The Philosophy Discussion Forum

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/proo ... tuAntiReal

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), 9–16
https://doi.org/10.1007/s11245-011-9107-6

Apparently no one.

% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

Prolog finally once and for all resolves the Liar Paradox as
semantically incoherent within the analytical framework
of Proof Theoretical Semantics. It does this on the basis
that the LP specifies a cycle in the directed graph of its
evaluation sequence, thus not a well founded justification tree.

There are purely analytic expressions such that the meaning
of some expressions are defined in terms of other expressions.
Example: 5 > 3.

There are also what s historically been called synthetic expressions
that are empirically grounded in a verbal model of the world.
Example: The shape of the Earth is approximately spherical.

'True in Russell's system' means, as was said: proved in
Russell's system; and 'false in Russell's system' means:
the opposite has been proved in Russell's system
https://www.liarparadox.org/Wittgenstein.pdf

When one understands that the entire body of true on the basis
of meaning expressed in language is composed entirely of
(a) Expressions that are stipulated to be true "atomic facts"
(b) Expressions derived by semantic entailment from (a)

then it becomes obvious that Wittgenstein's critique of
Gödel's 1931 incompleteness was spot on exactly right.
Proof Theoretic Semantics in its most basic essence is
saying this exact same thing since

Truth as an Epistemic Notion Dag 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
https://link.springer.com/article/10.10 ... 011-9107-6