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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Analytic Truth-makers
Date: Mon, 22 Jul 2024 21:12:08 -0500
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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.

> If so, why can't Godel's G be?
> 

Gödel's G is true in MM.

>>
>>> In PA, G (not g, that is the variable) is shown to be TRUE, but
>>> only estblished by an infinite series of truth preserving
>>> operations, that we can show exist by a proof in MM.
>>>
>>
>> No stupid that is not it. A finite sequence of truth preserving
>> operations in MM proves that G is true in MM. Some people use lower
>> case g.
> 
> But the rules of construction of MM prove that statements matching
> certain conditions that are proven in MM are also true in PA.
> 

That is merely a false assumption.

> And G meets that requirements. (note g is the number, not the statement)
> 
> We can show in MM, that no natural number g CAN satisfy that
> relationship, because we know of some additional properties of that
> relationship from our knowledge in MM that still apply in PA.
> 
> Thus, Godel PROVED that G is true in PA as well as in MM.
> 

That is merely a false assumption. Truth-makers cannot cross system
boundaries.

> He also PROVED that there can't be a proof in PA for it.
> 
>>
>> Here is the convoluted mess that Gödel uses 
>> https://www.liarparadox.org/G%C3%B6del_Sentence(1931).pdf
> 
> And your inability to understand it doesn't make it wrong.
> 

It is only his false conclusion that makes him wrong.
His false conclusion is anchored in an incorrect
foundation of expressions that are true on the basis
of their meaning.

> It makes YOU wrong.
> 
>>
>>> The truth of G transfers, because it uses nothing of MM, the Proof
>>>  does not, as it depends on factors in MM, so can't be expressed in
>>> PA.
>>
>> No stupid that is not how it actually works. Haskell Curry is the
>> only one that I know that is not too stupid to understand this. 
>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>
> 
> Really, then show what number g could possibly sattisfy the relationship.
> 

Incorrect foundation of truth-makers.

> I don't think you even undertstand what Curry is talking about, in fact, 
> from some of your past comments, I am sure of that. (Note, not all 
> "true" statements in L are "elementary statements" for the theory L as I 
> believe you have stated in the past.

Mere stupidly empty rhetoric entirely bereft of any supporting
reasoning probably used to try to hide your own ignorance.

A theory is thus a way of picking out from the statements of F
a certain subclass of true statements.


Curry, Harkell B. 1977. Foundations of Mathematical Logic. Page:45

  The statements of F are called elementary statements to distinguish 
them from other statements which we may form from them … A theory (over 
F is defined as a conceptual class of these elementary statements. Let T 
be such a theory. Then the elementary statements which belong to T we 
shall call the elementary theorems of T; we also say that these 
elementary statements are true for T. Thus, given T, an elementary 
theorem is an elementary statement which is true. A theory is thus a way 
of picking out from the statements of F a certain subclass of true 
statements.
https://www.liarparadox.org/Haskell_Curry_45.pdf

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