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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 08:29:33 -0600
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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:
> 
> [ .... ]
> 
>>>>> There is another sense in which something could be a lie.  If, for
>>>>> example, I emphatically asserted some view about the minutiae of
>>>>> medical surgery, in opposition to the standard view accepted by
>>>>> practicing surgeons, no matter how sincere I might be in that
>>>>> belief, I would be lying.  Lying by ignorance.
> 
> 
>>>> That is a lie unless you qualify your statement with X is a
>>>> lie(unintentional false statement). It is more truthful to
>>>> say that statement X is rejected as untrue by a consensus of
>>>> medical opinion.
> 
>>> No, as so often, you've missed the nuances.  The essence of the
>>> scenario is making emphatic statements in a topic which requires
>>> expertise, but that expertise is missing.  Such as me laying down the
>>> law about surgery or you doing the same in mathematical logic.
> 
>> It is not at all my lack of expertise on mathematical logic
>> it is your ignorance of philosophy of logic as shown by you
>> lack of understanding of the difference between "a priori"
>> and "a posteriori" knowledge.
> 
> Garbage.
> 
>> Surgical procedures and mathematical logic are in fundamentally
>> different classes of knowledge.
> 
> But the necessity of expertise is present in both, equally.  Emphatically
> to assert falsehoods when expertise is lacking is a form of lying.  That
> is what you do.
> 
>>>> This allows for the possibility that the consensus is not
>>>> infallible. No one here allows for the possibility that the
>>>> current received view is not infallible. Textbooks on the
>>>> theory of computation are NOT the INFALLIBLE word of God.
> 
>>> Gods have got nothing to do with it.  2 + 2 = 4, the fact that the
>>> world is a ball, not flat, Gödel's theorem, and the halting problem,
>>> have all been demonstrated beyond any doubt whatsoever.
> 
>> Regarding the last two they would have said the same thing about
>> Russell's Paradox and what is now known as naive set theory at the
>> time.
> 
> There's no "would have said" regarding Russell's paradox.  Nobody would
> have asserted the correctness of naive set theory, a part of mathematics
> then at the forefront of research and still in flux.  We've moved beyond
> that point in the last hundred years.
> 
> And you are continually stating that theorems like 2 + 2 = 4 are false.

That is a lie. I never said anything like that and you know it.
Here is what I actually said:

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


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