Originally posted by Alphanos
You are saying that the statement is false because UTM could say it is true.

the other way around, I'm saying the statement is false because UTM says it is true.
UTM cannot say that it is true if doing so would make it false.
thats the point, its now proven false.
The statement is only false if UTM does state it to be true, and only true if it does not. Thus the question is one that the UTM can never produce a correct answer to.
"UTM doesn't say this is true" is true
<=> UTM doesn't say this is true

"UTM doesn't say this is true" is false
<=> UTM says this is true

both are independently correct, where's the problem?

DiGiTaIErRoR
Thats my point, and I think Gödel's theorem is one of them