Gödel's Ontological Failure

Kurt Gödel
Kurt Gödel

In 2013 a pair of computer researchers reportedly "verified" an ontological theorem* proposed by the late mathematician Kurt Gödel. Predictably, the media irresponsibly hailed this event as science "proving" Gödel's argument for God's existence. Just as predictably, some have unquestionably accepted it as a validation of their own religious beliefs.

What is uniformly ignored is that it was a mathematical "translation" (using Henkin semantics) -- NOT Gödel's original argument -- which was supposedly "proven." What remains is to thoroughly analyze the actual original theorem to determine its logical, philosophical or factual value (and whether the mathematical syntax truly constitutes a valid translation).

Translation

The essence of every ontological argument is the attribution of some quality exclusively to God. By assuming the quality exists, and asserting that only God possesses that quality, we presumably conclude that God exists. The inherent weakness of such arguments is that the attribution is wholly arbitrary, and the quality itself is often arbitrarily defined, and is usually so generic or abstract that it can be applied to practically anything, rendering the argument useless.

In Anselm's classic argument, he urged us to imagine a being "than which no greater can be conceived." Descartes proposed a supremely perfect being. Gödel suggests a being that "possesses all positive properties" in a theorem that can be distilled into three fundamental premises:

1) A "God-like being" possesses all existing properties.

2) The property of possessing all existing properties is an "essence."

3) Essences necessarily demonstrate an individual's existence.

Since a "God-like being" has the "essence" of possessing all existing properties, and since an essence necessarily demonstrates an individual's existence, then a "God-like being" must exist.

By far the most crucial task (and greatest initial difficulty) in assessing Gödel's theorem is comprehending his particular meaning for words and phrases -- often possible only by considering the context in which they are used. For example, Gödel appears to use the term "positive" in a strictly logical (not evaluative) sense. Hence, a "positive" property means a property that actually exists, as opposed to not existing (affirmed in his very first axiom, below).

In his translation, mathematician Dana Scott assigned alpha-numeric designations to each of Gödel's axioms, definitions, corollaries and component theorems (for example, A1 is "axiom 1"), listed below in original order and quoted verbatim. To make sense of Gödel's vague, redundant and often circular phrasing, I've offered more conventional translations or clarifications (in parentheses):

A1 -- "Either a property or its negation is positive, but not both" (Either a property positively exists or doesn't positively exist, but can't do both). This is an expression of the logical principle of non-contradiction.

A2 -- "A property necessarily implied by a positive property is positive" (If a positively existing property necessarily implies another property, that second property must also positively exist).

T1 -- "Positive properties are possibly exemplified" (If a property positively exists, it is possible to demonstrate it).

D1 -- "A God-like being possesses all positive properties" (positively existing properties).

A3 -- "The property of being God-like is positive" (The property of being "God-like" positively exists).

C1 -- "Possibly, God exists" (Self-explanatory).

A4 -- "Positive properties are necessarily positive" (By definition, positively existing properties must exist).

D2 -- "An essence of an individual is a property possessed by it and necessarily implying any of its properties" (If any property of an individual necessarily implies any of that individual's properties, it is an "essence").

T2 -- "Being God-like is an essence of any God-like being" (Every "God-like being" possesses the essence known by name as "being God-like").

D3 -- "Necessary existence of an individual is the necessary exemplification of all its essences" (An individual's existence is an inevitable or unavoidable representation or demonstration of all its essences (properties that "necessarily imply" other properties). If an individual posesses these "essences," he must "necessarily exist").

A5 -- "Necessary existence is a positive property" (The necessary existence of an individual is a property that positively exists).

T3 -- "Necessarily, God exists" (Self-explanatory).

Definitional Problems

A comprehensive analysis reveals problems regarding a number of Gödel's specific concepts. For example:

"Necessarily implied" (A2, D2) -- Gödel insists that, if a positively existing property "necessarily implies" another, the implied property must also positively exist. But he offers no proof that a property can actually be "necessarily implied" (that circumstances make the implied existence of a property essential or inevitable), and he offers no guidance for determining WHICH specific properties are "necessarily implied," and which are not. Thus, it is open to interpretation which "implied" properties positively exist.

"Necessary existence" (D3, A5, T3) -- Even if we accept the concept of "necessary existence" -- that the existence of ANY individual is logically inevitable or essential -- it is a "positive property" ONLY if the individual actually exists. If the individual DOESN'T exist, such a property can ONLY be hypothetical.

"God-like beings" (D1, T2) -- Gödel declares -- without qualification -- that "a God-like being possesses all positive properties" (not "some" or "may" or "possibly"), thereby eliminating potential exceptions. Thus, to demonstrate the definition's counterfactuality, one need provide only a single, specific example of a "God-like being" who possesses only SOME (but not all) positive properties -- and mythology is FULL of them!

"Being God-like" (A3, T2) -- Gödel insists that such a property (or "essence") positively exists, yet offers no proof beyond his own assertion -- again, making it valid ONLY as a hypothetical premise.

