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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Analytic Truth-makers
Date: Tue, 23 Jul 2024 09:55:20 -0500
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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.

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

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer