we mention them?

--Pokipsy76 (talk) 12:19, 8 May 2016 (UTC)


 * The article dishonestly only mentions C55 claiming that Gödel is wrong, and does not include C40 which claims that Gödel is right. Actually, both papers prove Gödel is right. C55's only claim is that there is a "bug" in Gödel's proof if you introduce the bug yourself, so it only serves to clarify that there is one definition provided by Leibniz and Scott that cannot be ommitted from the final proof. 5.151.198.248 (talk) 17:07, 18 December 2016 (UTC)

Ultrafilter
Note 3 currently says: If one considers the partial order $$ \preceq $$ defined by $$ \varphi \preceq \psi $$ iff $$ \square \forall y (\varphi(y) \to \psi(y)) $$, then Axioms 1-3 can be summarized by saying that positive properties form an ultrafilter on this ordering. Definition 1 and Axiom 4 are needed to establish the Godlike property as principal element of the ultrafilter. I suggest to change the definition of $$ \varphi \preceq \psi $$ to $$ \forall y (\varphi(y) \to \psi(y)) $$ &mdash; i.e. without the "necessarily" square. With this definition, it is easy to prove that $$P$$ corresponds to an ultrafilter with principal element $$G$$ as follows: Hence, $$P(\varphi) \iff G \preceq \varphi$$.
 * $$G \preceq \varphi$$ implies $$P(\varphi)$$ by Ax.3 and 1.
 * Conversely, $$P(\varphi)$$ implies $$G(x) \to \varphi(x)$$ for each $$x$$ by Df.1, that is, $$G \preceq \varphi$$.

This proof could be included in the note. Ax.4 isn't yet involved. This is as it should be, since Ax.4 shouldn't be mentioned before Th.2 and Df.2, to ease following the "Symbolic notation" outline.

I guess, $$ \varphi \preceq \psi $$ defined by $$ \square \forall y (\varphi(y) \to \psi(y)) $$ &mdash; i.e., now including the square &mdash; can be shown to lead to an ultrafilter with principal element $$G$$ as well, using Ax.4 in an appropriate way. However, being unexperienced in modal reasoning, I'm unable to come up with a proof for this. Provided there is one, a corresponding note should be added at an appropriate later place (I suggest right after "Requiring positive properties being positive in every possible world (axiom 4),"), and Note 3 could be shortened or even omitted. - Jochen Burghardt (talk) 10:17, 3 June 2019 (UTC)

Modal collapse / ("Dubious")
Some remarks on modal collapse:

Benzmüller and Woltzenlogel have shown that Godel's proof (in Scott's version) implies modal collapse, that is, it implies that $$\diamond p$$ is equivalent to $$p$$, and in turn equivalent to $$\Box p$$. Using these equivalences (I'll call them MCE for short), the proof from section Gödel's_ontological_proof can be drastically simplified to:

$$ \begin{array}{rl} \text{Ax.1'.} & \left(P(\varphi) \;\wedge\; \forall x (\varphi(x) \Rightarrow \psi(x))\right) \;\Rightarrow\; P(\psi) \\ \text{Ax.2.} & P(\neg \varphi) \;\Leftrightarrow\; \neg P(\varphi) \\ \text{Th.1'.} & P(\varphi) \;\Rightarrow\; \exists x \; \varphi(x) \\ \text{Df.1.} & G(x) \;\Leftrightarrow\; \forall \varphi (P(\varphi) \Rightarrow \varphi(x)) \\ \text{Ax.3.} & P(G) \\ \text{Th.2'.} & \exists x \; G(x) \\ \end{array} $$

Here, the dashed variants are obtained from the original ones by removing all modal operators per MCE. This proof is the one mentioned in [note 4].In presence of modal collapse, it is pointless to use modal logic.

Whoever likes to stick to modal logic, may apply MCE to Th.2'. to obtain the original Th.4. ("$$ \Box \; \exists x \; G(x)$$"). This proof doesn't use Df.2,3 and Ax.4,5, but only some consequences of them (viz. MCE). That is, it needs weaker assumptions than Godel's/Scott's proof. Therefore, it would be preferred by logicians.

Many (or all?) philosophers would interpret modal collapse as determinism, including absence of free will ("If it is possible that I kill somebody, then it is necessary that I do that"). As discussed in footnote [11], Godel may have been aware that his axioms imply modal collapse, but he wanted it to follow from the existence of God.

