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Unanswerable multiple choice question

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Re: Unanswerable multiple choice question

#31

Post by ElliotH »

jaekwon wrote: post #24
[deleted] wrote: post #21

Earlier quoted context omitted.

[deleted]

Can you prove or disprove this statement? "Godel's first incompleteness theorem is a Godel sentence" Anyways, it is my belief that Godel's Incompleteness Theorem is false by definition of Truth. That is, what is true is provable and vice versa. Once you depart from this definition, you get statements that are paradoxical, and by my definition of Truth, the Godel Incompleteness Theorem is certainly paradoxical (thus F…

But he proved his theorems. Thus it is provable and by your own definition is true regardless of what the theorem actually says.

Re: Unanswerable multiple choice question

#32

Post by tdmackey »

[deleted] wrote: post #30
jaekwon wrote: post #24

Earlier quoted context omitted.

Can you prove or disprove this statement? "Godel's first incompleteness theorem is a Godel sentence" Anyways, it is my belief that Godel's Incompleteness Theorem is false by definition of Truth. That is, what is true is provable and vice versa. Once you depart from this definition, you get statements that are paradoxical, and by my definition of Truth, the Godel Incompleteness Theorem is certainly paradoxical (thus F…

[deleted]

So be it, but it doesn't imply that Godel's incompleteness theorem applies.

Metaphorically they may somehow be similar given someone's viewpoint, but it doesn't make it so.

Re: Unanswerable multiple choice question

#33

Post by Chirono »

jaekwon wrote: post #24
[deleted] wrote: post #21

Earlier quoted context omitted.

[deleted]

Can you prove or disprove this statement? "Godel's first incompleteness theorem is a Godel sentence" Anyways, it is my belief that Godel's Incompleteness Theorem is false by definition of Truth. That is, what is true is provable and vice versa. Once you depart from this definition, you get statements that are paradoxical, and by my definition of Truth, the Godel Incompleteness Theorem is certainly paradoxical (thus F…

The thing is, that Godel's theorem is provable. So by your definition, it is true.

The usual definition of false is not "I can't prove it's true" as that is pretty hard to decide. Suppose I have a statement S that I can't prove. Is it false, or am I just not clever enough to prove that it is true?

The normal definition of S being false is that the negation of S is true.

Part of what the incompleteness theorem says is that in any system of logic that doesn't contradict itself, there will be statements that are neither provably true nor provably false. Thus you can take these statements to be true OR false as an axiom and it won't lead to contradictions.

Re: Unanswerable multiple choice question

#34

Post by [deleted] »

ElliotH wrote: post #31
jaekwon wrote: post #24

Earlier quoted context omitted.

Can you prove or disprove this statement? "Godel's first incompleteness theorem is a Godel sentence" Anyways, it is my belief that Godel's Incompleteness Theorem is false by definition of Truth. That is, what is true is provable and vice versa. Once you depart from this definition, you get statements that are paradoxical, and by my definition of Truth, the Godel Incompleteness Theorem is certainly paradoxical (thus F…

But he proved his theorems. Thus it is provable and by your own definition is true regardless of what the theorem actually says.

[deleted]

Re: Unanswerable multiple choice question

#36

Post by jaekwon »

Chirono wrote: post #33
jaekwon wrote: post #24

Earlier quoted context omitted.

Can you prove or disprove this statement? "Godel's first incompleteness theorem is a Godel sentence" Anyways, it is my belief that Godel's Incompleteness Theorem is false by definition of Truth. That is, what is true is provable and vice versa. Once you depart from this definition, you get statements that are paradoxical, and by my definition of Truth, the Godel Incompleteness Theorem is certainly paradoxical (thus F…

The thing is, that Godel's theorem is provable. So by your definition, it is true. The usual definition of false is not "I can't prove it's true" as that is pretty hard to decide. Suppose I have a statement S that I can't prove. Is it false, or am I just not clever enough to prove that it is true? The normal definition of S being false is that the negation of S is true. Part of what the incompleteness theorem says is…

Godel's "proof" states that G is undecidable, and since that is what G states, G must be True, and this G is a True statement that cannot be proven (or disproven). I say that the conclusion that G is True does not follow. Calling G True is no better than calling G False.

Nobody can prove GIT (Godel's Incompleteness Theorem). I tried to disprove it, but I can't do that either. Godel's Incompleteness Theorem itself is a Godel Sentence.

You can add GIT as an axiom in my system, then it would become True. I'm saying that you don't need to do that to have a complete system. You can either have a complete and consistent system, OR you can have GIT.

Re: Unanswerable multiple choice question

#39

Post by jjs »

0% chance.

Answering randomly may give you a result that coincidentally matches the truth, but you have provided no logical or epistemological support for your choice, nor any chain of reasoning that leads you from the available evidence to a conclusion that there even is a correct answer.

You have a 25% chance of randomly choosing the "right" answer, (C) 0%, but no paradox is created because you answered without establishing knowledge of the answer, and therefore your answer cannot rightly be called correct.

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