On 5/1/2022 1:33 PM, André G. Isaak wrote:
> On 2022-05-01 12:28, olcott wrote:
>> On 5/1/2022 12:59 PM, Mr Flibble wrote:
>>> On Sun, 1 May 2022 12:01:01 -0500
>>> olcott <NoOne@NoWhere.com> wrote:
>>>
>>>> On 5/1/2022 11:21 AM, André G. Isaak wrote:
>>>>> On 2022-05-01 10:08, olcott wrote:
>>>>>
>>>>> <snip>
>>>>>
>>>>> Why are you making the same reply twice under two different
>>>>> handles? A single reply should suffice.
>>>>>
>>>>> André
>>>>
>>>> I wanted Flibble to see what I said. He may have me on Plonk
>>> You are not in my kill file: I don't always reply to what you say
>>> because I either agree with what you are saying or the point is
>>> uninteresting to me.
>>>
>>> /Flibble
>>>
>>
>> I do think that your idea of "category error" is a brilliant new
>> insight into pathological self-reference problems such as:
>> (1) The Halting Problem proofs
>> (2) Gödel's 1930 Incompleteness
>> (3) The 1936 Undefinability theorem
>>
>> It very succinctly sums up the entire gist of the semantic error in
>> all of these cases. When it is summed up so effectively it becomes
>> much easier to see exactly what is going on. I have said that it is a
>> semantic error, you pointed out exactly what kind of semantic error.
>
> So which categories are you claiming are involved? Claiming something is
> a 'category error' means nothing if you don't specify the actual
> categories involved.
>
> André
>

My original thinking was that (1) and (2) and the Liar Paradox all
demonstrate the exact same error. I only have considered (3) in recent
years, prior to that I never heard of (3).

The category error would be that none of them is in the category of
truth bearers. For Gödel's G and Tarski's p it would mean that the
category error is that G and p are not logic sentences.
https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)

https://liarparadox.org/Tarski_275_276.pdf

My current thinking on (1) is that a TM is smart enough to see this
issue and report on it.

--
Copyright 2022 Pete Olcott

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