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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Analytic Truth-makers
Date: Mon, 22 Jul 2024 21:42:03 -0400
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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?

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

> 
>> 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.

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.

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 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.

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.