Comment on How Gödel's Proof Works (2020)parentComments−GoblinSlayer29dThat won't work. Gödel number encodes a paradox, but a halting execution of a TM is not a paradox, so can't be written as a Gödel number.−pfdietz29dYour word salad is not even wrong. For example:Gödel number encodes a paradoxWTF do you mean by this?−GoblinSlayer28dA statement that can't be proved true or false and thus demonstrates incompleteness of logic.−pfdietz28dHow is that a paradox? And how does that imply the correct argument I gave doesn't work? (It doesn't imply that.)−GoblinSlayer28dParadox is a statement that can't be proved true or false; "this statement is false" is an example of Gödel statement. The argument doesn't work, because execution of a Turing machine can't be expressed as a Gödel number.−pfdietz28dParadox is a statement that can't be proved true or falseNo it isn't.execution of a Turing machine can't be expressed as a Gödel numberYes it can.
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That won't work. Gödel number encodes a paradox, but a halting execution of a TM is not a paradox, so can't be written as a Gödel number.
Your word salad is not even wrong. For example:
WTF do you mean by this?
A statement that can't be proved true or false and thus demonstrates incompleteness of logic.
How is that a paradox? And how does that imply the correct argument I gave doesn't work? (It doesn't imply that.)
Paradox is a statement that can't be proved true or false; "this statement is false" is an example of Gödel statement. The argument doesn't work, because execution of a Turing machine can't be expressed as a Gödel number.
No it isn't.
Yes it can.