As far as I saw, Benzmüller and Woltzenlogel never said that modal collapse is not necessarily a flaw. Neither did they say it is a flaw. They just pointed out some consequences along the above lines.

Maybe the remarks on modal collaps in the article should be collected in an own subsection, and maybe, some of the above remarks should be included there, too. - Jochen Burghardt (talk) 10:59, 30 June 2019 (UTC)

'This planet/our world' confusion
The following passage:

''A truth is necessary if it is true in all possible worlds. By contrast, a truth is contingent if it just happens to be the case. For instance, "more than half of this planet is covered by water" is a contingent truth, that relies upon which planet "this planet" is. If a statement happens to be true in our world, but is false in another world, then it is a contingent truth.''

is misleading at best, if not outright mistaken. Specifically, it's worded in such a way that many readers not familiar with modal logic will think that "our world" and "this planet" are being used synonymously. If they are being used synonymously, then "If a statement happens to be true in our world, but is false in another world, then it is a contingent truth" is a wrong explanation of the notion of contingent truth in modal logic. If they aren't meant to be synonymous here, then it ought to be made clear that "our world" means the actual world among the possible worlds, in the modal-logic technical sense, and not the planet Earth.

I'd also say that if you are going to define necessary truth in terms of possible worlds ("A truth is necessary if it is true in all possible worlds"), then the subsequent definition of non-necessary (contingent) truth should also be given in terms of possible worlds. "A truth is contingent if it just happens to be the case" doesn't do that, and is unnecessarily vague. JohnMason 16:38, 29 July 2020 (UTC)


 * I agree, but I am unable to come up with a good example to illustrate what "possible world" means without introducing the Kripke-semantics formalism. Do you have an idea for that? - Jochen Burghardt (talk) 19:17, 29 July 2020 (UTC)


 * Why not just link to the Wikipedia article Possible world? Anyway, even if an explanation isn't explicitly given, the definitions ought to be parallel, I'd say.JohnMason (talk) 21:13, 29 July 2020 (UTC)


 * I removed the misleading planet example and the "happens to be the case" definition, for now. However, I feel, a better example would be necessary here. - "Possible world" is already linked in that section, and I prefer its current target, the mathematical possible worlds, over the philosophical Possible world, since Godel's proof is a mathematical one. - Jochen Burghardt (talk) 08:08, 30 July 2020 (UTC)


 * I understand your preference for that "possible worlds" target (even if I'd regard Gödel's proof as more metaphysics than mathematics), but that level of technical detail is probably going to be impenetrable for a lot of readers of this article. The "philosophical" possible world target is (somewhat) more approachable, and is enough to give a general reader a sense of the relevant notion of "possible world." Thank you for making those changes.JohnMason (talk) 14:00, 30 July 2020 (UTC)


 * Also, as an example of the kind of parallel definition I had in mind, for the level this section is pitched at, I think it would be fine to say, e.g., "A truth is necessary if it is true in all possible worlds. By contrast, a truth is contingent if it is true in some, but not all, possible worlds." (including the link to the 'philosophical' Possible world page.) This looks fine to me as a general, not very technical explanation of the notion.JohnMason (talk) 14:09, 30 July 2020 (UTC)


 * I see that you've changed the passage -- thank you for that, and for correctly stating that a contingent truth has to be true in the actual world, not just "some, but not all, possible worlds" (as I carelessly got it wrong above).JohnMason (talk) 11:41, 31 July 2020 (UTC)

Adele, two days after Gödel's death, told Wang ... ?
Wang reports that Gödel's wife, Adele, two days after Gödel's death, told Wang that ... - didn't Adele die before Gödel ?? DamjanB52 (talk) 12:53, 25 October 2020 (UTC) DamjanB52
 * No, she survived him by several years. Quick web search indicates that she died in 1981.  2601:648:8200:970:0:0:0:1A5F (talk) 10:10, 25 March 2021 (UTC)

Friedman
Maybe add this?

https://u.osu.edu/friedman.8/files/2014/01/ConMathThe122512-1iea8ps.pdf

I don't know if it was formally published. It's entry #74 from Friedman's manuscripts page, which says it was submitted in 2012. 2601:648:8200:970:0:0:0:1A5F (talk) 10:18, 25 March 2021 (UTC)

Requested move 1 May 2021

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion. 