"Essence" (D2, T2, D3) -- If one accepts that an individual has "essences" to "exemplify" its existence, one must FIRST presuppose that the individual actually exists -- which already establishes the individual's "necessary existence" BEFORE any "exemplification." The "necessary existence" of an individual ISN'T the exemplification of its essences, but an exemplification of a PRIOR PRESUMPTION of the individual's existence.

Final Analysis

Throughout his argument, Gödel offers theorems that are highly speculative, definitions that are unsupported or outright counterfactual, and numerous examples of the logical fallacy of "begging the question" (wherein the expected conclusion is inherent in an argument's propositions). In the end, an argument is only as valid as its premises, and Gödel's are a nebulous, unsubstantiated, presuppositional mess.


*To view the pdf version of Gödel's theorem, including the mathematical "translation," visit


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Comments 69 comments

JMcFarland profile image

JMcFarland 2 years ago from The US of A, but I'm Open to Suggestions

Awesome hub, as ever. Can't wait to see what some comment-ready theists have to day, since they often point to this as definitive proof, which is obviously isn't. I'm so impressed you tackled the subject so thoroughly.


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Thanks, JM!

This was an especially tough one, as Gödel's language is so generic, repetitive and circular that it took me what seemed like forever just to completely understand what he was trying to say! Hopefully, my efforts can save others a similar struggle.


JMcFarland profile image

JMcFarland 2 years ago from The US of A, but I'm Open to Suggestions

I've only scratched the surface of this type of argument, add most theists avoid it like the plague (probably because most don't understand it or recognize how circular it is) but this hub explained it perfectly. I will certainly link to it when it comes up.


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Thanks for the promotion, JM!

Your comment about theists not understanding Gödel's theorem is one of the reasons I tackled this topic in the first place. There is one fellow here on HubPages who regularly cites the theorem as "proof" of God's existence, yet admitted to me that he hasn't even analyzed it on his own. In fact, he insists that neither he nor I are even "qualified" to do so.

He simply cites the theorem as authoritative because he agrees with its conclusion, then hides behind Gödel's great reputation as a mathematician and the respect that Einstein had for the man.

I'm willing to bet he isn't so unquestioning when it comes to the atheistic notions of Bertrand Russel -- another great mathematician (and Nobel laureate) for whom Einstein had respect (and with whom he even collaborated!).

Such hypocrisy is just another sad example of the sort theologically-induced dishonesty with which we must so often grapple.


JMcFarland profile image

JMcFarland 2 years ago from The US of A, but I'm Open to Suggestions

I agree, Paladin - and while I am familiar with the more common examples of the ontological arguments often put forth as "proof" by some theists and apologists, that particular user is the first time I heard of Godel's theorem. I since looked it up and came to many of the same conclusions that you put in your hub, but hadn't even considered writing on it because it was so obscure, circular, ridden with poor semantic examples, etc. I'm glad to find that you were able to do it much more thoroughly than I would have been able to - and I'm happy to point others to this hub when and if it comes up in future conversations. You did an excellent job - voted up.


TheOdinSeeker profile image

TheOdinSeeker 2 years ago from Fairfield, OH

Great hub, Paladin.

I've never encountered this argument before. While reading Gödel's theorem, even common sense will show how flawed it is. As with Pascal's Wager, assumptions about unsubstantiated claims must be accepted before the argument can hold any water.

Voted up!


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Thanks, Seeker!

I'd never heard of it (or it's author, Kurt Gödel) either, until a certain Hubber began citing it as "proof" of God's existence. So I looked into it, and found it to be just another half-baked ontological and presuppositional argument.

I'm hoping this hub can be a resource for both believers and non-believers who may have trouble navigating Gödel's tortured syntax. I especially hope it proves useful for atheists confronted with the theorem who (like us) have never heard of it before.


TheOdinSeeker profile image

TheOdinSeeker 2 years ago from Fairfield, OH

I shared it to my FB and Twitter accounts. Hopefully it gets out there!


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Cool! Thanks again! :-)


kylclk profile image

kylclk 2 years ago from Alabama

Hey Paladin, how well do you know modal logic?


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Not very well, which is why I stuck to analyzing Gödel's original theorem, and not the translation in Henkin semantics (though I do have doubts regarding the accuracy of the translation).


kylclk profile image

kylclk 2 years ago from Alabama

I think that's where your misunderstanding of the "necessary" and "possibly" are coming from. I don't think Godel's ontological argument is correct (Godel is a logical genius, and he never actually proved his argument is correct). But perhaps for future reference, you should look up on some modal logic, as your critiques of the use of "necessary" is (I believe) wrong.


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

It could very well be that "necessary" has some sort of different meaning in the syntax of modal logic, but please keep in mind that Gödel's original theorem is in conventional language. Hence, conventional interpretations of such words should be valid.

It seems clear that Gödel semantically constructed the original language of his theorem so it could be more easily translated into mathematical language, which is surely why it seems to generic and redundant. Yet, like any other argument, it must still stand on its own, in whatever language it's in.

In any case, I will, indeed, take your advice and look up the interpretation of the words "necessary" and "possibly" in the context of modal logic. Thanks for the read, and the comments!


