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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: The Tarski Undefinability Theorem failed to understand truthmaker
 theory
Date: Tue, 2 Jul 2024 22:39:52 -0500
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On 7/2/2024 10:18 PM, Richard Damon wrote:
> On 7/2/24 11:00 PM, olcott wrote:
>> Every {analytic} proposition X having a truth-maker is true.
>> Every {analytic} proposition X having a truth-maker for ~X is false.
>> Those expressions of language left over are not not truth bearers.
> 
> And the "truth-maker" in a formal system needs to be from the formal 
> system itself, unless the proposition IS a truth-maker itself of the 
> formal system.
> 

Yes.

> Also, most propositions actually need MULTIPLE truth-makers to make them 
> true.
> 

Yes.

>>
>> True(L,x) and False(L,x) where L is the language and x is the
>> expression of that language rejects self-contradictory undecidable
>> propositions as not truth-bearers.
> 
> So, what is the value of:
> 
> True(L,x) where x, in language L is the statement "not True(L,x)"
> 
It is that as I have always been saying, that x is not a truth bearer.

> Or is your True(L,x) not a predicate that always gives an True or False 
> answer? (which is the requirement that Tarski has)
> 

As I have always been saying X is true, or false or not a truth bearer.
"a fish" is not a truth bearer.

>>
>> Only expressions of language requiring an infinite number of steps
>> such as Goldbach's conjecture slip through the cracks. These can
>> be separately recognized.
> 
> How?
> 

We ourselves can see that it can be proven in an infinite
sequence of steps thus an algorithm can see this too.

> Why do they need a seperate rule?
> 
It is the only thing that does not fit perfectly in truth-maker theory.

>>
>> {Analytic} propositions are expressions of formal or natural language
>> that are linked by a sequence of truth preserving operations to the
>> verbal meanings that make them true or false. This includes expressions
>> of language that form the accurate verbal model of the actual world.
> 
> But that isn't correct for formal systems. so you just wrote yourself 
> out of the problems.
> 
It is correct in the correct notion of formal systems.

> Formal systems are NOT based on "Natural Language" but ONLY their own 
> Formal Language, and need not have any direct bearing on the "actual 
> world", but tend to create there own world, which may be used as a way 
> to modle ideas about our actual world, or maybe not.
> 

I already included that. By tacking on that it can
be in natural or formal language and include an accurate
model of the actual world Quine's objections that there
is no separately identifiable body of {analytic truth}
are overcome.

>>
>> Modern day philosophers at best only have a vague understanding
>> of what a truth-maker or truth-bearer is.
> 
> Which is one reason to try to stay out of that realm, and stay in the 
> formal systems without that problem.
> 

That most everyone else is ignorant is no excuse for
me to not make these things clear.

>>
>> Truthmakers
>> This much is agreed: “x makes it true that p” is a construction that 
>> signifies, if it signifies anything at all, a relation borne to a 
>> truth-bearer by something else, a truth-maker. But it isn’t generally 
>> agreed what that something else might be, or what truth-bearers are, 
>> or what the character might be of the relationship that holds, if it 
>> does, between them, or even whether such a relationship ever does 
>> hold. https://plato.stanford.edu/entries/truthmakers/
>>
> 
> So, it seems that part of your problem is that you don't understand that 
> Tarski is talking PURELY in Formal Systems, with the rules there-in, and 
> not your vague philospoplical systems.
> 

I take his scope and broaden it.
Within his narrow scope and my foundation of analytical truth
When X not provable or refutable from axioms merely means X is
not a truth-bearer in L.

Haskell Curry presents an equivalent idea.
https://www.liarparadox.org/Haskell_Curry_45.pdf

I have always known this for the whole two decades that I have
been working on this yet only now have all of the words to say it.

> In Formal systems, there is no question about "Truth Makers" as Truth in 
> a formal system is (generally) DEFINED as having a finite or infinite 
> chain of semantic connections (Your truth preserving operations, which 
> are defined in the system) from the pre-defined list of fundamental 
> truths of the system (Your Truthmakers).
> 

Not quite. Some of the operations are not truth preserving.
https://en.wikipedia.org/wiki/Principle_of_explosion
In software engineering that would be called a kludge.

> The fundamental truths of the system have nothing making them true, 
> except the system itself defining them as such.

Kittens are baby cats and not fifteen story office building ONLY
by translating the accurate model of the actual world into the
arbitrary conventions of English.

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