All will fall prey to the fact that the program must produce the same output as its emulation of itself. It can never get around this fact. Therefore it either produces a finite amount of input and then stops waiting for its emulated self, or it never gets around to producing something different than itself.
Either way it fails to diagonalize itself. The exact cause will vary. The eventual result will not.
Classical mathematics gets around this by waving hands over constructions with impossible procedures based on undiscoverable truths. By assumption these procedures can never be the input to themselves. The result is an insane number of possible outputs about whose tenuous existence we can say little but our claim that they exist.
No argument of pure logic alone can demonstrate any form of existence for these impossibilities, you must make additional unprovable philosophical assumptions about the nature of truth and existence.
I know that these techniques and results seem natural to you. But that is a consequence of your indoctrination into a system of thought which glosses over these complications instead of exploring them.
All will fall prey to the fact that the program must produce the same output as its emulation of itself. It can never get around this fact. Therefore it either produces a finite amount of input and then stops waiting for its emulated self, or it never gets around to producing something different than itself.
Either way it fails to diagonalize itself. The exact cause will vary. The eventual result will not.
Classical mathematics gets around this by waving hands over constructions with impossible procedures based on undiscoverable truths. By assumption these procedures can never be the input to themselves. The result is an insane number of possible outputs about whose tenuous existence we can say little but our claim that they exist.
No argument of pure logic alone can demonstrate any form of existence for these impossibilities, you must make additional unprovable philosophical assumptions about the nature of truth and existence.
I know that these techniques and results seem natural to you. But that is a consequence of your indoctrination into a system of thought which glosses over these complications instead of exploring them.