Titen-Sxull profile image

Titen-Sxull 2 years ago from back in the lab again

I've always been a bit confused by Anselm's Ontological argument because even if we granted it it would only prove that the greatest conceivable being exists, it would not preclude the existence of a being we cannot properly conceive of which might be greater than that being in some way. So God could still just be a peon in an endless stream of even greater beings that are simply beyond our ability to conceive let alone perceive.

Godel's version appears to get bogged down in definitions and semantics, I like philosophy and all but good grief that's a lot of word salad.

Great hub :)


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Indeed! There's an even more fundamental problem with Anselm's argument -- if there IS a being "greater than which can be conceived, how can we even imagine such a being? After all, merely to conceive it is beyond our comprehensive abilities, so the very premise itself makes no sense.

Thanks for the compliment on the hub!


Oztinato profile image

Oztinato 2 years ago from Australia

1. Godel's math theorem or reasoning has not been disproved by any other scientist.

2. Godel showed that the topic of God can be treated quite rationally and scientifically

3. Other theories such as "string theory" also can't be proved by a scientific experiment and hence remain on par with the Godel theorem.

4. Godel has a legitimate historical claim to be THE successor to Einstein.

5. Godel was aware of the fact that the majority of modern scientists were out to prove God does not exist. He therefore enjoyed coming up with great math provable theories to contradict this trend.

6. No other math theorem is treated with such derision and emotion by mainly atheist critics who can't actually disprove the theory. Emotive responses and ridicule do not constitute valid scientific proof.

7. The idea of necessity is based on self evident truth and commonsense. it removes the "chicken and egg" or "dog chasing its tail" fault with physics.

8. Existential questions associated with the topic of God's provability are enormous and profound and changes the whole texture of scientific thought.


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

1. Gödel's math theorem doesn't need to be "disproved" by any other scientist. I just demonstrated how his original argument fails to prove anything.

2. Gödel DIDN'T show that the topic of God can be "treated quite rationally and scientifically." When you've proven to me that the mathematical translation of his original theorem is valid and accurate, then you may have a point. In any case, treating the topic of God "rationally and scientifically" isn't the ultimate issue. The ultimate issue is whether God actually exists. And NOBODY has come close to demonstrating that yet.

3. Other theories aren't the issue here, either -- including the one you love to keep mentioning (string theory, which, incidentally, is quickly falling out of favor).

4. Gödel's standing as a scientist or mathematican has NOTHING to do with whether he is correct on this specific issue, as I keep reminding you (to no avail). Einstein even admitted mistakes he made in his OWN THEORIES -- let alone other fields of inquiry. And Gödel was wrong here.

5. Gödel WASN'T aware that "the majority of modern scientists were out to prove God does not exist," because they AREN'T. Unlike you, scientists (at least those who are true to the scientific method) aren't out to prove some preconception. They are out to objectively seek the truth about the physical world.

6. If Gödel's mathematical theorem is "treated with derision," there's likely a very good reason for it. Personally, I can't treat it with "derision," because I don't know enough about modal logic. I CAN, however, examine his original theorem -- as I did here -- and I've found it lackluster and unconvincing. It's the same old ridiculous ontological BS apologists have been using for centuries.

7. The idea of necessity is NOT "based on self evident truth and commonsense." Necessity may have an objective tense in purely mathematical parlance, but in philosophical terms -- or in any other means of expression -- it is a purely SUBJECTIVE phrase. "Necessity" must be demonstrated convincingly, and Gödel doesn't even come close.

8. Existential questions with regard to God may, indeed, be "enormous and profound," but they don't change the "whole texture of scientific thought" one iota. Science is concerned with the way things actually ARE, not some fanciful, fictional notion of how we THINK they are.

Oz, I've noticed that, aside from briefly mentioning the notion of "necessity," you haven't really addressed any of my criticisms of Gödel's theorem. This doesn't surprise me, because I suspect that, deep down, even you recognize its inherent, insurmountable flaws.

However, I can at least observe that you've made some progress. Before, you weren't even willing to examine the theorem on your own. Though it's not even clear that you've actually read my criticisms here (and there's a good chance you haven't), you're at least here -- which is a tiny step in the right direction.

If I can get you to start genuinely thinking about the arguments for God's existence, perhaps you'll actually begin to force yourself to deal with the truth of the matter, instead of constantly hiding behind appeals to authority. One can only hope...


Oztinato profile image

Oztinato 2 years ago from Australia

I will address each of these in turn over the next few days/weeks.

1. Of course Godel's theorem needs to be challenged both logically and mathematically by qualified individuals. That's what science is all about.

I have never claimed to be qualified to challenge the math and I don't think we have a hubber here that can. I believe I can defend the reasoning of such a great scientist as Godel.

7. The principle of necessity is where I would like to start: to we believers it is an obvious truism and a self evident truth. One of Godel's other theorems states that science can NEVER answer all questions and is qualified by Stephen Hawking himself! Hence atheist science lacks the "ultimate reason for everything" or any sense of necessity therefore it will always (by math and logic) be flawed and destined to chase its own tail until eternity.


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Oz, it's true that you've never claimed to be qualified to "challenge the math" of Gödel's theorem (and I never said you did). The problem is that you're ASSUMING that it's correct. If you can't understand the math, how can you possibly know whether or not it is IS correct?

