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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Analytic Truth-makers
Date: Tue, 23 Jul 2024 22:15:28 -0400
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On 7/23/24 10:55 AM, olcott wrote:
> On 7/23/2024 6:30 AM, Richard Damon wrote:
>> On 7/23/24 12:07 AM, olcott wrote:
>>> On 7/22/2024 9:56 PM, Richard Damon wrote:
>>>> On 7/22/24 10:12 PM, olcott wrote:
>>>>> On 7/22/2024 8:42 PM, Richard Damon wrote:
>>>>>> On 7/22/24 8:44 PM, olcott wrote:
>>>>>>> On 7/22/2024 7:17 PM, Richard Damon wrote:
>>>>>>>> On 7/22/24 8:11 PM, olcott wrote:
>>>>>>>>> On 7/22/2024 7:01 PM, Richard Damon wrote:
>>>>>>>>>> On 7/22/24 12:42 PM, olcott wrote:
>>>>>>>>>>> I have focused on analytic truth-makers where an expression
>>>>>>>>>>> of language x is shown to be true in language L by a sequence
>>>>>>>>>>> of truth preserving operations from the semantic meaning of x
>>>>>>>>>>> in L to x in L.
>>>>>>>>>>>
>>>>>>>>>>> In rare cases such as the Goldbach conjecture this may
>>>>>>>>>>> require an infinite sequence of truth preserving operations
>>>>>>>>>>> thus making analytic knowledge a subset of analytic truth. 
>>>>>>>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>>>>>>>>
>>>>>>>>>>> There are cases where there is no finite or infinite sequence
>>>>>>>>>>> of truth preserving operations to x or ~x in L because x is
>>>>>>>>>>> self- contradictory in L. In this case x is not a
>>>>>>>>>>> truth-bearer in L.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> So, now you ADMIT that Formal Logical systems can be
>>>>>>>>>> "incomplete" because there exist analytic truths in them that
>>>>>>>>>> can not be proven with an actual formal proof (which, by
>>>>>>>>>> definition, must be finite).
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> *No stupid I have never been saying anything like that* If g and
>>>>>>>>> ~g is not provable in PA then g is not a truth-bearer in PA.
>>>>>>>>>
>>>>>>>>
>>>>>>>> What makes it different fron Goldbach's conjecture?
>>>>>>>>
>>>>>>>>
>>>>>>>> You are just caught in your own lies.
>>>>>>>>
>>>>>>>> YOU ADMITTED that statements, like Goldbach's conjecture, might be
>>>>>>>>  true based on being only established by an infinite series of
>>>>>>>> truth preserving operations.
>>>>>>>>
>>>>>>>
>>>>>>> You seem to be too stupid about this too. You are too stupid to 
>>>>>>> grasp
>>>>>>> the idea of true and unknowable.
>>>>>>>
>>>>>>> In any case you are not too stupid to know that every expression 
>>>>>>> that
>>>>>>> requires an infinite sequence of truth preserving operations would
>>>>>>> not be true in any formal system.
>>>>>>
>>>>>> So, is Goldbach'c conjecture possibly true in the formal system of
>>>>>> Mathematics, even if it can't be proven?
>>>>>>
>>>>>
>>>>> No. If it requires an infinite sequence of truth preserving
>>>>> operations it is not true in any system requiring a finite
>>>>> sequence.
>>>>
>>>>
>>>> So you LIED when you said Goldbach's conjuecture could bve actually 
>>>> TRUE even if it could only be established to be true by an infinite 
>>>> sequence of truth preserving operations.
>>>>
>>>
>>> That you stupidly screw up the meaning of what I said in your own head
>>> is your stupidity and not my dishonesty.
>>
>> So, what does it mean that it is analytic truth, if not that it is a 
>> truth?
>>
>>
> 
> 
> L is the language of a formal mathematical system.
> x is an expression of that language.
> 
> When we understand that True(L,x) means that there is a finite
> sequence of truth preserving operations in L from the semantic
> meaning of x to x in L, then mathematical incompleteness is abolished.

Except that it doesn't mean that, except to a liar.

You even agreed that not a true statements have a finite sequence of 
steps, you are admit that you definition here is just false and your 
stating it a a definition to be a LIE.

> 
> ~True(L,x) ∧ ~True(L,~x)
> means that x is not a truth-bearer in L.
> It does not mean that L is incomplete
> 

And thus you show yourself to be a LIAR, as you just said that the 
Goldbach's conjecture COULD be an Analytic Truth, and thus a Truth 
Bearer, even if it didn't meet your supposed new definitoion of "Truth".

All you have done is LIED and named the "Provable" predicate to be now 
called "True" in your system. It CAN'T be a "truth" predicate, because 
it doesn't correctly handle statement you have agreed are true.