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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis ---
Date: Fri, 8 Nov 2024 16:59:59 -0500
Organization: i2pn2 (i2pn.org)
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On 11/8/24 4:17 PM, olcott wrote:
> On 11/8/2024 12:31 PM, Richard Damon wrote:
>> On 11/8/24 1:08 PM, olcott wrote:
>>> On 11/8/2024 12:02 PM, Richard Damon wrote:
>>>> On 11/8/24 12:25 PM, olcott wrote:
>>>>
>>>>>
>>>>> That formal systems that only apply truth preserving
>>>>> operations to expressions of their formal language
>>>>> that have been stipulated to be true cannot possibly
>>>>> be undecidable is proven to be over-your-head on the
>>>>> basis that you have no actual reasoning as a rebuttal.
>>>>>
>>>>
>>>> No, all you have done is shown that you don't undertstand what you 
>>>> are talking about.
>>>>
>>>> Godel PROVED that the FORMAL SYSTEM that his proof started in, is 
>>>> unable to PROVE that the statement G, being "that no Natural Number 
>>>> g, that satifies a particularly designed Primitive Recursive 
>>>> Relationship" is true, but also shows (using the Meta-Mathematics 
>>>> that derived the PRR for the original Formal System) that no such 
>>>> number can exist.
>>>>
>>>
>>> The equivocation of switching formal systems from PA to meta-math.
>>>
>>
>>
>> No, it just shows you don't understand how meta-systems work.
>>
> 
> IT SHOWS THAT I KNOW IT IS STUPID TO
> CONSTRUE TRUE IN META-MATH AS TRUE IN PA.
> THAT YOU DON'T UNDERSTAND THIS IS STUPID IS YOUR ERROR.

But, as I pointed out, the way Meta-Math is derived from PA, statements 
that are true in MM that do not use terms added in MM, are true in PA, 
as their sequence of truth preserving steps used to show them true in MM 
used nothing just in MM.

That you just blindly say this isn't true just proves your stupidity.

> 
>> The Formal System is PA. that defines the basic axioms that are to be 
>> used to establish the truth of the statement and where to attempt the 
>> proof of it.
>>
>> The Meta-Math, is an EXTENSION to PA, where we add a number of 
>> additional axioms, none that contradict any of the axions of PA, but 
>> in particular, assign each axiom and needed proven statement in PA to 
>> a prime number. These provide the additional semantics in the Meta- 
>> Math to understand the new meaning that a number could have, and with 
>> that semantics, using just the mathematics of PA, the PRR is derived 
>> that with the semantics of the MM becomes a proof-checker.
>>
>> Note, the Meta-Math is carefully constructed so that there is a 
>> correlation of truth, such that anything true in PA is true in MM, and 
>> anything statement shown in MM to be true, that doesn't use the 
>> additional terms defined, is also true in PA.
>>
>> There is no equivocation in that, as nothing changed meaning, only 
>> some things that didn't have a semantic meaning (like a number) now does.
>>
>> If you want to try to show an actual error or equivocation, go ahead 
>> and try, but so far, all you have done is shown that you don't even 
>> seem to understand what a Formal System is, since you keep on wanting 
>> to "re- invent them" but just repeat the basic definition of them.
> 
>