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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 10:21:55 -0600
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On 11/8/2024 10:02 AM, Alan Mackenzie wrote:
> 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 = 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.
> 
> Hahahaha!  There is no actual Hell.
> 
> Let me repeat: you have frequently denied the truth of proven
> mathematical facts like 2 + 2 = 4.
> 
>>> 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.
> 
> It is you who has misconceptions, evident to all in this newsgroup who
> have studied the subject.
> 

My "mistakes" are merely the presumption that the current
received view of these things is infallible.

>> 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. 

Within their faulty foundations.
In the same way that naive set theory was a faulty foundation.
It was not initially called naive set theory. It was only called
that when someone noticed its error.

>  In that respect they are all
> like 2 + 2 = 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.
> 

OK good some honesty.

>>>> 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.
> 
> 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.

You understand what the received view is.
My view is inconsistent with the received view therefore
(when one assumes that the received view is infallible)
I must be wrong.

> I reject what you say because it's objectively wrong.  Just as if you
> said 2 + 2 = 5.
> 
>> 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.
> 
> No.  You lack the expertise.
> 

I know how the current systems work and I disagree
that they are correct. This is not any lack of expertise.

As you already admitted you don't understand these
things well enough to even see what I am saying.

Truth preserving operations applied to known truths is an
airtight system where incompleteness and undecidability
cannot possibly enter.


>>> 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