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Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable

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On 2025-05-06 08:30:28 +0000, Alan Mackenzie said:

> [ Followup-To: set ]
> 
> In comp.theory olcott <polcott333@gmail.com> wrote:
>> On 5/5/2025 3:12 PM, Alan Mackenzie wrote:
>>> olcott <polcott333@gmail.com> wrote:
>>>> On 5/5/2025 2:34 PM, Alan Mackenzie wrote:
>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>> On 5/5/2025 1:52 PM, Alan Mackenzie wrote:
>>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>>> On 5/5/2025 1:19 PM, Alan Mackenzie wrote:
>>>>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>>>>> On 5/5/2025 11:05 AM, Alan Mackenzie wrote:
> 
>>>>>>> [ .... ]
> 
>>>>>>>>>>> Follow the details of the proof of Gödel's Incompleteness
>>>>>>>>>>> Theorem, and apply them to your "system".  That will give you
>>>>>>>>>>> your counter example.
> 
>>>>>>>>>> My system does not do "provable" instead it does "provably true".
> 
>>>>>>>>> I don't know anything about your "system" and I don't care.  If
>>>>>>>>> it's a formal system with anything above minimal capabilities,
>>>>>>>>> Gödel's Theorem applies to it, and the "system" will be incomplete
>>>>>>>>> (in Gödel's sense).
> 
>>>>>>>> I reformulate the entire notion of "formal system"
>>>>>>>> so that undecidability ceases to be possible.
> 
>>>>>>> Liar.  That is impossible.
> 
>>>>>>> [ Irrelevant nonsense snipped. ]
> 
>>>>>> When you start with truth and only apply truth preserving
>>>>>> operations then you necessarily end up with truth.
>>>>>> Is that too difficult for you?
> 
>>>>> Not at all.  One of the truths you inescapably end up with is Gödel's
>>>>> Theorem.  Either that, or the system is self-contradictory or too weak
>>>>> to do anything at all.
> 
>>>> Gödel's theorem cannot possibly be recreated when
>>>> True(x) is defined to apply truth preserving
>>>> operations to basic facts.
> 
>>> On the contrary, whether or not True(x) can be so defined, Gödel's
>>> theorem cannot be avoided.
> 
>>> [ .... ]
> 
>>>>> That would appear to be well beyond your level of understanding.  You
>>>>> ought to show some respect towards those who do understand these things.
> 
>>>> I have spent 22 years focusing on pathological self-reference.
>>>> My understanding really is deeper.
> 
>>> It might be a little deeper than it was, but that's not saying very much.
>>> The concept of proof by contradiction, for example, is way beyond you.
>>> Even the very idea of a mathematical proof, its status, its significance
>>> is beyond you.  You don't even understand what it is you're lacking.
> 
>>> Those 22 years have been suboptimally spent.
> 
>>> As I said, you ought to show a bit of respect to those who understand
>>> these mathematical things.
> 
>> So you don't understand that when True(x) is
>> defined to only apply truth preserving operations
>> to basic facts that are stipulated to be true
>> that every input including random gibberish
>> and self-contradiction IS DECIDABLE AS TRUE OR ~TRUE.
> 
> That's like being challenged by a young child to understand some detail
> of his newest fantasy.  Except you're not a child, and ought to have an
> adult's sense of proportion and reality, and a sense of your own
> limitations.  You're lacking these.

Senility can be like infantility expept that senility is permanent.

-- 
Mikko

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Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-04 21:23 -0500
  Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mikko <mikko.levanto@iki.fi> - 2025-05-05 12:50 +0300
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 10:39 -0500
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mikko <mikko.levanto@iki.fi> - 2025-05-06 13:02 +0300
  Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Alan Mackenzie <acm@muc.de> - 2025-05-05 10:47 +0000
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 16:03 -0500
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Alan Mackenzie <acm@muc.de> - 2025-05-06 08:30 +0000
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mikko <mikko.levanto@iki.fi> - 2025-05-06 13:04 +0300
  Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-05 07:04 -0400
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mr Flibble <flibble@red-dwarf.jmc.corp> - 2025-05-05 14:46 +0000
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Heathfield <rjh@cpax.org.uk> - 2025-05-05 16:51 +0100
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mr Flibble <flibble@red-dwarf.jmc.corp> - 2025-05-05 16:10 +0000
          Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Heathfield <rjh@cpax.org.uk> - 2025-05-05 17:59 +0100
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-05 21:08 -0400
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 10:31 -0500
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-05 21:11 -0400
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 21:26 -0500
          Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-06 07:16 -0400
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 23:27 -0500
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Alan Mackenzie <acm@muc.de> - 2025-05-06 08:17 +0000
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-06 07:20 -0400
          Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable ---ELABORATED olcott <polcott333@gmail.com> - 2025-05-06 12:46 -0500
            Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable ---ELABORATED Richard Damon <richard@damon-family.org> - 2025-05-06 22:07 -0400
  Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-15 16:24 +0000
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-11-15 10:55 -0600
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-15 17:30 +0000
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-11-15 11:43 -0600
  Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-15 16:49 +0000
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-11-15 11:19 -0600
  Re: Kaz ---Keith said DDD simulated by HHH is equivalent to DDD calling itself olcott <polcott333@gmail.com> - 2025-11-16 09:29 -0600
    Re: Kaz ---Keith said DDD simulated by HHH is equivalent to DDD calling itself HAL 9000 <hal@discovery.nasa> - 2025-11-16 16:46 +0000
      Re: Kaz ---Keith said DDD simulated by HHH is equivalent to DDD calling itself olcott <polcott333@gmail.com> - 2025-11-16 11:07 -0600
      DD simulated by HHH cannot possibly terminate normally olcott <polcott333@gmail.com> - 2025-11-16 11:20 -0600
      Re: Kaz ---Keith said DDD simulated by HHH is equivalent to DDD calling itself "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-16 13:18 -0800

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