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Godel's Inconsistency Theorem

Duxwing

I've Overcome Existential Despair
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#1
Dear Forum,

After a long and difficult debate, I had a horrifying realization: how can we decide when a debate is won or lost if, as Godel proved, no logical system can be proven to be consistent without assuming that another logical system is consistent in order to test the first system against the second? That is to say, "Who or what referees a debate?". For if we can't, then I don't see the point in debating or reasoning anymore, and I feel sad about that.

:(

So am I screwed?

-Duxwing
 
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#3
Dux. Why worry about this truth? You cannot pull yourself up by your bootstraps. Just go to a higher level to settle it. If you don't like the higher level, then feel free to overrule it. Reach for the stars. It can be done.
 

Architect

Professional INTP
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#4
When living on a desert island you have to make do with what you have. If that means eating seaweed and grass then so be it.
Gödel's theorem (and variations from other fields, I believe information theory contains a version) need to be taken as fact. This means that it's our fancy that something can be absolutely proved. As it turns out our Universe doesn't allow for that kind of proof for anything.

This is useful to know. For example I find debates of religion humorous, the religious would say "prove to me that god doesn't exist!" Gödel tells us that there isn't that kind of proof, for anything! What we have is evidence, and we conduct our daily life on the knowledge that enough evidence does give you the truth, it's just not Truth. In this example the overwhelming evidence is that god doesn't exist.

Think of it like Quantum Mechanics - we'd like for the sub atomic to be nice and tidy with billiard balls following deterministic paths. It doesn't - oh well, that doesn't prevent us from creating quantum computers, IC's that depend on QM, and quantum communications systems.

Likewise we'd like proof to be absolute, but that's not in the laws of this universe.
 

Duxwing

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#5
Dux. Why worry about this truth? You cannot pull yourself up by your bootstraps. Just go to a higher level to settle it. If you don't like the higher level, then feel free to overrule it. Reach for the stars. It can be done.
Would you please go into more detail?

-Duxwing
 

Chad

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#6
I don't know about you but I argue for knowledge sack. Arguments allows you too see the wholes in your own viewpoint as much as the wholes of you the others persons viewpoint. No, one is perfect and no one has a perfect understanding of you universe. threw arguments and discussion we imporve our understanding of the world becoming more logical as we go. We start realizing fallacies and understanding truth better.

In the end you really can't prove anything but that doesn't mean you didn't learn something form the argument. Rather that was something about yourself or the opposing opinions. Debating is fun, if the only reason you debate is to prove others that you are right and they are wrong than you are completely missing the point.

There need not be a winner for a debate to be productive. I don't know how old you are but from what other have said I assume you are a teenager (feel free to correct me if I am wrong.). However, if you are a teenager or even a young adult you still have a lot to learn about life. I am 27 and I still have a lot to learn about life. I hope I keep on learning until I die (or I live forever and never stop learning, the later is preferred).
 
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#7
@Duxwing
Would you please go into more detail?
This wouldn't mean you seek elaboration, would it? Very well.

Dear Forum,

After a long and difficult debate, I had a horrifying realization: how can we decide when a debate is won or lost if, as Godel proved, no logical system can be proven to be consistent without assuming that another logical system is consistent in order to test the first system against the second? That is to say, "Who or what referees a debate?". For if we can't, then I don't see the point in debating or reasoning anymore, and I feel sad about that.
You described yourself as experiencing horror. This is something to avoid as the reality behind horror can be quite debilitating ... unless you are into horror movies.

A debate implies a side and another side. Neither side can see the other without conceding something. It is often the case a "sider" is bewildered or even horrified when bombarded by views seemingly impossibly contradictory to their own. The debate is not decided at the debate level. One side can only impose on the other.

The only way to see both is to rise above both sides and combine them. This combination is an emergence ... something not there before. This may be the referee you are looking for. This new view of seeing both sides rises above and itself can be disputed. If one wishes to surmount this dispute they must rise even higher. It depends on one's wishes (circumstances). One may decide no further progress is necessary and be at peace with the latest overview even though Godel would say in theory one can go further.