You can't. In fact, for all you or I know, the mathematical translation of Gödel's theorem could be talking about Major League batting averages. The only thing we both CAN understand is his theorem in its original language. That's why we're here.

As for Gödel's Incompleteness Theorem (actually TWO theorems, but that's another story), I believe you're wrong on two counts:

First, you're misinterpreting its implications with regard to science. The theorem DOESN'T state that "science can never answer all questions." Rather, it proposes that there are limits to the "provability" (or, more correctly, "derivability") of statements within "consistent" formal mathematical systems.

While this has been applied more broadly to such subjects as physical science, even Stephen Hawking admitted that it's relationship is only analogous. Which brings me to your second error.

While Hawking does personally believe that "our search for understanding will never come to an end," he makes it clear that it is only his OPINION. According to Hawking, Gödel's theorem (at least as it applies to physics) only SUGGESTS that attempts to answer the ultimate questions of physics will remain incomplete.

In any case, Hawking's voice is not the definitive authority on the limits of potential scientific discovery, any more than Bertrand Russell's voice is the definitive authority on the existence of God. They are both expressing opinions. You're simply picking and choosing which one you'll respect, based upon your own theological predelictions.

---------------------------

Incidentally, I'm curious as to what you mean, exactly, by the term "atheist science." If you mean that honestly and diligently pursuing the scientific method increases the likelihood that one will become an atheist (i.e. a realist), then I wholeheartedly agree with you!

If, on the other hand, you're suggesting that "atheist science" is some sort of science that is separate from the genuine scientific method, then you're full of hogwash. When it comes to the scientific method, there is no "atheist" approach. There is only the genuine scientific approach.


Oztinato profile image

Oztinato 2 years ago from Australia

By atheist science I mean scientists who have an agenda to disprove and disparage the God theorem or other attempts to prove God exists etc.

As we both agree we can't analyse the maths we certainly can't either confirm or deny Godels complex maths. Therefore we should have a wait and see attitude.

Godels maths rigorously holds up the reasoning you want to debate. I have tried to start at the beginning and debate Godels point about Necessity (as oulined above). This relates to your request to discuss Godels logic.

Therefore one of those things that I (and Stephen Hawking!) and math agree on is that science can't answer the central question of the "necessity" of creation or "the ultimate answer for everything".


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Oz, if scientists examine the issue of God's existence using the scientific method, that's not "atheist science." That's just science -- as long as they don't let their personal philosophical predelictions avert them from an honest and objective examination.

As for your "wait and see" statement, that's not what you're doing. AT ALL. More than once, you've cited Gödel's theorem as mathematical proof of God's existence. And immediately after saying you're going to "wait and see," you make the claim that his theorem "holds up [to] the reasoning you want to debate."

So, you're NOT "waiting" at all. You've already decided that it is correct, even though you've repeatedly admitted you don't have the knowledge to do so. You can't make the assertion that Gödel's math "rigorously holds up" to ANYTHING, because you lack the understanding to make that claim.

As for Hawking, he has definitively rejected the notion that a "creator" was needed for the origin of the universe. He actually favors M-theory -- a conglomeration of various string theories -- as a more plausible explanation.

So, I'm waiting to see how eagerly you'll agree with Stephen Hawking now!


Oztinato profile image

Oztinato 2 years ago from Australia

I have said its proved by maths and remains unchallenged by math. This so far is fact.

No, I said atheist "science" is that which disparages the math proven Godel God theorem.

Also I have noted string or M theory is also proved by maths but has no experiment to back it up (exactly the state of affairs with the God theorem as both are a priori theories based on necessity). I am not, repeat not, saying the God theorem is the same as M. I am not saying Hawking believes in God just that he agrees with Godel that science CAN'T solve the most important question about a theory of everything or questions about necessity.

I am still waiting for your thoughts about the Godel concept of necessity in regards to his reasoning. Please remember in your answer that Mtheory also relies on necessity ie. how to reconcile both properties of waves and particles NECESSITATES a "vibrating string."


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Oz, you can't seem to make up your mind. In one sentence, you claim you don't have the ability to analyze the mathematical translation of Gödel's theorem, yet in another, you continue to state that it is "faultless," "unchallenged by math" or that it "rigorously holds up to reasoning."

I'm sorry, but you can't have it both ways. You either DON'T understand it enough to analyze it (as you've claimed), or you DO understand it enough to claim that it "holds up to reasoning." Make up your mind, then we can talk.

Your claim that Gödel's ontological theorem (as well as M-theory) is an "a priori" theory leads me to suspect that you don't understand what that phrase actually means. Just because a theory can be expressed mathematically doesn't make it "a priori" or self-evident. Anyone can CLEARLY see that by reading Gödel's argument for themselves, above.

As for my thoughts regarding the concept of "necessity" in Gödel's argument, you don't need to wait. All you need to do is READ THIS HUB!


Oztinato profile image

Oztinato 2 years ago from Australia

The Godel theorem is proven by math and remains unchallenged. How can I be any clearer on that point?

You have asked for a debate about Godels reasoning and I have put forward a clear argument which also remains unchallenged by you or any other hubber.


