Re: The philosophy of logic reformulates existing ideas on a new basis ---

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.

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 = 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) ≡ (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.
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.

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

--
Alan Mackenzie (Nuremberg, Germany).