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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis --- infallibly correct
Date: Sat, 9 Nov 2024 12:05:38 -0600
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On 11/9/2024 11:58 AM, Alan Mackenzie wrote:
> olcott <polcott333@gmail.com> wrote:
>> On 11/9/2024 10:03 AM, Alan Mackenzie wrote:
>>> olcott <polcott333@gmail.com> wrote:
>>>> On 11/9/2024 5:01 AM, joes 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.
>>>>> Gödel showed otherwise.
> 
>>>> That is counter-factual within my precise specification.
> 
>>> That's untrue - you don't have a precise specification.  And even if you
>>> did, Gödel's theorem would still hold.
> 
>>>> When truth is only derived by starting with
>>>> truth and applying truth preserving operations
>>>> then unprovable in PA becomes untrue in PA.
> 
>>> No.  Unprovable will remain.
> 
>> *Like I said you don't pay f-cking attention*
> 
> Stop swearing.  I don't pay much attention to your provably false
> utterances, no.  Life is too short.
> 

That you denigrate what I say without paying attention to what
I say <is> the definition of reckless disregard for the truth
that loses defamation cases.

> Hint: Gödel's theorem applies in any sufficiently powerful logical
> system, and the bar for "sufficiently powerful" is not high.
> 

Unless it is stipulated at the foundation of the notion of
formal systems that ~Provable(PA, g) simply means ~True(PA, g).

>> Unprovable(L,x) means Untrue(L,x)
>> Unprovable(L,~x) means Unfalse(L,x)
>> ~True(L,x) ^ ~True(L, ~x) means ~Truth-Bearer(L,x)
> 
> If you're going to change the standard meaning of standard words, you'll
> find communicating with other people somewhat strained and difficult.
> 

ZFC did the same thing and that was the ONLY way
that Russell's Paradox was resolved.

When ~Provable(PA,g) means ~True(PA,g) then
incompleteness cannot exist.

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


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