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

There are a number of problems with your assertion (which I've already related to you, but I'll remind you once again):

First, you have no way of knowing if Gödel's theorem has been "proven by math," as you've repeatedly admitted your ignorance with regard to the modal logic he utilizes.

Second, you have no way of knowing if the mathetical translation of Gödel's theorem is even accurate. If you don't understand the math, how could you possibly know that the mathematical syntax used in the translation is correct? YOU DON'T.

Third, if the translation IS accurate (especially if it is!), then the theorem is a failure in both its original semantic form AND in its mathematical syntax -- because I've clearly demonstrated the flaws in the original in this hub. If the phrases and syntax have been accurately translated, so have the flaws.

Fourth, you're confusing the concepts of mathematical "proof" and evidentiary proof. The former is simply a logical derivation, based upon axioms or definitions which could be flawed or even false (as they are in Gödel's theorem). The latter is more empirical.

How can I be any clearer on these points?

You have put forward NO clear argument regarding Gödel's reasoning, other than some superflous comments about "necessity" -- which HAS been challenged, if you'd bother to actually read the hub.

But if you actually read a concise but comprehensive critique of Gödel's reasoning (which is what this hub offers), you run the risk of actually thinking about what Gödel had to say, instead of simply hiding behind the opacity of the mathematical translation.

We can't have that, can we?


Oztinato profile image

Oztinato 2 years ago from Australia

If you have a serious challenge to the math or logic you would have made international headlines. You haven't.

The math has been verified by computers.

I have asked for a comparison with the necessity of string theory. You've said nothing about it.

All I see is the usual atheist denial and baseless ridicule of an eminent scientist.


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Oz, this has nothing to do with string theory. It is about one theorem, which you consistently refuse to even analyze for yourself.

If there's anyone in denial here, it's obviously you -- and I'm certain any objective reader of our comments here can see that.

I've tried a number of times -- both here and in my "Ten Reasons" hub (where this discussion began) -- to get you to engage in an honest examination of Gödel's theorem, but each and every time you hide behind its mathematical translation, claiming that the math "has been verified" or "remains unchallenged."

Yet even the scientists who supposedly "verified" the modal logic of the mathematical translations stated in their paper that it remains for humans to analyze the merits of the actual theorem, in its original language -- a proposition you continue to ignore.

From the very first moment you tried to introduce Gödel's theorem as "proof" of God's existence, your approach has been one of denial, obfuscation and diversion. It's not wholly unexpected, as I realize such tactics are necessary in religious apologetics, but it does eventually grow tiresome. When you're ready to actually engage in an honest discussion, please let me know.


Oztinato profile image

Oztinato 2 years ago from Australia

So now we are back to square one: Its up to us to analyze and I have started by discussing the concept of necessity using a logical comparison with the use of that concept in other scientific ideas that are taken seriously by yourself and others.

I repeat: you have failed to respond to the comparison.


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

But Oz, you're mistaken. As I already told you in our discussion in my other hub ("Ten Reasons To Not Believe In God"), I don't subscribe to string theory, and DON'T take it seriously. So how can you expect me to use it as a logical comparison for Gödel's concept of necessity?

I appreciate that you're now at least trying to address at least one of the concepts in Gödel's theorem, but a comparison with a theory that I also find somewhat dubious and ridiculous (like string theory) isn't the way to go about it.


Oztinato profile image

Oztinato 2 years ago from Australia

The fact is many scientific theories are based on the principle of necessity.

I am still waiting for reasons why scientists take the concept of necessity seriously in the case of other theories (in general) but not in Godel's theorem.


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Oz, nobody's denying the concept of necessity out of hand. The relevant question (one of many, actually, if you read my hub) regards the concept of necessity in the context of Gödel's theorem.

Just in case you merely skimmed over the hub or have forgotten my comments regarding necessity (in Gödel's theorem) , I'll quote them again here:

-- "Gödel insists that, if a positively existing property "necessarily implies" another, the implied property must also positively exist. But he offers no proof that a property can actually be "necessarily implied" (that circumstances make the implied existence of a property essential or inevitable), and he offers no guidance for determining WHICH specific properties are "necessarily implied," and which are not. Thus, it is open to interpretation which "implied" properties positively exist."

-- "Even if we accept the concept of "necessary existence" -- that the existence of ANY individual is logically inevitable or essential -- it is a "positive property" ONLY if the individual actually exists. If the individual DOESN'T exist, such a property can ONLY be hypothetical."

-- "If one accepts that an individual has "essences" to "exemplify" its existence, one must FIRST presuppose that the individual actually exists -- which already establishes the individual's "necessary existence" BEFORE any "exemplification." The "necessary existence" of an individual ISN'T the exemplification of its essences, but an exemplification of a PRIOR PRESUMPTION of the individual's existence."

I hope that clarifies things a bit.


Oztinato profile image

Oztinato 2 years ago from Australia

The only thing that needs clarifying is why Godel's use of the idea of necessity is not given the same respect as other theories.

For example, I have just read about a whole new theory regarding a 4D universe, black holes and the alleged creation of the universe: all based on "a priori" theories (hence prior assumption) reliant on necessity and proven by math; but in this case it is all taken very seriously and with much excitement by the scientific atheist community. Even when it is criticized it is not done so with venom and/or ignorance of attitudes to Godel. This venom is simply born out of malice and disregard to the idea of God and is not based on a purely scientific attitude.

