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

On 11/10/24 10:08 PM, olcott wrote:

On 11/10/2024 3:52 AM, Mikko wrote:

On 2024-11-09 18:05:38 +0000, olcott said:
>

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.

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No.  Unprovable will remain.

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*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.

>
But it doesn't. "Provable(PA,g)" means that there is a proof on g in PA
and "~Provable(PA,g)" means that there is not. These meanings are don't
involve your "True" in any way. You may define "True" as a synonym to
"Provable" but formal synonyms are not useful.
>

 We can ALWAYS prove that any expression of language is true or
not on the basis of other expressions of language when we have a
coherent definition of True(L,x).
 

No, we can't.
We can sometimes prove it is true if we can find the sequence of steps that establish it.
We can sometime prove it is false if we can find the sequence of steps that refute it.
Since there are potentially an INFINITE number of possible proofs for either of these until we find one of them, we don't know if the statement IS provable or refutable.
Your problem is you think that knowledge and truth are the same, but knowledge is only a subset of truth, and there are unknown truths, and even unknowable truths in any reasonably complicated system.
Part of your issue is you seem to only think in very simple systems where exhaustive searching might actually be viable.

That Gödel relies on True(meta-math, g) to mean True(PA, g)
is a stupid mistake that enables Incomplete(PA) to exist.
 

Which just shows you don't understand how formal systems, and their meta-systems are constructed.
Your ignorance doesn't make the claim not true, just shows that you are just stupid and a pathological liar.