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  • Re: Foundations of Logic

    From Richard Damon@21:1/5 to olcott on Fri Dec 15 20:05:43 2023
    On 12/15/23 4:12 PM, olcott wrote:
    On 12/15/2023 1:51 PM, Ross Finlayson wrote:
    One theory, ....  "The", logic.

    It's pretty simple as a universe of consistent objects, ..., to begin.

    The foundations of logic from a logicians POV is whatever they learned
    by rote. foundations of logic from a philosophers POV is every coherent
    set of ideas that can possibly exist.

    Gödel proved that expression G in PA cannot be proved in PA yet
    can be proved in metamathematics. This assumes that different
    orders of logic must be in different formal systems.

    When we hypothesize a single formal system having ALL orders
    of logic then instead of G cannot be proved in PA and can be
    proved in metamathematics we have G cannot be proved in F[n]
    and can be proved in F[n+1]. Thus incompleteness ceases to be
    possible.


    Which means you just don't understand what a "Formal System" actually
    is, or what an "Order" is in Logic.

    Note, "Orders of Logic" is a completely different thing then "Levels of Meta-Logic", and thus your arguement is based on a Category Error.

    --- SoupGate-Win32 v1.05
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  • From Mikko@21:1/5 to Ross Finlayson on Sat Dec 16 10:08:58 2023
    On 2023-12-15 19:51:16 +0000, Ross Finlayson said:

    One theory, .... "The", logic.

    It's pretty simple as a universe of consistent objects, ..., to begin.

    That is not a reliable foundation before you have enough
    foundtaions that you can define "consistent".

    Mikko

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Sat Dec 16 09:06:35 2023
    On 12/16/23 12:54 AM, olcott wrote:
    On 12/15/2023 3:12 PM, olcott wrote:
    On 12/15/2023 1:51 PM, Ross Finlayson wrote:
    One theory, ....  "The", logic.

    It's pretty simple as a universe of consistent objects, ..., to begin.

    The foundations of logic from a logicians POV is whatever they learned
    by rote. foundations of logic from a philosophers POV is every coherent
    set of ideas that can possibly exist.

    Gödel proved that expression G in PA cannot be proved in PA yet
    can be proved in metamathematics. This assumes that different
    orders of logic must be in different formal systems.

    When we hypothesize a single formal system having ALL orders
    of logic then instead of G cannot be proved in PA and can be
    proved in metamathematics we have G cannot be proved in F[n]
    and can be proved in F[n+1]. Thus incompleteness ceases to be
    possible.


    As a concrete example:
    This sentence is not true: "This sentence is not true" is true
    because the inner sentence is not a truth bearer.
    These two are one order of logic (level of indirect reference) apart.
    "Order of Logic" is NOT "Level of Indirection" but the category of what
    Qualifiers span.

    So, you are showing your ignorance of the theory,

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)