Many interesting statements aren't a property of the code alone. They're a property of the code when it's run in a particular environment. If you want the proof to be portable then it should only make assumptions that are true in any environment.
Aye, but in many cases a theoretical limit can be ignored in practice. (Stupid example: I need more cooling = "I need more fans", not "I'm running out of air".)
I dispute the infinity of stupidity! It can only be infinite on an infinite timeline, as there are a finite number of people at any given time! But is time infinite?