I trust this in not too detailed. If you find it so, I can always tone it down.:D
 

snafupants

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#8
Dear Forum,

After a long and difficult debate, I had a horrifying realization: how can we decide when a debate is won or lost if, as Godel proved, no logical system can be proven to be consistent without assuming that another logical system is consistent in order to test the first system against the second? That is to say, "Who or what referees a debate?". For if we can't, then I don't see the point in debating or reasoning anymore, and I feel sad about that.

:(

So am I screwed?

-Duxwing
@Duxwing

Wouldn't an agreed upon fact be the touchstone?

If someone argues eight feet, and someone else argues nine feet, you just measure the thing to discern who is "right," right?

Obviously, one couldn't readily measure a theoretical or future-oriented construct. The past too for that matter. History is just strung together stories, many of which are apocryphal.

There isn't an ironclad predicate by which to definitely crown a debate winner or judge the ultimate veracity of the claims. Everything is probability.

I guess if you had video of a past event, and you could show it wasn't doctored, that might do something. It might not.

The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.
How broadly are you looking to apply Godel's theorems on math logic?

This is useful to know. For example I find debates of religion humorous, the religious would say "prove to me that god doesn't exist!" Gödel tells us that there isn't that kind of proof, for anything! What we have is evidence, and we conduct our daily life on the knowledge that enough evidence does give you the truth, it's just not Truth. In this example the overwhelming evidence is that god doesn't exist.
@Architect

I just tell the theists that burden of proof doesn't work that way. :D
 
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#9
This is why well run debates generally have preset criteria to help outline what is considered a "win" for one side or the other.

Despite looking wishy-washy I ask why must a debate be win-lose? Why can't it be a mutual discovery of differing points of view?

Debates don't always have to be adversarial.
 

Duxwing

I've Overcome Existential Despair
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#10
@Duxwing
This wouldn't mean you seek elaboration, would it? Very well.


You described yourself as experiencing horror. This is something to avoid as the reality behind horror can be quite debilitating ... unless you are into horror movies.

A debate implies a side and another side. Neither side can see the other without conceding something. It is often the case a "sider" is bewildered or even horrified when bombarded by views seemingly impossibly contradictory to their own. The debate is not decided at the debate level. One side can only impose on the other.

The only way to see both is to rise above both sides and combine them. This combination is an emergence ... something not there before. This may be the referee you are looking for. This new view of seeing both sides rises above and itself can be disputed. If one wishes to surmount this dispute they must rise even higher. It depends on one's wishes (circumstances). One may decide no further progress is necessary and be at peace with the latest overview even though Godel would say in theory one can go further.

I trust this in not too detailed. If you find it so, I can always tone it down.:D
Right, right, dialectics. But what happens when the debate concerns a matter of fact?

-Duxwing
 

Duxwing

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#11
This is why well run debates generally have preset criteria to help outline what is considered a "win" for one side or the other.
How do you determine that the given system is consistent?

Despite looking wishy-washy I ask why must a debate be win-lose? Why can't it be a mutual discovery of differing points of view?

Debates don't always have to be adversarial.
Indeed, they do not. Adversarial debate is but one application of the overarching idea that systems cannot be proven consistent from within themselves.

-Duxwing
 

Duxwing

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#12
@Duxwing

Wouldn't an agreed upon fact be the touchstone?


Just agreeing on a fact doesn't make it true.

If someone argues eight feet, and someone else argues nine feet, you just measure the thing to discern who is "right," right?
But what proves that the yardstick is consistent? You're just taking its consistency on faith.

Obviously, one couldn't readily measure a theoretical or future-oriented construct. The past too for that matter. History is just strung together stories, many of which are apocryphal.
There isn't an ironclad predicate by which to definitely crown a debate winner or judge the ultimate veracity of the claims. Everything is probability.
Indeed, and the lack of such a predicate is most frustrating.


