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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 16:02:57 -0000 (UTC)
Organization: muc.de e.V.
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olcott <polcott333@gmail.com> wrote:
> 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:

[ .... ]

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

>>> 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.=20=20

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

Hahahaha!  There is no actual Hell.

Let me repeat: 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=
 theorem,
>> and Tarski's theorem.

> Your misconceptions are not my errors.

It is you who has misconceptions, evident to all in this newsgroup who
have studied the subject.

> You cannot possibly prove that they are infallible
> that best that you can show is that you believe they
> are infallible.

Here is where your lack of expertise shows itself.  All the above
theorems have been proven beyond any doubt.  In that respect they are all
like 2 + 2 =3D 4.  But you're right in a sense.  I couldn't personally
prove these things any more; but I know where to go to find the proofs.
And I don't "believe they are infallible"; I've studied, understood, and
checked proofs that they are true.

>>> 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

> 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.

As I said, it's not a matter of "belief".  It's a matter of certain
knowledge stemming from having studied for and having a degree in maths.
I reject what you say because it's objectively wrong.  Just as if you
said 2 + 2 =3D 5.

> What I said about is a semantic tautology just like
> 2 + 3 =3D 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.

No.  You lack the expertise.

>> 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).