If it is undecidable, then that means no proof exists (that H will or will not halt.)
H
If no proof exists, then H will loop forever searching for one.
Therefore undecidability implies H will run forever. You’ve just proved this.
Therefore a proof exists that H will run forever (that one), and H will eventually find it.
Paradox...
As people have been saying, if H can make this argument it is inconsistent and does not work properly (i.e. it does not return True or False in the correct situations.)
If it is undecidable, then that means no proof exists (that
Hwill or will not halt.)If no proof exists, then
Hwill loop forever searching for one.Therefore undecidability implies
Hwill run forever. You’ve just proved this.Therefore a proof exists that
Hwill run forever (that one), andHwill eventually find it.Paradox...
As people have been saying, if H can make this argument it is inconsistent and does not work properly (i.e. it does not return True or False in the correct situations.)