When I get time I will try to find out how many other theories are out there reliant upon necessity. From memory it seems to be about 50% of thousands of theories.


Oztinato profile image

Oztinato 2 years ago from Australia

PS your explanations seem to trip themselves up over each other. I don't find them illuminating or logical.

Although I admit to an admiration of your enthusiasm as it has a hint of sincerity, I don't think you should try to be overly complex. Simplify.


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Oz, I don't know if you simply don't understand the meaning of "context" or if you're purposely trying to broaden the discussion of "necessity" so that you can move the discussion onto what you believe to be firmer logical or philosophical ground.

"Necessity" is a rather generic and subjective term that becomes more definitive and objective ONLY when applied in a specific context. This is what Gödel does in his theorem. If other scientists discuss the concept of "necessity," it is in a context specific and particular to THEIR theories or theorems!

What matters here is how Gödel uses the word in HIS theorem -- not how other scientists use it in THEIRS!

As for the complexity issue, if there is some specific concept that I discussed in my hub that is difficult to read, please direct me to it and help me rephrase it so my meaning is more clear. Perhaps I can even update the hub for those who follow (this would be very helpful!).

In my analysis of Gödel's theorem, I tried desperately to simplify my explanations as best I could. I even distilled his entire theorem down into three essential premises to try to make it less confusing.

I must admit, I've never worked so hard trying to decipher someone's philosophical argument. I literally spent HOURS trying to decipher single words, phrases and sentences, returning to them again and again until I was finally able to discern the most likely meaning or context. To be honest, it took me about three weeks before I finally felt that I understood it completely enough to write my analysis.

This difficulty isn't because Gödel's theorem is logically or intellectually complex or advanced beyond the average person's (or my) abilities. Rather, it was because, on the whole, his language and semantics are practically unintelligible.

In my hub, I described his language as "vague, redundant and circular," but that's an understatement. Trying to decipher the meaning of his axioms, definitions and component theorems was a monumentally difficult task. So if you find my analysis overly complex, blame Gödel, not me.


Oztinato profile image

Oztinato 2 years ago from Australia

No one is going to accept that you have a better understanding of logic or math than Goel! Its not going to happen. Unless of course you are a professor?


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Oz, that's the old "argument from authority" logical fallacy, and I've already illustrated to you a number of times how such an argument is completely absurd.

For example, I noted how Drs. Einstein and Hawking -- both whom you have cited as authorities for their supposed agreement with Gödel -- have admitted making mistakes -- even in THEIR OWN FIELD! What does this say about Gödel, whose theorem is arguing about something OUTSIDE his field of expertise!

I've also offered the example of Bertrand Russell -- another Nobel laureate and legendary mathematician (MUCH more legendary than Gödel, by the way) -- who also happened to be a committed atheist. But it appears the old "argument from authority" doesn't carry as much weight when the person of "authority" happens to disagree with you!

Oz, you've been using this dodge for far too long. Every time we move closer to genuinely examining some aspect of Gödel's argument, you scurry back to your "he was a professor/mathematical genius, so you can't question him" argument -- even though the theorem in question is outside his field of expertise.

When you're truly ready to examine Gödel's theorem honestly, please let me know. Until then, please quit wasting everyone's time.


Oztinato profile image

Oztinato 2 years ago from Australia

I have responded to all these points a number of times. I have also made concise points about a priori theorems. I don't accept your convoluted reasoning regarding this at all. End


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

I'm sorry, Oz, but all you've done with regard to these "points" is try to brush them off as irrelevant and ignore them. While it's true they aren't directly relevant to Gödel's theorem, they ARE relevant to your reliance on the logical fallacy of the argument from authority. It's a tactic you've used CONSTANTLY to avoid any honest discussion of Gödel's theorem.

Another tactic you use is trying to diverge the discussion onto some tangent regarding what you refer to as "a priori theorems" -- specifically string theory. But this isn't about "string theory" or any other theory you wish to call "a priori" (or any scientific theory AT ALL, for that matter). It's about GODEL'S theorem!

The fundamental flaw in your approach is that you absolutely REFUSE to associate the translation of Gödel's theorem (into the language of modal logic) with the original theorem itself! You've fought like hell to keep them separate -- focusing exclusively on the mathematical translation, while completely ignoring the original argument (aside from a very brief mention of "necessity").

This is all very understandable, of course. We both realize that, if we actually engage in a comprehensive discussion of Gödel's ACTUAL argument, you won't have a leg to stand on. Thus, you try to make your stand on the only ground upon which you feel safe -- the mathematical translation, which neither of us is yet qualified to fully decipher. As an apologist, it's really the only thing you can do.

In any case, my invitation to you remains open: Whenever you're ready for an honest discussion, you can return anytime. Until then, fare thee well.


jonnycomelately profile image

jonnycomelately 2 years ago from Tasmania

Thank you Paladin for "hanging in" and remaining honest in your arguments.

I see Oz as somewhat defensive, since he/she has been found wanting in the credibility basket.

