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

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.

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).

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

[ .... ]
 

-- 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