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

olcott <polcott333@gmail.com> wrote:

On 11/9/2024 11:58 AM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 11/9/2024 10:03 AM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 11/9/2024 5:01 AM, joes wrote:

On 11/8/24 12:25 PM, olcott wrote:

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.

Gödel showed otherwise.

That is counter-factual within my precise specification.

That's untrue - you don't have a precise specification.  And even if you
did, Gödel's theorem would still hold.

When truth is only derived by starting with
truth and applying truth preserving operations
then unprovable in PA becomes untrue in PA.

No.  Unprovable will remain.

*Like I said you don't pay f-cking attention*

Stop swearing.  I don't pay much attention to your provably false
utterances, no.  Life is too short.

That you denigrate what I say without paying attention to what
I say <is> the definition of reckless disregard for the truth
that loses defamation cases.

Not at all.  I denigrate your lies, where by lies I mean the emphatic
utterances of falsehood due to a lack of expertise in the subject matter.
See the beginning of this subthread.

You are the one with reckless disregard for the truth.  You haven't even
bothered to read the introductory texts which would help you understand
what the truth is.

I have no fear of you starting a defamation case against me.  For a
start, you'd have to learn some German, and for another thing, I'd win on
the merits.

Hint: Gödel's theorem applies in any sufficiently powerful logical
system, and the bar for "sufficiently powerful" is not high.

Unless it is stipulated at the foundation of the notion of
formal systems that ~Provable(PA, g) simply means ~True(PA, g).

If you're going to redefine the word provable to mean something else,
you'll need some other word to mean what provable means to everybody
else.

Unprovable(L,x) means Untrue(L,x)
Unprovable(L,~x) means Unfalse(L,x)
~True(L,x) ^ ~True(L, ~x) means ~Truth-Bearer(L,x)

If you're going to change the standard meaning of standard words, you'll
find communicating with other people somewhat strained and difficult.

ZFC did the same thing and that was the ONLY way
that Russell's Paradox was resolved.

No, they didn't do the same thing.  They stayed within the bounds of
logic.  And yes, they resolved a paradox.  There is no paradox for your
"system" to resolve, even if it were logically coherent.

When ~Provable(PA,g) means ~True(PA,g) then
incompleteness cannot exist.

OK, That's a proof by contradiction that ~provable cannot mean ~true.  We
know, by Gödel's Theorem that incompleteness does exist.  So the initial
proposition cannot hold, or it is in an inconsistent system.

[ .... ]

--
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).