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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 19:18:38 -0400
Organization: i2pn2 (i2pn.org)
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On 7/3/24 10:14 AM, olcott wrote:
> 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.

Neither, so True(L, "a fish") is false. (assume "a fish" is a 
syntactically expressible statement in L)

The True predicate saying false doesn't mean the statement is false, 
just that it isn't true.

The problem comes when the language is expressive enough to build 
statement that are self-referential (even indirectly self-referential).

If we can form the statement x in L to be "~True(L, x)", then that 
system can not have a Truth Predicate, which is what Tarski is showing.

> 
>>  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"

Then so does your True predicacte, and thus isn't a predicate.

Thus, making you a LIAR.

> 
>> 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.

But the Truth Predicate, as Tarski defines it, can take as input 
non-truth-bearing statements, and indicate they are not true.

> 
>>>
>>>> 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.

Right so if x is defined as ~True(L, x) is not a truth bearer, and thus 
True(L, x) returns false, the x is defined as the negation of a false 
expression which is true. So you now have a true express also being a 
non-truth bearer and you system is inconsistant.

> 
> 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.

and if True(L, x) where x in L is ~True(L, x) says that x isn't true 
because it is not a truth bearer, you system breaks.

> 
>> 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.

No, because a "Proof" is BY DEFINTION a finite sequence.

> 
>>>
>>>> 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.

The is no such thing as an infinite proof, not in classic logic.

There are statements that are TRUE due to an infinite sequence of truth 
persevering steps, but that sequence of steps is not a proof.


It seems you don't understand the difference between truth and knowledge.

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