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From: Alan Mackenzie <acm@muc.de>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new basis ---
Date: Fri, 8 Nov 2024 15:05:58 -0000 (UTC)
Organization: muc.de e.V.
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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 th=
e
>>>> 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.  Emphatica=
lly
>> to assert falsehoods when expertise is lacking is a form of lying.  Th=
at
>> 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 =3D 4, the fact that the
>>>> world is a ball, not flat, G=C3=B6del's theorem, and the halting pro=
blem,
>>>> 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 woul=
d
>> have asserted the correctness of naive set theory, a part of mathemati=
cs
>> then at the forefront of research and still in flux.  We've moved beyo=
nd
>> that point in the last hundred years.

>> And you are continually stating that theorems like 2 + 2 =3D 4 are fal=
se.

> 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 =3D 4.  As I have continually made clear in
my posts "like 2 + 2 =3D 4" includes the halting theorem, G=C3=B6del's th=
eorem,
and Tarski's theorem.

> 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) =E2=89=A1 (L =E2=8A=A2 x) and False(L, x) =E2=89=A1 (L =E2=8A=
=A2 ~x)

> Then
> (Incomplete(L) =E2=89=A1  =E2=88=83x =E2=88=88 Language(L) ((L =E2=8A=AC=
 x) =E2=88=A7 (L =E2=8A=AC =C2=ACx)))
> becomes
> (=C2=ACTruthBearer(L,x) =E2=89=A1  =E2=88=83x =E2=88=88 Language(L) ((L=
 =E2=8A=AC x) =E2=88=A7 (L =E2=8A=AC =C2=ACx)))
> Incompleteness utterly ceases to exist

Incompleteness is an essential property of logic systems 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.

> --=20
> Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer

--=20
Alan Mackenzie (Nuremberg, Germany).