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  • =?UTF-8?Q?Re=3A_Simply_defining_G=C3=B6del_Incompleteness_and_Tarsk?==?UTF-8?Q?i_Undefinability_away_V24_=28Mapping_to_Boolean=29?=

    From olcott@NoOne@NoWhere.com to comp.theory,comp.ai.philosophy,comp.ai.nat-lang,sci.lang.semantics,sci.logic on Mon Jan 19 09:59:12 2026
    From Newsgroup: comp.ai.philosophy

    On 7/15/2020 9:57 AM, olcott wrote:
    On 7/14/2020 11:13 PM, olcott wrote:
    On 7/14/2020 10:30 PM, David Kleinecke wrote:
    On Tuesday, July 14, 2020 at 7:55:25 PM UTC-7, olcott wrote:

    These terms were used perfectly according to their standard meaning:
      >>>mathematical mapping in T from φ to a Boolean value<<<
    Lt occurs to me that we all would be happier if that was:
        mapping in T from φ onto the two-member set {true, false}


    You improved my words yet again, good job.

    https://en.wikipedia.org/wiki/Bijection,_injection_and_surjection

    The function is surjective, or onto, if each element of the codomain
    is mapped to by at least one element of the domain.


    A map is a way of associating unique objects to every element in a given set. So a map f : A ↦ B from A to B is a function f such that for every
    a ∈ A, there is a unique object f(a) ∈ B. The terms function and mapping are synonymous for map. https://mathworld.wolfram.com/Map.html

    ∀φ (TruthBearer(T,φ) ↔ f(T,φ) ∈ {true, false})

    For all φ of theory T φ is a truth bearer in T if and only if there is a function in T from φ to exactly one element of the set of {true, false}.


    --
    Copyright 2026 Olcott

    My 28 year goal has been to make
    "true on the basis of meaning expressed in language"
    reliably computable.

    This required establishing a new foundation
    for correct reasoning.
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