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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2 --Tarski
 Proof--
Date: Tue, 23 Apr 2024 09:31:00 -0500
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On 4/23/2024 3:21 AM, Mikko wrote:
> On 2024-04-22 17:37:55 +0000, olcott said:
> 
>> On 4/22/2024 10:27 AM, Mikko wrote:
>>> On 2024-04-22 14:10:54 +0000, olcott said:
>>>
>>>> On 4/22/2024 4:35 AM, Mikko wrote:
>>>>> On 2024-04-21 14:44:37 +0000, olcott said:
>>>>>
>>>>>> On 4/21/2024 2:57 AM, Mikko wrote:
>>>>>>> On 2024-04-20 15:20:05 +0000, olcott said:
>>>>>>>
>>>>>>>> On 4/20/2024 2:54 AM, Mikko wrote:
>>>>>>>>> On 2024-04-19 18:04:48 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> When we create a three-valued logic system that has these
>>>>>>>>>> three values: {True, False, Nonsense}
>>>>>>>>>> https://en.wikipedia.org/wiki/Three-valued_logic
>>>>>>>>>
>>>>>>>>> Such three valued logic has the problem that a tautology of the
>>>>>>>>> ordinary propositional logic cannot be trusted to be true. For
>>>>>>>>> example, in ordinary logic A ∨ ¬A is always true. This means that
>>>>>>>>> some ordinary proofs of ordinary theorems are no longer valid and
>>>>>>>>> you need to accept the possibility that a theory that is complete
>>>>>>>>> in ordinary logic is incomplete in your logic.
>>>>>>>>>
>>>>>>>>
>>>>>>>> I only used three-valued logic as a teaching device. Whenever an
>>>>>>>> expression of language has the value of {Nonsense} then it is
>>>>>>>> rejected and not allowed to be used in any logical operations. It
>>>>>>>> is basically invalid input.
>>>>>>>
>>>>>>> You cannot teach because you lack necessary skills. Therefore you
>>>>>>> don't need any teaching device.
>>>>>>>
>>>>>>
>>>>>> That is too close to ad homimen.
>>>>>> If you think my reasoning is incorrect then point to the error
>>>>>> in my reasoning. Saying that in your opinion I am a bad teacher
>>>>>> is too close to ad hominem because it refers to your opinion of
>>>>>> me and utterly bypasses any of my reasoning.
>>>>>
>>>>> No, it isn't. You introduced youtself as a topic of discussion so
>>>>> you are a legitimate topic of discussion.
>>>>>
>>>>> I didn't claim that there be any reasoning, incorrect or otherwise.
>>>>>
>>>>
>>>> If you claim I am a bad teacher you must point out what is wrong with
>>>> the lesson otherwise your claim that I am a bad teacher is essentially
>>>> an as hominem attack.
>>>
>>> You are not a teacher, bad or otherwise. That you lack skills that
>>> happen to be necessary for teaching is obvious from you postings
>>> here. A teacher needs to understand human psychology but you don't.
>>>
>>
>> You may be correct that I am a terrible teacher.
>> None-the-less Mathematicians might not have very much understanding
>> of the link between proof theory and computability.
> 
> Sume mathematicians do have very much understanding of that. But that
> link is not needed for understanding and solving problems separately
> in the two areas.
> 
>> When I refer to rejecting an invalid input math would seem to construe
>> this as nonsense, where as computability theory would totally understand.
> 
> People working on computability theory do not understand "invalid input"
> as "impossible input". 

The proof then shows, for any program f that might determine whether
programs halt, that a "pathological" program g, called with some input,
can pass its own source and its input to f and then specifically do the
opposite of what f predicts g will do. No f can exist that handles this
case, thus showing undecidability.
https://en.wikipedia.org/wiki/Halting_problem#

So then they must believe that there exists an H that does correctly
determine the halt status of every input, some inputs are simply
more difficult than others, no inputs are impossible.

> They understand it as an input that must be
> handled differently from ordinary input. Likewise, mathematicians do
> understand that some inputs must be considered separately and differently.
> But mathematicians don't call those inputs "invalid".
> 

It is so dead obvious that the whole world must be wired with a short
circuit in their brains. Formal bivalent mathematical systems of logic
must reject every expression that cannot possibly have a value of true
or false as a type mismatch error.

A proposition is a central concept in the philosophy of language,
semantics, logic, and related fields, often characterized as the primary
bearer of truth or falsity. https://en.wikipedia.org/wiki/Proposition




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