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

olcott <polcott333@gmail.com> wrote:

On 11/10/2024 10:37 AM, Alan Mackenzie wrote:

In comp.theory olcott <polcott333@gmail.com> wrote:

On 11/10/2024 4:03 AM, Alan Mackenzie wrote:

In comp.theory olcott <polcott333@gmail.com> wrote:

On 11/9/2024 4:28 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 11/9/2024 3:45 PM, Alan Mackenzie wrote:

[ .... ]

Gödel understood mathematical logic full well (indeed, played a
significant part in its development),

He utterly failed to understand that his understanding
of provable in meta-math cannot mean true in PA unless
also provable in PA according to the deductive inference
foundation of all logic.

You're lying in your usual fashion, namely by lack of expertise.  It
is entirely your lack of understanding.  If Gödel's proof was not
rigorously correct, his result would have been long discarded.  It
is correct.

Even if every other detail is 100% correct without
"true and unprovable" (the heart of incompleteness)
it utterly fails to make its incompleteness conclusion.

You are, of course, wrong here.  You are too ignorant to make such a
judgment.  I believe you've never even read through and verified a proof
of Gödel's theorem.

If you had a basis in reasoning to show that I was wrong
on this specific point you could provide it.

I have read through and understood a proof of Gödel's theorem, and it was
correct.  Therefore you are wrong in what you assert.  You have never
read such a proof, otherwise you would have said so.  Therefore, on this
matter, you are ignorant, certainly when compared with me.

You have no basis in reasoning on this specific point all you have is
presumption.

It is you who is lacking any basis in what you say.  I have already given
my bases for calling out your falsehoods.

Perhaps you simply don't understand it at that level
thus will never have any idea that I proved I am correct.

More lies.  You don't even understand what the word "proved" means.

Here is what Mathworld construes as proof ....

I didn't say you couldn't search the web and find descriptions of what a
proof is.  I said that you, you personally, don't understand those
descriptions.

I would furthermore propose you have never read and understood a
mathematical proof, and I also propose you have never constructed such a
proof yourself.  If I am wrong here, feel free to counter these
propositions.

A thorough understanding of mathematical proof is a prerequisite for
talking meaningfully about things like Gödel's therem.  You lack that
prerequisite, therefore all your false statements about it are lies by
lack of expertise.

In other words you can only dodge and thus not address my
specific point ....

I have addressed your point perfectly well.  Gödel's theorem is correct,
therefore you are wrong.  What part of that don't you understand?

.... and can only assert that you generally believe that I must somehow
be wrong ....

<sigh>.  It's not a matter of "belief", it's a matter of 100% certainty.
How often do I have to repeat this before it sinks into your cranium?

.... even if you yourself can't possibly point out exact where and how
this specific point is in any way incorrect:

I don't need to point out exactly where and how your "proof" of 2 + 2 = 5
is wrong.  The knowledge that 2 + 2 = 4 is sufficient to dismiss it as
false.

  Even if every other detail of Gödel's proof is 100% correct
  when we require that true in PA requires a sequence of truth
  preserving operations from the axioms of PA, then unprovable
  is PA merely means untrue in PA and does not show that PA is
  in any way incomplete.

You can't so require.  If you try, you will end up fairly quickly with an
inconsistent mess.  The precise details of that process aren't
interesting.

You don't actually understand these things ....

You can't stop lying, can you?  As I've said several times, I've been
through a proof of Gödel's theorem in full detail and thus do understand
it.  It is correct.

.... you merely dogmatically accept that Gödel must be correct entirely
on the basis that so many people believe that he is correct.

See above.

And stop lying.  It doesn't advance your life in any way whatsoever.

--
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).