GENIUS FORUMS

http://www.simplygodel.com/interviews.htm

Q. David Hilbert believed that eventually all mathematical things would be defined. Gödel's theorem disproves that. Are there any other commonly held beliefs / theories that the incompleteness theorem puts into doubt?

A: Incompleteness shows that mathematics, logic and axiomatic reasoning do not furnish us with absolute truth. It shows that the truth is not totally black or white, not even in pure math, not even in the domain of pure reason. This is very difficult emotionally for mathematicians to accept.

Are you posting an appeal to authority?

Gregory Chaitin's interpretation of Gödel is disputable [and being disputed by his peers]. For starters: it doesn't address truth, it deals with mathematical and formal logical provability. The axiomatic truths of a system would derive ultimate truth value from a higher system, that's all.

Existence appears to be a given, even so, it seems to lead to circular reasoning. Of course, circular logics might also lead to new knowledge.

Some might argue that absolute truths must apply for all possible worlds. I don't know...

It seems that our total knowldege of truth is just a small pebble on the tip of a giant iceburg of knowledge. What can we say about reality?

Expect the unexpected...


We are much more intelligent than our dogs and cats. Abstract concepts mean nothing to the mind of our pets. Now imagine a being of higher intelligence, such, that the being's intelligence is as far above our intelligence as our intelligence is above our dogs and cats.

We would have no understanding of the abstract concepts spoken by the advanced being. The advanced being has much greater understanding regarding properties of existence like truth, etc. His knowledge and understanding would be much more complete than ours.

All truths are not known. We can only work within certain limited parameters of knowledge and understanding, at the present time.

What can we say about those unknown truths or whatever they are?

Not much?

We can only use self referential "circular" reasoning with a limited amount of knowledge and limited understanding.

yahooyoda wrote:

We are much more intelligent than our dogs and cats.

No "we" are not. You must be countered amongst the dogs and cats for your heinous ignorance of the concept 'absolute'.

You, Yahoo wrote: Some might argue that absolute truths must apply for all possible worlds. I don't know...

"Absolute truths must apply for all possible worlds", because they ARE absolute truths. That is: they are truths that are everlasting and the same everywhere.

But, you were instinctively correct about one thing:

We would have no understanding of the abstract concepts spoken by the advanced being.

In this case, the advanced being is speaking English.

Sue Hindmarsh wrote:
yahooyoda wrote:

"We are much more intelligent than our dogs and cats."

No "we" are not. You must be countered amongst the dogs and cats for your heinous ignorance of the concept 'absolute'.

Humans do not have higher abstract reasoning abilities than do dogs and cats? You could be right... probably not.

Sue Hindmarsh wrote: You, Yahoo wrote: "Some might argue that absolute truths must apply for all possible worlds. I don't know..."

"Absolute truths must apply for all possible worlds", because they ARE absolute truths. That is: they are truths that are everlasting and the same everywhere.

Emphatically stating that something is everlasting does not make it true.

Sue Hindmarsh wrote:But, you were instinctively correct about one thing:
"We would have no understanding of the abstract concepts spoken by the advanced being".

In this case, the advanced being is speaking English.

Your argument appears to be a few spiteful quips and insults. Not really an argument at all.

yahooyoda wrote:

Sue Hindmarsh wrote: You, Yahoo wrote: "Some might argue that absolute truths must apply for all possible worlds. I don't know..."

"Absolute truths must apply for all possible worlds", because they ARE absolute truths. That is: they are truths that are everlasting and the same everywhere.

Emphatically stating that something is everlasting does not make it true.

I think you misunderstood her argument, Yoda. For something to be considered absolute it has to be considered being everlasting and the same everywhere. It's part of the definition. Because if an absolute had some limitation, meaning that it would be depending on a particular context or time, it would be relative, not?

Diebert van Rhijn wrote:
I think you misunderstood her argument, Yoda. For something to be considered absolute it has to be considered being everlasting and the same everywhere. It's part of the definition. Because if an absolute had some limitation, meaning that it would be depending on a particular context or time, it would be relative, not?

Absolutes cannot have limitations from within their specified[defined] domains of applicability. Logical deduction could not hold true if they did. But since human knowledge is limited then those domains are included within a larger domain of unknown understanding and knowledge.

yahooyoda wrote: Absolutes cannot have limitation from within their specified[defined] domains of applicability. Logical deduction could not hold true if they did. But since human knowledge is limited then those domains are included within a larger domain of unknown understanding and knowledge.

In general there's a problem with imagining that there's always a 'larger' domain or body of understanding out there. Because even if it would be so: it would only become understanding and knowledge when it enters the realm where our earlier defined absolutes rule. So to become a form of understanding or meaningful experience, they will not overturn the absolute, defined as the axiom of all our understanding.

