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On 4/27/2024 3:16 AM, Lawrence D'Oliveiro wrote:I kind of think about Montague as about Russell: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.
>
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