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

On 11/13/24 5:58 PM, olcott wrote:

On 11/13/2024 5:52 AM, Richard Damon wrote:

On 11/12/24 11:37 PM, olcott wrote:

On 11/11/2024 9:06 AM, Richard Damon wrote:

On 11/10/24 5:01 PM, olcott wrote:

On 11/10/2024 2:39 PM, joes wrote:

Am Sun, 10 Nov 2024 14:07:44 -0600 schrieb olcott:

On 11/10/2024 1:13 PM, Richard Damon wrote:

On 11/10/24 10:11 AM, olcott wrote:

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:

>

Sorry, but until you actually and formally fully define your logic
system, you can't start using it.

When C is a necessary consequence of the Haskell Curry elementary
theorems of L (Thus stipulated to be true in L) then and only then is C
is True in L.
This simple change does get rid of incompleteness because Incomplete(L)
is superseded and replaced by Incorrect(L,x).

I still can’t see how this makes ~C provable.
>

>
If C is not provable it is merely rejected as incorrect
not used as any basis to determine that L is incomplete.
>
For many reasons: "A sequence of truth preserving operations"
is a much better term than the term "provable".
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>
But since there exist statements that are True but not Provable. except by your incorrect definition of Provable, your logic is just broken.
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>
There cannot possibly be any expressions of language that
are true in L that are not determined to be true on the
basis of applying a sequence of truth preserving operations
in L to Haskell_Curry_Elementary_Theorems in L.
>

>
Right, but there can be expressions of language that are true in L by an INFINITE sequence of truth-preserving operations that are not provable which needs a FINITE sequence of truth-preserving operations.
>

 That is not relevant to my point. The Goldbach conjecture
is provable or refutable by Proof(Olcott).

So, Proof(Olcott) is not what determines Incompleteness, as Proof(Olcott) doesn't establish Knowledge, because Proof(Olcott) is just a worthless synonym for Truth.

 Expressions that are not provable or refutable by
Proof(Olcott) are rejected as erroneous rather than
ruling Formal System(Olcott) is incomplete.

So, Proof(Olcott) isn't a viable term for knowledge, and thus is worthless.

 It never has been the case the the inability to prove or
refute a self-contradictory expression of language ever
makes its formal system in any way incomplete.

Since that is the DEFINITION of "Completeness" you are just proving your stupidity.

 The only reason that Gödel incompleteness ever worked
is that it relied on a screwed up definition of True(),
that diverges from the way that truth really works.

Nope. It uses the totally normal definition of True, and Provable.
YOU are the one that has diverges from the way that truth really works, as you have shown it to be a concept foreign to you.

 Every expression that derives all of its truth on the
basis of relations to other expressions is simply untrue
when it totally lacks these relations.

But G doesn't do that. G is established in PA based on an infinite chain of truth perserving operation in PA from the elementary truths of PA.

 The only other kind of truth that exists is truth that
relies on direct observation of physical stimuli.

Which is irelevent, just showing your stupidity.

 

INFINITE is not FINITE so there is a difference.
>

https://www.liarparadox.org/Haskell_Curry_45.pdf
Everything that is true on the basis of its meaning
expressed in language is shown to be true this exact
same way.
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But not provable.
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Truth allows infinite sequences.
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Provable does.
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Trying to Define Olcott-Provable to allow infinite sequences, doesn't make actual Provable allow it.
>
It is just a LIE to use mis-defined terms in your logic, and that shows that you fundamentally don't understand what you are talking about.