From Newsgroup: sci.math

On 2/12/2026 11:23 AM, Tristan Wibberley wrote:

On 11/02/2026 21:53, Alan Mackenzie wrote:

Mathematicians have proven that many decision problems can not be
answered, all the nonsense about "idiosyncrasies of self-referential
logic" notwithstanding.

It's not at all clear to me that those unanswerables are properly
classified as "decision problem" unless one uses an auto-explication (my
term for when a term is both an explicatum and explicandum of an explication). Carnap's definition of explication excludes such an act
(though I don't know if he'd picked up the bad habit of using "decision problem" as an explicatum).

I think Carnap would have admitted "L-decision problem" as an explicatum
of the explicandum "decision problem". The nonsense act of calling pathologically self-referential problems as "L-decision problems" would
be obvious because one does not have a problem of choosing between only classifications "true" and "false" when one has merely been fooled into thinking those are candidates without a whole heap of others beside.

I hereby indulge myself with some old-timey assertive logistic
philosophy, you might call it a strawman, something to ponder and burn down:

We can understand the fallacy by making explicit the implicit false assumption: "the sentence after the conjunctive connector following can
be assigned no valuation but 'true' or 'false' AND blah-blah". That is
the cultural synergy covertly induced in the ponderer by a poetic form
of expression ("proposition" the explicatum, not the explicandum, it's another auto-explication) but it's not /well/ formalised in that it's a
mess of massive description and wonderment. I think usage of AND gives
us falsity for pathologically self-referential 'blah-blah' if we have
the right type-system but other connectives give us other, non-truth, classifications. A connective that means the implication of neither
truth nor falsity is also available. Of course, the ponderer has the inducement in the form of a volition to be disobedient and choose to
react in a variety of unassertive ways.

A proof is a proof.

Tautology.

*My pair of axioms is confirmed by peer reviewed papers*
reCx (Provable(T, x) rco Meaningful(T, x)) --- (Schroeder-Heister 2024)
reCx (Provable(x) rcA True(x)) --- Anchored in (Prawitz, 2012)

What is the appropriate notion of truth for sentences whose meanings are understood in epistemic terms such as proof or ground for an assertion?
It seems that the truth of such sentences has to be identified with the existence of proofs or grounds...
Prawitz, D. (2012). Truth as an Epistemic Notion. Topoi, 31(1), 9rCo16 https://doi.org/10.1007/s11245-011-9107-6

1.2 Inferentialism, intuitionism, anti-realism
Proof-theoretic semantics is inherently inferential, as it is
inferential activity which manifests itself in proofs. It thus belongs
to inferentialism (a term coined by Brandom, see his 1994; 2000)
according to which inferences and the rules of inference establish the
meaning of expressions...
Schroeder-Heister, Peter, 2024 "Proof-Theoretic Semantics" https://plato.stanford.edu/entries/proof-theoretic-semantics/#InfeIntuAntiReal --
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable for the entire body of knowledge.<br><br>

This required establishing a new foundation<br>
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