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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, because Olcott doesn't undestand
Date: Wed, 3 Jul 2024 07:45:29 -0400
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On 7/2/24 11:39 PM, olcott wrote:
> 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.

And so True(L, x) must be false, and thus we are saying that x, which is 
defined to "not True(L, x)" must be true, so not only are you wrong 
about it not being a truth bearer, you are wrong about not being true.

Or, does your logic say that "not false" as a logical expresion isn't 
true? and thus your logic fails to hold to the rule of the excluded middle?

> 
>> 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.

And "True(L, x)" needs to return True if x is True, and False if x is 
False, or not a truth bearer.

So, since x defined as "not True(L,x)" is True if True(L, x) says no, 
then True failed to live up to its requirements.

And you show you are unable to understand what requirements are.

> 
>>>
>>> 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.

So, you think the Goldbach's conjecture IS true? Show your proof and win 
the prize,

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

But there are MANY such statements, so you are just admitting that your 
theory is just full of holes.

> 
>>>
>>> {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.

No, it isn't the case that the VERBAL meanings have anything to do with it.

It is the FORMAL meanings, defined in the system that define it.

And Infinite Chains genrate semantic truth.

Also, just because something is true in a "verbal model" of the world 
doesn't make it true in a given formal system.

> 
>> 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.

But formal systems do not need to be "accurate models of the actual 
world", and what Quine was pointing out was that natural language is 
inherently a bad model as words can have too many different meanings.

> 
>>>
>>> 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.

Then go in and get out of Formal systems. The rules are different, and 
what works in one place doesn't necessarily work in the other.

> 
>>>
>>> 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.

Nope, that is a LIE, and shows your ignorance, and that your foundation 
of anaklytc truth just can't handle the logic.

You just admitted that there were statements you "truth-maker" logic 
can't handle, because they need infinite steps.

So, now it seems you are saying that there are statements with actual 
truth value of true or false that are not "truth-bearers", in other 
words, you are admitting you definition is a self-contradiction.

> 
> 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.

You mean you have MISUNDERSTOOD It for two decades.

> 
>> 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 
========== REMAINDER OF ARTICLE TRUNCATED ==========