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

olcott <polcott333@gmail.com> wrote:

On 11/9/2024 2:53 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 11/9/2024 1:32 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

[ .... ]

The way that sound deductive inference is defined
to work is that they must be identical.

Whatever "sound deductive inference" means.  If you are right, then
"sound deductive inference" is incoherent garbage.

*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/

Thus your ignorance and not mine.

No.  I suspected you were using the phrase as a sort of trademark for one
of your own fancies, like you've done in the past with other phrases.
Seeing how you actually mean what those words mean, then you are simply
wrong again, as so often.

A conclusion IS ONLY true when applying truth
preserving operations to true premises.

I'm not sure what that adds to the argument.

It is already specified that a conclusion can only be
true when truth preserving operations are applied to
expressions of language known to be true.

That Gödel's proof didn't understand that this <is>
the actual foundation of mathematical logic is his
mistake.

You're lying by lack of expertise, again.  Gödel understood mathematical
logic full well (indeed, played a significant part in its development),
and he made no mistakes in his proof.  Had he done so, they would have
been identified by other mathematicians by now.

Unprovable in PA has always meant untrue in PA when
viewed within the deductive inference foundation of
mathematical logic.

Yet another lie by lack of expertise.  Unprovable and untrue have been
proven to be different things, whether in the system of counting numbers
or anything else containing it.  Whatever you might mean by "the
deductive inference foundation of mathematical logic" - is that another
one of your "trademarks"?

[ .... ]

--
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).