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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 09:15:29 -0600
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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:
> 
>>> [ .... ]
> 
>>>>>>> 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.
> 
> Now who's lying?  You have frequently denied the truth of proven
> mathematical facts like 2 + 2 = 4.  

Never and you are a damned (going to actual Hell) liar for
saying so.

> 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.

>> 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
> 
> Incompleteness is an essential property of logic systems

Rejecting what I say out-of-hand on the basis that you don't
believe what I say is far far less than no rebuttal at all.

What I said about is a semantic tautology just like
2 + 3 = 5. Formal systems are only incomplete when
the term "incomplete" is a euphemism for the inability
of formal systems to correctly determine the truth
value of non-truth-bearers.

> 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
> 


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