And of course: when something is unknown it can not yet qualify as understanding or knowledge. Perhaps the knowledge that one doesn't know [something], forms a particular knowledge of the lack but then it seizes to be merely unknown.

Diebert van Rhijn wrote:

yahooyoda wrote: Absolutes cannot have limitation from within their specified[defined] domains of applicability. Logical deduction could not hold true if they did. But since human knowledge is limited then those domains are included within a larger domain of unknown understanding and knowledge.

In general there's a problem with imagining that there's always a 'larger' domain or body of understanding out there. Because even if it would be so: it would only become understanding and knowledge when it enters the realm where our earlier defined absolutes rule. So to become a form of understanding or meaningful experience, they will not overturn the absolute, defined as the axiom of all our understanding.

It is unknown whether or not there will always be a larger body of understandng and knowledge. It seems reasonable to assume that new truths can always expand understanding of the previously known truths.


"The opposite of a correct statement is a false statement. The opposite of a profound truth may well be another profound truth. " (Niels Bohr)

yahooyoda wrote:

Diebert van Rhijn wrote:

yahooyoda wrote: Absolutes cannot have limitation from within their specified[defined] domains of applicability. Logical deduction could not hold true if they did. But since human knowledge is limited then those domains are included within a larger domain of unknown understanding and knowledge.

In general there's a problem with imagining that there's always a 'larger' domain or body of understanding out there. Because even if it would be so: it would only become understanding and knowledge when it enters the realm where our earlier defined absolutes rule. So to become a form of understanding or meaningful experience, they will not overturn the absolute, defined as the axiom of all our understanding.

It is unknown whether or not there will always be a larger body of understandng and knowledge. It seems reasonable to assume that new truths can always expand understanding of the previously known truths.

But this doesn't have anything to do with absolutes. The absolute is truth itself, not a truth.

"The opposite of a correct statement is a false statement. The opposite of a profound truth may well be another profound truth. " (Niels Bohr)

Yes, the higher the truth, the less opposition there can be.

Diebert van Rhijn wrote:
The absolute is truth itself, not a truth.

Truth itself, is not a truth? Interesting reasoning there...

Forgive me for the slight ramble that follows but what the heck...

The absolute truth as the ultimate truth i.e. "truth itself" is analogous to the most inclusive truth - or the set of all sets. Is the set of all possible sets also a set? The inclusivity and exclusivity criteria beholden to the set of all possible sets seems to necessitate a requirement for a non-contradictory emancipation of our mental prisons of finite construction.

Perhaps if a dialectic process can be expressed in terms of a duality it could lead to a solution of sorts whereby we realize that objectification and subjectification form a duality of perception. It is still possible to objectivise the subjective with meditative practices, of course. The idea of containment is very subjective-like concept for the mind. It is an entrapment of thought that could lead to logical trouble.

The absolute is not its definition? Is not a thing isomorphic to its own description, if that description is complete in every respect?

Is not the absolute also an absolute, according to the definition of an absolute? Does the absolute have its own identity? If not then you agree with my reasoning that AN absolute truth pertains to specified domains regarding its definitive properties and does not apply to the ultimate truth, ultimate reality, ultimate whatever, which you call "The Absolute".

Yahoo, you ask others to:

Forgive me for the slight ramble that follows but what the heck...

"What the heck", indeed! Your desire to intentionally mutilate the concept 'absolute' for your own fun is unforgivable. It shows a clear disinterest by you to take your own mind seriously. (If you are a teenager, that's perfectly understandable, but if you are older, it is a sure sign of an arrested development.)

The point is, Yahoo, if don't take your own mind seriously enough to understand a simple and straightforward term such as 'absolute', how do you expect anyone else to take seriously you supposedly having a discussion about it?

Diebert and I have laid out simply what 'absolute' means. Look the word up in the dictionary, and you will see that we are correct.

Using that definition, you will then be able to see why your earlier posts on this thread are confused and unfocused. You'll also be able to see what Diebert meant when he wrote:

The absolute is truth itself, not a truth.

And also what I meant when I wrote:

"Absolute truths must apply for all possible worlds", because they ARE absolute truths. That is: they are truths that are everlasting and the same everywhere.

'Absolute' is an extremely important term, as you can see. You would know by now that it is an essential one here at this forum, as the focus is on discussing nothing less.

-

So, how about you start over with the definition of 'absolute' in mind. You could begin again with your set of quotes; seeing where they diverge from, or accord with the definition of 'absolute'.

