• Halting problem proof converted to Liar Paradox --- never resolves to a truth value

    From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,sci.lang on Sun Oct 12 10:09:08 2025
    From Newsgroup: sci.lang

    On 10/12/2025 4:25 AM, Mikko wrote:
    On 2025-10-11 13:44:09 +0000, olcott said:

    On 10/11/2025 8:41 AM, dbush wrote:
    On 10/11/2025 9:40 AM, olcott wrote:
    That is only because you stupidly ignore the expressly
    stated details of correctly matching correct non-halting
    behavior patterns.
    But the pattern in question is *not* a non-halting behavior pattern
    because it exists in the halting computation DD.

    Turing machine deciders only compute the mapping
    from their finite string inputs to an accept state
    or reject state on the basis that this input finite
    string specifies a semantic or syntactic property.

    The only way to correctly determine the actual behavior
    that an actual input actually specifies is for simulating
    halt decider H to simulate its input D.

    Another way is to use partial halting deciders that are proven to
    never give a wrong answer until one of them gives some answer.


    Determining the halt status of an input that
    does the opposite of whatever value is returned
    is as bogus as determining whether or not this
    Liar Paradox sentence is true or false:
    "This sentence is not true".

    ?- LP = not(true(LP)).
    LP = not(true(LP)).

    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.

    This proves that LP has an infinitely recursive
    structure that never resolves to a truth value.

    My own Minimal Type Theory proves the same thing.
    LP := ~True(LP)
    00 ~ 01
    01 True 00

    Minimal Type Theory (YACC BNF) https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF --
    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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