XPost: comp.theory, comp.ai.philosophy, sci.lang.semantics
On 8/19/2020 9:32 PM, Newberry wrote:
Let H(P, n) be a program with two possible outcomes: TRUE and FALSE. The parameter P is a program and n is its input. Suppose that H(P, n) = TRUE
if and only if P halts on n. Suppose further that if H(P, n) = FALSE
then P does not halt on n, and suppose that H is sound. Let furthermore
P* be a program with itself as a parameter. The claim is that there
exists a program H such that H(H, H*) = FALSE, that is, H proves that it
does not prove that H* halts.
https://www.researchgate.net/publication/316562253_Getting_around_the_Halting_Problem
When this is studied abstractly key details slip through the cracks of
the abstractions. When this is studied concretely every detail is
totally specified, nothing slips through the cracks.
When we understand that the abstract model of computation specified by
the x86 language directly provides access to unlimited memory and can
simulate a UTM, then we understand that the x86 language defines a
Turing Complete model.
Within this model we can succinctly and concretely encode the key self-referential halting problem counter-example. Only when we do this
can we "see" what the abstractions have kept hidden.
--
Copyright 2020 Pete Olcott
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