• Re: Proof Theoretic Semantics Blocks Pathological Self-Reference

    From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,sci.math,comp.ai.philosophy,comp.lang.prolog on Sun Jan 18 11:51:43 2026
    From Newsgroup: sci.math

    On 17/01/2026 17:53, olcott wrote:
    On 1/17/2026 3:22 AM, Mikko wrote:
    On 16/01/2026 19:47, olcott wrote:

    The system uses proof-theoretic semantics, where the
    meaning of a statement is determined entirely by its
    inferential role within a theory. A theory T consists
    of a finite set of basic statements together with
    everything that can be derived from them using the
    inference rules. The statements derivable in this
    way are the theorems of T. A statement is true in
    T exactly when T proves it.

    Usually the expression "is a theorem of T" is used instead of "is true
    in T". THe words "true" and "false" are usually reserved for truth in
    a particular interpretation.

    That is what I changed. That is how Incompleteness arises.

    No, it isn't. Changing words does not change the things the words
    refer to. It may be useful for deception by equivocation but does
    not serve any other useful purpose.
    --
    Mikko
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