The result of the move request was: not moved. (closed by non-admin page mover) ~ Aseleste  (t, e &#124; c, l) 06:23, 19 May 2021 (UTC)

Gödel's ontological proof → Gödel's ontological argument – "Gödel's ontological proof" is slightly more common on Google Scholar, but I would consider this to be a WP:POVTITLE since many people would not agree that this argument proves the existence of God. This title would also be WP:CONSISTENT with the more general article on ontological arguments. (t &#183; c)  buidhe  23:01, 1 May 2021 (UTC) —Relisting. ~ Aseleste  (t, e &#124; c, l) 03:57, 9 May 2021 (UTC)
 * Weak don't move I don't care a whole lot which title it's under, but I don't think the move rationale is convincing. In this ambit calling something a "proof" is traditional, and doesn't necessarily mean that it proves what it purports to prove. --Trovatore (talk) 23:43, 1 May 2021 (UTC)
 * Don't move The proof of Godel, as given in section "Symbolic notation", is formally correct, cf. the section about computer verification. Therefore, it deserves to be called "proof" more than most other philosophical arguments. (Of course, this does not mean that it proves any claim of any religion, as discussed in section "Criticism"). - Jochen Burghardt (talk) 14:06, 2 May 2021 (UTC)
 * Oppose, per above comments and common name. Randy Kryn (talk) 11:16, 9 May 2021 (UTC)
 * Oppose per above. It's a formal proof, so I don't see a POV problem. Srnec (talk) 16:10, 9 May 2021 (UTC)
 * Oppose. Can be argued both ways but we need to go one way or another. So by default I think, no move. But see, and also Andrew's Principle. Andrewa (talk) 08:39, 17 May 2021 (UTC)

Discussion
As per my !vote above, IMO this is something of a line call. It's POV either way, and both titles can claim to be the common name depending on who you consider reliable and how you compare the attestation counts.

Gödel's ontological proof will tend to be preferred among:
 * Sources who believe in God (with an exception noted below)
 * Sources who are particularly interested in proof theory and computer-assisted proof
 * And as proof theory is relatively recent and computers even more so, recent sources may support it, but that brings up a can of worms... how do we compare the count of attestations (or occurrences) in publications in two different fields?

Gödel's ontological argument will tend to be preferred among:
 * Sources who do not believe in God
 * Sources who are particularly interested in the history of similar arguments
 * Perhaps surprisingly, sources who are particularly concerned with the theology of faith (which I disclose is my personal POV, see this off-this-wiki essay, and note that my !vote goes against this personal bias but for other reasons)

Food for thought? Andrewa (talk) 08:39, 17 May 2021 (UTC) The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Capitalizing a theoretical deity
I was surprised by the use of orthography "God" in the proof section, expecting that form to be restricted to the Christian "God", rather than a theoretical single deity. This seems to be backed up by God_(word) which says "In the English language, capitalization is used for names by which a god is known, including 'God'. Consequently, its capitalized form is not used for multiple gods or when referring to the generic idea of a deity." (my emphasis added). For me, the article would benefit from clearly distinguishing between "God" (the Abrahamic god in, eg, sentences about Gödel's personal beliefs) and "god" (a generic single deity, the subject of the proof). As nothing in the proof relates to any specific theology, it would be more accurate to use the uncapitalised form. Scarabocchio (talk) 15:23, 19 September 2021 (UTC)

[continued] In the History section of the article we find "Morgenstern's diary is an important and usually reliable source for Gödel's later years, but the implication of the August 1970 diary entry—that Gödel did not believe in God—is not consistent with the other evidence. In letters to his mother, ... Gödel argued at length for a belief in an afterlife." The juxtaposition of these sentences implies this is an inconsistency. There is none. The Kurt Gödel article includes this quote ""I am convinced of this [the afterlife], independently of any theology." It is "possible today to perceive, by pure reasoning" that it "is entirely consistent with known facts." "If the world is rationally constructed and has meaning, then there must be such a thing [as an afterlife]."" The words "independent of any theology" are critical here. Gödel was a theist. The introduction of the Abrahamic god into the proof is unwarranted. Scarabocchio (talk) 15:59, 19 September 2021 (UTC)
 * I think any time you use the word as the personal name of the deity, it has to be capitalized. That's just the basic rules of English; personal names are capitalized, whether the name is God or Fred.  That's how I think it's being used here, not as specific to Abrahamic theology.
 * It would be possible to reword the arguments so that they don't use a personal name, but it would be awkward and would alter the flavor of them in a way I don't think Gödel would have approved. --Trovatore (talk) 17:50, 19 September 2021 (UTC)