XPost: comp.theory, sci.logic, sci.math
From: polcott333@gmail.com
On 1/19/2026 11:29 PM, Richard Damon wrote:
> On 1/19/26 2:11 PM, olcott wrote:
>> Formerly Re: Analytic Truth-makers
>> in sci/logic and comp.theory
>>
>> On 7/23/2024 11:26 AM, olcott wrote:
>>>
>>> I am establishing a new meaning for
>>> {true on the basis of meaning expressed in language}
>>> Formerly known as {analytic truth}.
>>> This makes True(L,x) computable and definable.
>>>
>>> L is the language of a formal mathematical system.
>>> x is an expression of that language.
>>>
>>> When we understand that True(L,x) means that there is a finite
>>> sequence of truth preserving operations in L from the semantic
>>> meaning of x to x in L, then mathematical incompleteness is abolished.
>>>
>>> ~True(L,x) ∧ ~True(L,~x)
>>> means that x is not a truth-bearer in L.
>>> It does not mean that L is incomplete
>>>
>>
>> On 7/23/2024 11:26 AM, olcott in sci.logic, comp.theory
>>
>>
>> The above post is when I bridged the analytic/synthetic
>> divide that has existed since 1952
>> https://en.wikipedia.org/wiki/Two_Dogmas_of_Empiricism
>
> Which isn't about "Formal Logic Systems" and thus not applicable to what
> you have been trying to talk about.
>
"true on the basis of meaning expressed in language"
Is the sharp line of demarcation between objects
of math and computation and things that are not
objects of math and computation.
This line was blurred by Willard Van Orman Quine's
(1952) "Two Dogmas of Empiricism" until 18 months
ago when I came up with that.
> Note, that is about Philosophy, which argues about what is true about
> the world, NOT Formal Logic System, which talk about what is true in a
> Formal Logic system, which is ALWAYS what would be called analytic in
> that paper, as there is no "reality" except what derives from the
> analytic rules, so "syntetic" or emperical doesn't really exist, but is
> sometimes used to indicate things whose truth derives from an infinite
> chain of operatations, and thus are not analytically provable.
>
*Russell’s Logical Atomism*
the claim that the world consists of a plurality
of independently existing things exhibiting qualities
and standing in relations. According to logical atomism,
all truths are ultimately dependent upon a layer of
atomic facts, which consist either of a simple particular
exhibiting a quality, or multiple simple particulars
standing in a relation.
https://plato.stanford.edu/entries/logical-atomism/
This is exactly the "atomic facts" that are the axioms
of my formal system of all knowledge. To make such a
system physically implementable in a finite set of
atomic facts the details of most events are not stored
directly in the system. The system is at least the
complete body of general knowledge. It is augmented
with details of high priority events.
>>
>> with: "true on the basis of meaning expressed in language"
>
> Which you break by changing the meaning of words.
>
> All you do here is show you don't understand what you are talking about.
>
When the foundations of formal systems anchored in
model theoretic semantics are replaced by proof theoretic
semantics and each formal system has its own truth
predicate anchored in the Haskell Curry notion of
"true in the system" then the conflation error of
what was previously mistaken for "true in the system"
is corrected.
--
Copyright 2026 Olcott
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.
This required establishing a new foundation
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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