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

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

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
A rigorous mathematical argument which unequivocally
demonstrates the truth of a given proposition. A
mathematical statement that has been proven is called
a theorem. https://mathworld.wolfram.com/Proof.html
the principle of explosion is the law according to which any statement can be proven from a contradiction.
https://en.wikipedia.org/wiki/Principle_of_explosion
Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. Otherwise, a deductive argument is said
to be invalid.
A deductive argument is sound if and only if it is
both valid, and all of its premises are actually true.
Otherwise, a deductive argument is unsound.
https://iep.utm.edu/val-snd/
Here is the PL Olcott correction / clarification of all of
them. A proof begins with a set of expressions of language
known to be true (true premises) and derives a conclusion
that is a necessary consequence by applying truth preserving
operations to the true premises.
Mathworld
is correct yet fails to provide enough details.
The principle of explosion
is incorrect because its conclusion is not a necessary
consequence of applying truth preserving operations.
It fails to require semantic relevance.
Validity and Soundness
is incorrect because its conclusion is not a necessary
consequence of applying truth preserving operations.
It fails to require semantic relevance.

-- 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