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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: The Tarski Undefinability Theorem failed to understand truthmaker
 theory
Date: Tue, 2 Jul 2024 23:18:42 -0400
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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.

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

> 
> 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)"

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

> 
> 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?

Why do they need a seperate rule?

> 
> {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.

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.

> 
> 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.

> 
> 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.

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).

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