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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Can there be a truth without a truthmaker?
Date: Sat, 27 Apr 2024 12:37:23 -0500
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On 4/27/2024 3:16 AM, Lawrence D'Oliveiro wrote:
> On Sat, 6 Apr 2024 21:26:16 -0700, Ross Finlayson wrote:
> 
>> ... and the usual old idea that mathematics is analytic while experience
>> is empirical ...
> 
> What about that distinction itself, though: can it be characterized as
> “analytic” (coming from mathematics) or “empirical” (coming from
> experience)?

I have worked very diligently on this for about two decades.
It seems that I may have fixed the issues with the analytic/synthetic
distinction such that my redefinition becomes unequivocal.

My system is not at all about the nature of reality it is only about
the nature of meaning expressed using language.

Expressions that are {true on the basis of their meaning} are
simply relations between finite strings of formalized semantic meaning.

This does include Frege's Principle of compositionality
https://en.wikipedia.org/wiki/Principle_of_compositionality

This is anchored in Proof theory rather than model theory
https://en.wikipedia.org/wiki/Proof_theory

All of the general Facts of the world are assumed to be
already encoded as relations between finite strings thus
axioms of a formal system.

Natural language expressions are formalized using
https://plato.stanford.edu/entries/montague-semantics/

Many expressions that are {true on the basis of observation}
have already been encoded as axioms that represent general
Facts of the world.

The details of current situations that are not general
facts of the world can be formalized as a discourse context.
This forms a mapping from {true on the basis of observation}
to {true on the basis of meaning}.

∃L ∈ Formal_Systems, ∃x ∈ L (True(L, x)  ≡ (L ⊢ x))
∃L ∈ Formal_Systems, ∃x ∈ L (False(L, x) ≡ (L ⊢ ~x))
∃L ∈ Formal_Systems, ∃x ∈ L (Truth_Bearer(L, x) ≡ (True(L, x) ∨ False(L, 
x)))

The great thing about all of this is that any expression that
lacks a truthmaker is simply construed as untrue. This eliminates
the mathematical notions of undecidability and incompleteness.

Such a system could screen out expressions like this:
"This sentence is not true"
and also apply two different order of logic thus conclude
This sentence is not true: "This sentence is not true" is true
because the inner sentence is not a truth bearer.

People that truly understand the Tarski Undefinability theorem
at its deepest philosophical levels as opposed to and contrast
with people that only know as a sequence of mechanical steps
might agree that my prior paragraph is a precisely accurate
summation of the philosophical issues involved.

We still have unknown truths that include but are not limited to
requiring an infinite sequence of inference steps, events having
no witnesses, or scientific knowledge that is not yet discovered.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer