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

On 11/8/2024 10:57 AM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

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:

 [ .... ]
 

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.

 No.  They're the presumptions of an arrogant ignoramus who has no respect
for, or even understanding of, truth.
 

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.

 That's another lie.  You lack the expertise to make any judgment about
the soundness of mathematical 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.

 No, not in the same way.
 

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.

 [ .... ]
 

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.

 You're lying by presuming to understand things you don't understand.
We're not talking about some "received view", we're talking about proven
mathematical fact.  You lack the expertise to distinguish these, and you
question things like 2 + 2 = 4.  You don't even understand the concept of
proof.
 

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

 Again, there's no assumption in play.  You _are_ wrong, objectively.
 

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.

 It is.  If you had the expertise, you would accept things like 2 + 2 = 4.
 

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

 That's a mendacious distortion of what I wrote.  I do understand these
thing perfectly well, and I see that what you're saying is objectively
wrong.
 [ .... ]
 

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

 

That formal systems that only apply truth preserving
operations to expressions of their formal language
that have been stipulated to be true cannot possibly
be undecidable is proven to be over-your-head on the
basis that you have no actual reasoning as a rebuttal.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer