Quote:
Originally Posted by Kriminal99
H retains its normal function when operated as part of the constructed machine which is given itself as input.
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Again, please state why this is a non-trivial assumption.
Stating that it results in infinite regress is not a valid conclusion, so I understand why you try to layer on this as an "additional implied assumption":
Quote:
Originally Posted by Kriminal99
and by logical consequence of that assumption
H does not trace computations of machines input into it, since doing so in the constructed composite machine would cause an infinite regress that would cease the machines normal function.
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Although I entertained your assumption that the theorem incorporates this infinite regress, in fact it does not.
The input to H is simply a function and its initial input. There is no mechanism either implied or required that that "input" causes a recursion: that is, if you do use H as its own input, the parameters have no way of knowing that the input is code to be called rather than being data.
Again, realize that the theorem refers specifically to algorithms and not (necessarily) to machines running those algorithms.
Do not bite at the bait of pleasure till you know there is no hook beneath it,
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