• =?UTF-8?Q?Re=3A_Within_Proof_Theoretic_Semantics_G=C3=B6del=27s_G_h?= =?UTF-8?Q?as_no_meaning_in_PA?=

    From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,sci.math on Mon Jul 13 10:50:43 2026
    From Newsgroup: comp.theory

    On 13/07/2026 00:23, olcott wrote:
    On 7/12/2026 4:16 PM, Tristan Wibberley wrote:
    On 28/04/2026 11:35, Alan Mackenzie wrote:
    [ Followup-To: set ]

    In comp.theory Scott Hoge <nospam@nospam.com> wrote:
    ...
    You're correct that the proof does not refer to directed graphs.
    What I want to argue, rather, is that such graphs can be used to
    /visualize the meaning/ of the G||del sentence.

    ...

    In the graph you drew, (still in the quoted text above), each node is
    identical to the others.

    Yes, a "network" (or the DAG variant of a network) is required. A
    network is a graph with labelled nodes.



    That can get the evaluation of an expression stuck
    in an infinite evaluation loop on the basis of the
    cycle in its directed graph. Knowledge is acyclic.

    Knowledge is not acyclic. There are many kinds of telations between
    the parts of knoledge, as can be determiend by asking questions like
    "how do you know" and "where did you get the idea" and "what else
    does the same" and so on and analyzing the answers. Some of these
    relatoins lead to opposte directions.
    --
    Mikko
    --- Synchronet 3.22a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to comp.theory on Mon Jul 13 11:29:58 2026
    From Newsgroup: comp.theory

    On 7/13/2026 2:50 AM, Mikko wrote:
    On 13/07/2026 00:23, olcott wrote:
    On 7/12/2026 4:16 PM, Tristan Wibberley wrote:
    On 28/04/2026 11:35, Alan Mackenzie wrote:
    [ Followup-To: set ]

    In comp.theory Scott Hoge <nospam@nospam.com> wrote:
    ...
    You're correct that the proof does not refer to directed graphs.
    What I want to argue, rather, is that such graphs can be used to
    /visualize the meaning/ of the G||del sentence.

    ...

    In the graph you drew, (still in the quoted text above), each node is
    identical to the others.

    Yes, a "network" (or the DAG variant of a network) is required. A
    network is a graph with labelled nodes.



    That can get the evaluation of an expression stuck
    in an infinite evaluation loop on the basis of the
    cycle in its directed graph. Knowledge is acyclic.

    Knowledge is not acyclic. There are many kinds of telations between
    the parts of knoledge, as can be determiend by asking questions like
    "how do you know" and "where did you get the idea" and "what else
    does the same" and so on and analyzing the answers. Some of these
    relatoins lead to opposte directions.


    directed graph cycles mean stuck in an infinite loop.
    --
    Copyright 2026 Olcott

    My 28 year goal has been to make
    "true on the basis of meaning expressed in language"
    reliably computable for the entire body of general knowledge.
    The complete structure of this system is now defined.

    The entire body of knowledge expressed in language is
    comprised of two types of relations between finite strings:
    (a) *Axioms* Expressions of language that are stipulated to be true.

    My system bridges the analytic/synthetic distinction by
    expressly encoding all empirical "atomic facts" in a formal
    language such as CycL of the Cyc project.

    (b) *Inference Rules* Expressions of language that are semantically
    entailed syntactically from (a) and/or (b).
    --- Synchronet 3.22a-Linux NewsLink 1.2
  • From Mikko@mikko.levanto@iki.fi to comp.theory on Tue Jul 14 10:15:01 2026
    From Newsgroup: comp.theory

    On 13/07/2026 19:29, olcott wrote:
    On 7/13/2026 2:50 AM, Mikko wrote:
    On 13/07/2026 00:23, olcott wrote:
    On 7/12/2026 4:16 PM, Tristan Wibberley wrote:
    On 28/04/2026 11:35, Alan Mackenzie wrote:
    [ Followup-To: set ]

    In comp.theory Scott Hoge <nospam@nospam.com> wrote:
    ...
    You're correct that the proof does not refer to directed graphs.
    What I want to argue, rather, is that such graphs can be used to
    /visualize the meaning/ of the G||del sentence.

    ...

    In the graph you drew, (still in the quoted text above), each node is >>>>> identical to the others.

    Yes, a "network" (or the DAG variant of a network) is required. A
    network is a graph with labelled nodes.



    That can get the evaluation of an expression stuck
    in an infinite evaluation loop on the basis of the
    cycle in its directed graph. Knowledge is acyclic.

    Knowledge is not acyclic. There are many kinds of telations between
    the parts of knoledge, as can be determiend by asking questions like
    "how do you know" and "where did you get the idea" and "what else
    does the same" and so on and analyzing the answers. Some of these
    relatoins lead to opposte directions.

    directed graph cycles mean stuck in an infinite loop.

    There are cycles in any street map of any city but drivers don't
    get stuck in inifinite loops.
    --
    Mikko
    --- Synchronet 3.22a-Linux NewsLink 1.2