Personally, I have no knowledge or ability in such logical studies or arguments. It's way beyond my thinking abilities,

However, I continue to be fully atheistic in my opinions of the universe, specifically in the area of a "judgmental, punishment-orientated super-being."

What mechanisms allowed our finite universe to come into existence we cannot know. I retain a sense of awe and respect for the beautiful complexity and integration that is here for all of us to see.


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Thanks for visiting and commenting, Jonny. It definitely takes some "hanging in" there sometimes, doesn't it, with certain apologists? ;-)


Oztinato profile image

Oztinato 2 years ago from Australia

JCL

we both have a Level 4 rating. So where's the credibility gap? In the social media imagination.

Godel's math has been proven and is still undisputed.


jonnycomelately profile image

jonnycomelately 2 years ago from Tasmania

Oz, are you familiar with the algorithms that HP uses to a lot Commenter Level? I am not. What does it mean?

Should we see our common level as a compliment or an insult?


Oztinato profile image

Oztinato 2 years ago from Australia

JCL

it means they do not agree with the troll or other attacks by certain unrepentent hubbers. I note here our sincere attempts to get over this.

It is neither compliment or insult but a paternalistic pat on the head in order to keep HP alive with people who contribute comments!


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

Jonny, just so you know, Gödel's math HASN'T been "proven," because the math isn't Gödel's. Rather, it is a translation of Gödel's theorem by computer mathematician Dana Scott using Henkin semantics.

And I see where you find Oz' credibility wanting. When a person consistently promotes a theorem as "proof" of something, yet readily admits that he doesn't personally understand the theorem himself, how can ANYONE take him seriously?


Oztinato profile image

Oztinato 2 years ago from Australia

Paladin

I can tell you are struggling with this. We both admit the math has been tested and proved by scientists. Unlike any other theorem you simply choose not to believe it could be true. Its science man.


jonnycomelately profile image

jonnycomelately 2 years ago from Tasmania

Oh! It's science - so that's ok then ..... silly me! Lol


Oztinato profile image

Oztinato 2 years ago from Australia

JCL

it merely means that it is to be taken the same way other provable theorems are.

Why make an exception just because it doesn't agree with atheism? That would be unscientific and prejudicial to the search for truth.


Paladin_ profile image

Paladin_ 2 years ago from Michigan, USA Author

As usual, Oz, you're completely incorrect, and you've misrepresented my views.

I've NEVER stated whether or not I "believe" the mathematical translation of Gödel's theorem, because I CAN'T. The math is largely beyond my current understanding.

What I HAVE stated, REPEATEDLY, is that I don't agree with Gödel's ACTUAL THEOREM -- the one he wrote that was later translated into Henkin semantics by Dana Scott.

You, on the other hand, refuse to even analyze Gödel's actual, original theorem, insisting instead that the mathematical translation -- the one you've admitted you DON'T UNDERSTAND -- is "proof" of God's existence.

For example, just now, you've asserted that the theorem "has been tested and proved by scientists." But how do you know it's been proved? Since you've admitted you don't understand the math, are you simply taking someone else's word for it? Or are you merely accepting it without question because you believe it agrees with your theological viewpoint?

I personally have no "problem" with Gödel's theorem. I've examined it and found it just as ridiculous and unconvincing as every other ontological argument that I've ever heard. I'm still waiting for you to examine it AT ALL.

Let's try this from another angle...

Oz, if I can demonstrate that Gödel's original theorem was mistranslated by Dana Scott, will you admit that the mathematical translation cannot therefore be considered authoritative "proof" of God's existence, and spare us from your tiresome nonsense?


Randy Godwin profile image

Randy Godwin 18 months ago from Southern Georgia

Great explanation re Godel's theorem, Paladin. Oz is indeed a trip... or perhaps on one. :P


Paladin_ profile image

Paladin_ 18 months ago from Michigan, USA Author

Hehe. Thanks, Randy. :-)

With regard to Oz, I've made numerous efforts to get him to honestly examine Gödel's actual arguments, but he appears quite satisfied to simply take it on faith that it's been mathematically 'proven' -- even though he has repeatedly admitted he doesn't understand the math.

In the end, I suppose that illustrates the great difference between skeptics and believers -- the skeptic actually wants to know what's TRUE, and will investigate to that end, while the believer only wants to know what supports his or her own belief, and is satisfied once they've found it.


Randy Godwin profile image

Randy Godwin 18 months ago from Southern Georgia

You've hit the nail on the head, Pal! :) I think Oz is fearful he WILL understand your points. LOL!


JMcFarland profile image

JMcFarland 18 months ago from The US of A, but I'm Open to Suggestions

I think Oz understands more than he wants to admit. It's been a long time since he's spammed hubs spouting this argument, he's moved on to others. To me, that says he recognizes that it failed, and can't argue against the rebuttals.


Randy Godwin profile image

Randy Godwin 18 months ago from Southern Georgia

I think he does too, Julie. H e seems to have a bit of the troll in him, but perhaps I'm mistaken about him. He sure is sensitive to be commenting on the religion forums and hubs though. Always worrying about personal attacks , unless of course, he's making them. LOL!


Oztinato profile image

Oztinato 18 months ago from Australia

I note the continuation of personal attacks by Randy and others. These will be reported immediately of course in keeping with strict Hub guidelines.


