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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2 --Tarski Proof--
Date: Tue, 23 Apr 2024 11:21:39 +0300
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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 some ordinary proofs of ordinary theorems are no longer valid and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". 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".

-- 
Mikko