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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: Sun, 10 Nov 2024 21:06:58 -0600
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On 11/10/2024 4:19 PM, Alan Mackenzie wrote:
> olcott <polcott333@gmail.com> wrote:
>> On 11/10/2024 2:36 PM, Alan Mackenzie wrote:
>>> olcott <polcott333@gmail.com> wrote:
>>>> On 11/10/2024 1:04 PM, Alan Mackenzie wrote:
> 
>>> [ .... ]
> 
>>>>> I have addressed your point perfectly well.  Gödel's theorem is correct,
>>>>> therefore you are wrong.  What part of that don't you understand?
> 
>>>> YOU FAIL TO SHOW THE DETAILS OF HOW THIS DOES
>>>> NOT GET RID OF INCOMPLETENESS.
> 
>>> The details are unimportant.  Gödel's theorem is correct.
> 
>> In other words you simply don't understand these
>> things well enough ....
> 
> Not at all.  It's you that doesn't understand them well enough to make it
> worthwhile trying to discuss things with you.
> 
>> .... to understand that when we change their basis the conclusion
>> changes.
> 
> You're at too high a level of abstraction.  When your new basis has
> counting numbers, it's either inconsistent, or Gödel's theorem applies to
> it.
> 

Finally we are getting somewhere.
You know what levels of abstraction are.

>> You are a learned-by-rote guy that accepts what you
>> memorized as infallible gospel.
> 
> You're an uneducated boor.  So uneducated that you don't grasp that
> learning by rote simply doesn't cut it at a university.
> 
>>> Your ideas contradict that theorem.
> 
>> When we start with a different foundation then incompleteness
>> ceases to exist just like the different foundation of ZFC
>> eliminates Russell's Paradox.
> 
> No.  You'd like it to, but it doesn't work that way.
> 
> [ .... ]
> 
>>> Therefore your ideas are incorrect.  Again, the precise details are
>>> unimportant,
> 
>> So you have no clue how ZFC eliminated Russell's Paradox.
>> The details are unimportant and you never heard of ZFC
>> or Russell's Paradox anyway.
> 
> Russell's paradox is a different thing from Gödel's theorem.  The latter
> put to rest for ever the vainglorious falsehood that we could prove
> everything that was true.
> 

Ah so you don't understand HOW ZFC eliminated Russell's Paradox.

We can ALWAYS prove that any expression of language is true or not
on the basis of other expressions of language when we have a coherent
definition of True(L,x).

That Gödel relies on True(meta-math, g) to mean True(PA, g)
is a stupid mistake that enables Incomplete(PA) to exist.


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