I guess if you had video of a past event, and you could show it wasn't doctored, that might do something. It might not.


How broadly are you looking to apply Godel's theorems on math logic?
I seek to apply them... get ready for the pun... consistently in all scenarios.

@Architect

I just tell the theists that burden of proof doesn't work that way. :D
Sometimes offering a proof of non-existence by internal contradiction or of un-provability by proof of unknowability is quite exciting... until the theists in question retreat into "It's our opinion and you can't take that away from us!". Certainly, I can't actually reach inside their minds and heal the psychological damage that religion has inflicted upon them but sufficient obstinance is not equivalent to sufficient evidence.

-Duxwing
 

Duxwing

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#13
I don't know about you but I argue for knowledge sack. Arguments allows you too see the wholes in your own viewpoint as much as the wholes of you the others persons viewpoint. No, one is perfect and no one has a perfect understanding of you universe. threw arguments and discussion we imporve our understanding of the world becoming more logical as we go. We start realizing fallacies and understanding truth better.
I also feel a certain sense of healthy growth in learning to recognize fallacies by intuition alone. Yet what of knowledge?

In the end you really can't prove anything but that doesn't mean you didn't learn something form the argument. Rather that was something about yourself or the opposing opinions. Debating is fun, if the only reason you debate is to prove others that you are right and they are wrong than you are completely missing the point.
If we cannot prove or justify any statement, then how can we learn, if learning is but the accumulation of knowledge, which, in turn is justified, true belief?

There need not be a winner for a debate to be productive. I don't know how old you are but from what other have said I assume you are a teenager (feel free to correct me if I am wrong.). However, if you are a teenager or even a young adult you still have a lot to learn about life. I am 27 and I still have a lot to learn about life. I hope I keep on learning until I die (or I live forever and never stop learning, the later is preferred).
I already know everything, I just can't remember it all at once! :D

And while I agree that debates needn't be adversarial, figuratively slamming someone's treasured beliefs and feelings into a hard wall of logic just feels so... right, like I'm doing the world a favor by eliminating illogic. Also, and equally figuratively, "pulling the rug out from under them" in an argument is also quite fun-- especially if you get to see the expression on their face as their argument falls to pieces in the blink of an eye.

^Am I a sick person because of the above?

-Duxwing
 

Chad

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#14
I also feel a certain sense of healthy growth in learning to recognize fallacies by intuition alone. Yet what of knowledge?



If we cannot prove or justify any statement, then how can we learn, if learning is but the accumulation of knowledge, which, in turn is justified, true belief?



I already know everything, I just can't remember it all at once! :D

And while I agree that debates needn't be adversarial, figuratively slamming someone's treasured beliefs and feelings into a hard wall of logic just feels so... right, like I'm doing the world a favor by eliminating illogic. Also, and equally figuratively, "pulling the rug out from under them" in an argument is also quite fun-- especially if you get to see the expression on their face as their argument falls to pieces in the blink of an eye.

^Am I a sick person because of the above?

-Duxwing
I would say sick but that just me. Maybe Egomaniac but not sick.
 
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#15
To Duxwing.
what happens when the debate concerns a matter of fact?
What fact? That's a good Q anyway. Note snafu. Do you mean like this:

If someone argues eight feet, and someone else argues nine feet, you just measure the thing to discern who is "right," right?
Measuring is going outside the opinion system. If someone says you have a bent measuring rod, you get a straight one. If someone says that wasn't straight, you get a bunch and average.
 

Absurdity

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#16
And while I agree that debates needn't be adversarial, figuratively slamming someone's treasured beliefs and feelings into a hard wall of logic just feels so... right, like I'm doing the world a favor by eliminating illogic. Also, and equally figuratively, "pulling the rug out from under them" in an argument is also quite fun-- especially if you get to see the expression on their face as their argument falls to pieces in the blink of an eye.