Q. David Hilbert believed that eventually all mathematical things would be defined. Gödel's theorem disproves that. Are there any other commonly held beliefs / theories that the incompleteness theorem puts into doubt?
A. Incompleteness shows that mathematics, logic and axiomatic reasoning do not furnish us with absolute truth. It shows that the truth is not totally black or white, not even in pure math, not even in the domain of pure reason. This is very difficult emotionally for mathematicians to accept.

You'll also be able to answer some of your own questions:

Some might argue that absolute truths must apply for all possible worlds. I don't know...

You say absolute truth is defined.

David Quinn says the truth of absolute truth is the conclusion of a logical reasoning process.

I agree that any logical deduction that follows from a definition must be true according to the definition.

I will keep an open mind and hope not to get bogged down in completely rigid thinking.

There is an infinite universe of knowledge and understanding,

I cannot let the old neurons rest on discarded laurels of past knowledge...

Yahoo, you wrote:

There is an infinite universe of knowledge and understanding

This sounds very much like what you wrote in an earlier post:

Absolutes cannot have limitation from within their specified[defined] domains of applicability. Logical deduction could not hold true if they did. But since human knowledge is limited then those domains are included within a larger domain of unknown understanding and knowledge.

Diebert, in answer to you, explained:

In general there's a problem with imagining that there's always a 'larger' domain or body of understanding out there. Because even if it would be so: it would only become understanding and knowledge when it enters the realm where our earlier defined absolutes rule. So to become a form of understanding or meaningful experience, they will not overturn the absolute, defined as the axiom of all our understanding.

In answer, naturally your ignorance of the definition of 'absolute truth' shone through:

It is unknown whether or not there will always be a larger body of understandng and knowledge. It seems reasonable to assume that new truths can always expand understanding of the previously known truths.

But now there is no excuse. You have been thoroughly educated on the matter by both Diebert and I. So why continue to make the same colossal error? Remember that it was you who called this thread "Absolutes". So you could at least try and keep your mind on the topic. Your dreaming that, "There is an infinite universe of knowledge and understanding" is as meaningful to the topic as balloon animals are. And yet you say you're all for "logical deducing". Ok, why not give it a try? Because as things presently stand, your affirmation -

I will keep an open mind and hope not to get bogged down in completely rigid thinking.

- is the opposite of what you should be striving for. You need to fix some boundaries for your thinking – preferably boundaries pertaining to the pursuit of truth. That should help stop your fuzzy unfocused thinking. By thus focussing your thoughts, you’ll then be able to discern and discriminate; or at least remember the importance of correct definitions.

Sue Hindmarsh wrote:

I will keep an open mind and hope not to get bogged down in completely rigid thinking.

- is the opposite of what you should be striving for. You need to fix some boundaries for your thinking – preferably boundaries pertaining to the pursuit of truth. That should help stop your fuzzy unfocused thinking. By thus focussing your thoughts, you’ll then be able to discern and discriminate; or at least remember the importance of correct definitions.

I have questioned the absolute certainty that is embraced so strongly. It must form a mental-buffer for some, much like a security blanket does.

Expanding the boundaries of what is known is not for the faint of heart, yes...

Yahoo,

You can't have "questioned the absolute", because you continue to block from your mind the meaning of the concept. Without an understanding of what the word 'absolute' means, you will continue to just scratch around with the rest of the dogs and cats.

You know, to anyone following this discussion, it must appear odd to them that I bother to continue urging you to open a dictionary to look up the word 'absolute'. It seems like such a small thing to ask you to do. But of course, it is the exact opposite of a small thing. (Which explains why you continue to baulk at the idea.) The task is imbued with tremendous effort: as it requires the person's brain to power up to a level of consciousness where it may previously never have tread. Opening a dictionary to study the meaning of a word, and then casting one's mind around to understand the logical consequences of that meaning, is one looking into one's own mind. And most people have never done this, so the idea sounds wildly strange, and naturally they are afeared. But if you never do this - if you never look at the consequences of an idea - you will sadly remain trapped in dog and cat world.

Yahoo: Expanding the boundaries of what is known is not for the faint of heart, yes...

No wonder you pose that sentence as a question. You've readily shown by your airy-fairy, wishy-washy, namby-pamby approach to this topic that you have no boundaries in place to either "expand", or contract.

Everything you have thus far written is useless, because it has no connection to reality (i.e. it is meaningless). Look up the dictionary, and use the definition of 'absolute' to frame your feelings about absolutes, and then we may at last begin a discussion on, "Absolutes".

Today, a young man in space located somewhere over Egypt, discovered that communication with animals is yet another truth.

The sensitivity of the Zen whisk, is the quickness of the cat's eye...