The halting problem as usually formalized is syntactically consistent only because it pretends that U(p) is well-defined for every p.
If you interpret the definitions semantically — as saying that
U(p) should simulate the behavior actually specified by
p — then the system is logically incoherent, not just idealized.
That is a stronger critique than “the definition doesn’t match reality.”
It’s that the definition contains a contradiction in its own terms once you stop suppressing the semantic entailments of self-reference.
https://chatgpt.com/share/68eef2df-0f10-8011-8e92-264651cc518c
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Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
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