^Am I a sick person because of the above?

-Duxwing
Textbook case of an Fe-rush.

PS: I thought you were a nihilist. Maybe an existential nihilist but not an epistemological one? Well a little nihilism is a dangerous thing; drink deep, son.
 
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#17
Duxwing said:
How do you determine that the given system is consistent?
I don't think it really matters so long as both parties agree on the system before hand. Basically, I think Godel makes a good point but I don't think his point really hinders our ability to debate.

And while I agree that debates needn't be adversarial, figuratively slamming someone's treasured beliefs and feelings into a hard wall of logic just feels so... right, like I'm doing the world a favor by eliminating illogic. Also, and equally figuratively, "pulling the rug out from under them" in an argument is also quite fun-- especially if you get to see the expression on their face as their argument falls to pieces in the blink of an eye.

^Am I a sick person because of the above?
So I've noticed. >.> You're a little sick but you're in good company.
 

Duxwing

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#18
Textbook case of an Fe-rush.

PS: I thought you were a nihilist. Maybe an existential nihilist but not an epistemological one? Well a little nihilism is a dangerous thing; drink deep, son.
Could you elaborate on the Fe-rush aspect?

I am a nihilist. In fact, I'm so much of a nihilist that I realized that philosophy is just a very, very fun game. The necessity of axioms means that we're ultimately just entertaining ourselves and not producing anything absolute, so feeling any worry or despair about our inability to know "the meaning of life" or "the Truth" is, in the words of Spock, highly illogical.

-Duxwing

P.S. New philosopher?
 

Duxwing

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#19
I don't think it really matters so long as both parties agree on the system before hand. Basically, I think Godel makes a good point but I don't think his point really hinders our ability to debate.
But what we agree to doesn't influence what is true. :(

So I've noticed. >.> You're a little sick but you're in good company.
Hehehe! :) By the way, what does ">.>" mean, exactly?

-Duxwing
 

Duxwing

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#20
To Duxwing.
What fact? That's a good Q anyway. Note snafu. Do you mean like this:
Measuring is going outside the opinion system. If someone says you have a bent measuring rod, you get a straight one. If someone says that wasn't straight, you get a bunch and average.
I think that this measuring analogy has gone off the rails. How can one average the standard of proof for a given debate?

-Duxwing
 

Coolydudey

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#21
@Duxwing,
Where you are taking this is that we cannot know anything, something which I happen to believe in (agnosticism in its fullest form). Nihilism stems directly from this belief. Accept it, and deal with the world as you experience it, making the most of this experience, is my take on it. Because why not.
 

Duxwing

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#22
@Duxwing,
Where you are taking this is that we cannot know anything, something which I happen to believe in (agnosticism in its fullest form). Nihilism stems directly from this belief. Accept it, and deal with the world as you experience it, making the most of this experience, is my take on it. Because why not.
We can go one step further: we are beyond Good and Evil, as Nietzsche put so well. One cannot judge the world in any objective sense; ergo, one can, if one so chooses, simply act. All "objective" codes of morality are ultimately rationalizations of the internal or internalized impulses found in their codifiers, and the cognitive dissonnace induced by the presence of Others who possess different impulses could be (I have no data) resolved by calling one's own ideas Good and differing ideas Evil. And we must embrace this ultimately psychological nature of moral philosophy: the study of morality is the study of how agents function in social groups.

So, to make this abstract philosophical construct more concrete, I'll pose the rhetorical question: what are we to do when we see an old lady being robbed in the street? Whatever we want.

-Duxwing
 

Absurdity

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#23
Could you elaborate on the Fe-rush aspect?

I am a nihilist. In fact, I'm so much of a nihilist that I realized that philosophy is just a very, very fun game. The necessity of axioms means that we're ultimately just entertaining ourselves and not producing anything absolute, so feeling any worry or despair about our inability to know "the meaning of life" or "the Truth" is, in the words of Spock, highly illogical.