Randy Godwin profile image

Randy Godwin 18 months ago from Southern Georgia

Why don't you simply stay off of the religious topics, Oz. You're apparently too sensitive to take part in them without getting your feelings hurt. Always reporting someone like a grammar school hall monitor. Grow up why don't you! Geesh!!


JMcFarland profile image

JMcFarland 18 months ago from The US of A, but I'm Open to Suggestions

I'm not sure that oz understands how reporting on hubs differs from that of the forums. I'm also not sure he knows how to define a personal attack, and seems to view an attack as synonymous with criticism and discussion.


Randy Godwin profile image

Randy Godwin 18 months ago from Southern Georgia

I'm seriously considering adding him to my "do not respond to" list which only has a few people which I abhor exchanging views with. They really have nothing to gain by discussing religion with those of us who are seeking facts about their beliefs. These self-proclaimed Christians are exactly the opposite of the man/god they claim to emulate. I suppose Oz will take this as a personal attack even though it is indeed the truth.

Catherine, do as you see fit with this comment. :)


Paladin_ profile image

Paladin_ 18 months ago from Michigan, USA Author

Actually, this is Paladin's hub, and I absolutely loathe deleting comments. Thus far, there have been only two instances where I've had to delete someone's comments.

The first is someone who insisted on posting his poetry in the comments of one of my hubs. The second is a blanket-deletion warning to one of HubPages' most notorious copy-and-paste spammers (who I won't mention by name, but many already know to whom I refer), informing him that all his future posts on my hubs will be pre-emptively deleted as soon as he posts them.

As for Oz, I don't want to beat a dead horse here, so I will only say that there has, indeed, been some personal criticism posted against him (and he has committed the same offense on other hubs).

However, I will allow a limited amount of this sort of back-and-forth -- as long as it doesn't replace actual discussion and debate. This isn't grade school, and I won't allow my hubs to become to become so sanitized and anaesthetized by political correctness that people are afraid to speak their minds.

We're all adults here, and as long as things don't get out of hand, I'm not going to play hall monitor.


Randy Godwin profile image

Randy Godwin 18 months ago from Southern Georgia

Sorry, Pal. I had this hub confused with Catherine's. :)


Oztinato profile image

Oztinato 18 months ago from Australia

When someone aims insults, accusations and falsehoods at a particular individual that is a personal attack. For example the ol chestnut re "trolling" or discussing that person in a derogatory manner as seen in the above posts. It looks, sounds and smells ugly.

If someone attacks an argument as opposed to an individual that is a debate.


Randy Godwin profile image

Randy Godwin 18 months ago from Southern Georgia

Thanks for clearing that up, Oz. I nominate you to decide who's doing what. I have extreme faith in you to be fair and impartial, as everyone else should. Your brilliance makes the rest us seem merely amateurs when matching wits with you. Your are clearly one of those who are selected by the one true God to advise the rest of us sinners as how to live our lives. I cannot thank you enough. :P


jonnycomelately profile image

jonnycomelately 18 months ago from Tasmania

So, when someone says to me: "Oh! My God!" I should not take that seriously, right?


Paladin_ profile image

Paladin_ 18 months ago from Michigan, USA Author

You're right, Oz. We shouldn't be discussing you in a derogatory manner in the third person, and for that, I apologize. Whether or not the criticisms are valid, it's still rude.

However, you're also at fault here, as you've often mischaracterized criticisms of your arguments as "personal attacks" in the past, and have threatened to "report" people on numerous occasions. You've 'cried wolf' so many times before that, now when somebody DOES make a snarky personal comment to you, your complaints just seem like more of the same.

And even those comments that could legitimately be called 'personal attacks' are nothing more than light-hearted mocking -- the sort of thing that anyone else would just let roll off their back. Thus, it tends to make us suspicious when you react so strongly to them, as if your intentions are to change the subject when your arguments are being eviscerated.

I'm just saying...


Randy Godwin profile image

Randy Godwin 18 months ago from Southern Georgia

I apologize for my rudeness. I try and refrain from such until I get hit with the first stone. After that.....the game is afoot. :)


Oztinato profile image

Oztinato 18 months ago from Australia

Peeps

accusations of trolling are almost at the bottom of the barrel and are not acceptable by anyone's standards. Why this personal attack was made by an allegedly educated person is mystifying. If it wasn't for the odd mystical attraction I feel to this female my anger would have no bounds.

To defend such attacks is equally puzzling.


JMcFarland profile image

JMcFarland 18 months ago from The US of A, but I'm Open to Suggestions

Randy is a female now?


Randy Godwin profile image

Randy Godwin 18 months ago from Southern Georgia

Ha! Me AND Bruce Jenner........LOL!


JMcFarland profile image

JMcFarland 18 months ago from The US of A, but I'm Open to Suggestions

Randy, and you didn't even let me know. Sheesh I feel left out. Does it make you feel better that there's apparently a certain mystical attraction to you though?


Randy Godwin profile image

Randy Godwin 18 months ago from Southern Georgia

Not really, Julie. I'm accustomed to attracting all sorts of......odd thinking strangers. :P

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