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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, because Olcott doesn't undestand
Date: Wed, 3 Jul 2024 09:14:26 -0500
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On 7/3/2024 6:45 AM, Richard Damon wrote:
> 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,

Is "a fish" true or false or neither?
That "a fish" is not true does not make it 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.
> 
It has the same truth value as "a fish"

> 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?
> 

Self-contradictory expressions are not truth-bearers
thus have no truth value.

>>
>>> 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.
> 

*That is not the way True(L,x) works*
True(L,x)
returns true if x is true and false if x not true.

False(L,x) is True(L,~x)
returns true if x is false and false if x not false.

True(L, "a fish") is false and False(L, "a fish") is false.

> 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,
> 

An infinite sequence can prove Goldbach's conjecture is true or false.

>>
>>> 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.
> 
All of the important things can be done in finite proofs.
Only the unimportant things require infinite proofs.

>>
>>>>
>>>> {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.
> 

To cover the entire body of all {analytic} truth we
have (a) formal systems of logic and math using formal languages.

To cover all the rest we have (b) a correct verbal model of
the actual world specified using formal language that can
be translated to and from natural language.

> It is the FORMAL meanings, defined in the system that define it.
> 
> And Infinite Chains genrate semantic truth.
> 

They have no significant practical application.

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

The accurate verbal model of the actual world contains
all of this.

>>
>>> 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.
> 

The formal system that is an accurate model of the actual world
has subsystems.

>>
>>>>
>>>> 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.
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