-Duxwing

P.S. New philosopher?
An Fe-rush is just my name for the feeling you described. Vanquishing an opponent in debate feels so good because the debate usually occurs in some sort of public forum and, as a result, strokes our inferior Fe as everyone realizes how super cool and smart we are. And even when it is a private debate, my theory is that it still feels good because we may see it as a victorious battle in a life-long crusade against ignorance, thus fulfilling our Fe's desire to serve a purpose greater than ourselves, which ultimately benefits the whole of humanity (at least from our arguably warped perspective ;)).

And if you're referring to my avatar, the answer is no, it is not a new philosopher, it is Italian actor Marcello Mastroianni who stars as Guido Anselmi in Federico Fellini's "8 1/2," which is a very good movie.
 

Duxwing

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#24
An Fe-rush is just my name for the feeling you described. Vanquishing an opponent in debate feels so good because the debate usually occurs in some sort of public forum and, as a result, strokes our inferior Fe as everyone realizes how super cool and smart we are. And even when it is a private debate, my theory is that it still feels good because we may see it as a victorious battle in a life-long crusade against ignorance, thus fulfilling our Fe's desire to serve a purpose greater than ourselves, which ultimately benefits the whole of humanity (at least from our arguably warped perspective ;)).
Whoa. That's deep insight; I feel as if you've crawled around my head awhile and produced my innermost thoughts before my eyes.

And if you're referring to my avatar, the answer is no, it is not a new philosopher, it is Italian actor Marcello Mastroianni who stars as Guido Anselmi in Federico Fellini's "8 1/2," which is a very good movie.
Oh, OK then.*

-Duxwing

*Philosopher>Actor :D
 
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#25
@Duxwing
I think that this measuring analogy has gone off the rails. How can one average the standard of proof for a given debate?
Some would say this is easily answered. Others would say, "I could tell you, but then I'd have to kill you." I prefer to say nothing.
 

joal0503

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#27
Dear Forum,

After a long and difficult debate, I had a horrifying realization: how can we decide when a debate is won or lost if, as Godel proved, no logical system can be proven to be consistent without assuming that another logical system is consistent in order to test the first system against the second? That is to say, "Who or what referees a debate?". For if we can't, then I don't see the point in debating or reasoning anymore, and I feel sad about that.

:(

So am I screwed?

-Duxwing
"The one who yells the loudest, will always win the debate." - Plato
 

Reluctantly

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#29
We can go one step further: we are beyond Good and Evil, as Nietzsche put so well. One cannot judge the world in any objective sense; ergo, one can, if one so chooses, simply act. All "objective" codes of morality are ultimately rationalizations of the internal or internalized impulses found in their codifiers, and the cognitive dissonnace induced by the presence of Others who possess different impulses could be (I have no data) resolved by calling one's own ideas Good and differing ideas Evil. And we must embrace this ultimately psychological nature of moral philosophy: the study of morality is the study of how agents function in social groups.

So, to make this abstract philosophical construct more concrete, I'll pose the rhetorical question: what are we to do when we see an old lady being robbed in the street? Whatever we want.

-Duxwing
Sometimes people care about others and they don't want to see them harmed. That's one kind of ethics. I suppose what you are talking about is a kind where people use it to harm people, but I'm not sure that's ethics...

What do you think about virtue ethics?
 
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#31
How do you determine that the given system is consistent?
I will tell you how to determine if a system is consistent if you are still reading this thread. Are you?
 
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#32
I believe you have got the reason for debating wrong.

And seriously, you've been told this one hundred times before already. Now you resort to nihilism. Pitiful.
 

Jennywocky

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#33
I believe you have got the reason for debating wrong.

And seriously, you've been told this one hundred times before already. Now you resort to nihilism. Pitiful.
If you're referring to Dux, this thread is 14 months old. So the info is probably out of date, especially considering his current usertitle.
 
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