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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 ---
Date: Fri, 8 Nov 2024 15:21:31 -0600
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On 11/8/2024 1:14 PM, joes wrote:
> Am Fri, 08 Nov 2024 09:15:29 -0600 schrieb olcott:
>> On 11/8/2024 9:05 AM, Alan Mackenzie wrote:
>>> olcott <polcott333@gmail.com> wrote:
>>>> On 11/8/2024 5:58 AM, Alan Mackenzie wrote:
>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>> On 11/6/2024 2:34 PM, Alan Mackenzie wrote:
>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>> On 11/6/2024 10:45 AM, Alan Mackenzie wrote:
> 
>>> As I have continually made clear in my posts "like 2 + 2 = 4" includes
>>> the halting theorem, Gödel's theorem, and Tarski's theorem.
>> Your misconceptions are not my errors.
>> You cannot possibly prove that they are infallible that best that you
>> can show is that you believe they are infallible.
> They are proven. Show the error.
> 
>>>> When the operations are limited to applying truth preserving
>>>> operations to expressions of language that are stipulated to be true
>>>> then True(L,x) ≡ (L ⊢ x) and False(L, x) ≡ (L ⊢ ~x)
>>>> Then (Incomplete(L) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))) becomes
>>>> (¬TruthBearer(L,x) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>>> Incompleteness utterly ceases to exist
>>> Incompleteness is an essential property of logic systems
>> What I said about is a semantic tautology just like 2 + 3 = 5. Formal
>> systems are only incomplete when the term "incomplete" is a dysphemism
>> for the inability of formal systems to correctly determine the truth
>> value of non-truth-bearers.
> What is the truth value of non-truth-bearers then?
> 

What time is it (YES or NO) ???  // not a truth bearer

>>> which can do anything at all.  If what you assert is true (which I
>>> doubt), then your system would be incapable of doing anything useful.


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