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Jan 4th, 2003, 08:56 AM
#1
Thread Starter
transcendental analytic
Gödel's theorem is a contradiction
This statement is true
If this statement was false then YES, that statement must have been false because not (this statement = true) this statement = false.
If this statement was true then YES, that statement must be true because This statement is true is true
but it can't be both true and false can it?
This statement is false
If this statement was true then no, it can't be because then it would be true, but then again it says its false etc...
Similarly,
"I wrote this statement"
If this is true, then YES its true, because i actually wrote it.
If this is false, then YES its false because i didn't write this statement (look at the assumption).
But then it would be a contradiction because a statement can't be both true and false
Gödel's theorem:
Gödel asks the UTM (Ultimate Truth Machine, which only can say if a statement is true or not) this question
"UTM will not say this statement is true."
and Gödel knows its true, but UTM can't say it thus its not a ultimate truth machine.
_________________________________________________
Is this true? Yes because UTM can't say its true since then he would contradict himself.
_________________________________________________
Is this false? Yes because that would mean "UTM will say this statement is true" and UTM could in practice say its false - thus making the whole statement false.
Thus Gödels theorem is a contradiction, it can't be both true and false.
Funny thing is looking back at the theorem it says:
Gödel asks the UTM (Ultimate Truth Machine, which only can say if a statement is true or not) this question
"UTM will not say this statement is true."
and Gödel knows its true, but UTM can't say it thus its not a ultimate truth machine.
Look at the bold statements, clearly its a contradiction!!! Because if its not a ultimate truth machine then it could in fact say that the statement is true, contradicting itself.. and Gödel would be wrong again, but he can't be both wrong and right can he?
Conclusions:
1. Phrases with Self references are not statements.
2. You can't reason as above by assuming that its either true or false to begin with without first checking that its a valid statement, and selfrerential phrases are not statements.
Ok, I might be wrong here but everyone have a look.
Last edited by kedaman; Jan 4th, 2003 at 08:59 AM.
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reverse (p (6*9)) where p x|x==0=""|True=chr (48+z): p y where (y,z)=divMod x 13
To throw away OOP for low level languages is myopia, to keep OOP is hyperopia. To throw away OOP for a high level language is insight.
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