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

On 11/15/2024 6:05 AM, Richard Damon wrote:

On 11/14/24 9:58 PM, olcott wrote:

On 11/14/2024 8:42 PM, Richard Damon wrote:

On 11/14/24 9:26 PM, olcott wrote:

On 11/14/2024 5:53 PM, Richard Damon wrote:

On 11/14/24 6:40 PM, olcott wrote:

On 11/14/2024 2:39 AM, Mikko wrote:

On 2024-11-13 23:01:50 +0000, olcott said:
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On 11/13/2024 4:45 AM, Mikko wrote:

On 2024-11-12 23:17:20 +0000, olcott said:
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On 11/10/2024 2:36 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 11/10/2024 1:04 PM, Alan Mackenzie wrote:

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[ .... ]
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I have addressed your point perfectly well.  Gödel's theorem is correct,
therefore you are wrong.  What part of that don't you understand?

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YOU FAIL TO SHOW THE DETAILS OF HOW THIS DOES
NOT GET RID OF INCOMPLETENESS.

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The details are unimportant.  Gödel's theorem is correct. Your ideas
contradict that theorem.  Therefore your ideas are incorrect. Again, the
precise details are unimportant, and you wouldn't understand them
anyway.  Your ideas are as coherent as 2 + 2 = 5.
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Incomplete(L) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))

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That's correct (although T is usually used instead of L).
Per this definition the first order group theory and the first order
Peano arithmetic are incomplete.

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Every language that can by any means express self-contradiction
incorrectly shows that its formal system is incomplete.

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That "incorrectly shows" is non-sense. A language does not show,
incorrectly or otherwise. A proof shows but not incorrectly. But
for a proof you need a theory, i.e. more than just a language.
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That a theory can't prove something is usually not provable in the
theory itself but usually needs be proven in another theory, one
that can be interpreted as a metatheory.
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*So in other words you just don't get it*
When you start with truth and only apply truth preserving
operations then you necessarily end up with truth.
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Right, but that truth might not be PROVABLE (by a finite proof that establishes Knowledge) as Truth is allowed to be established by infinite chains.
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All of analytic truth is specified as relations between
expressions of language. When these relations do not exist
neither does the truth of these expressions.

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But in FORMAL LOGIC, that analytic Truth is specified as the axioms of the system, and the approved logical operations for the system.
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You confuse "Formal Logic" with "Philosophy" due to your ignorance of them.
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I am looking at this on the basis of how truth itself
actually works. You are looking at this on the basis
of memorized dogma.
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No, because you logic is based on LIES, because you are trying to redefine fundamental terms within the system, as opposed to doiing the work to make a system the way you want, likely because you are just to ignorant to do the work,
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Logic never has been free to override and supersede how
truth itself fundamentally works.

 Logic DEFINES how "Truth" works in the system.
 

Logic inherits its notion of truth from the foundation
of truth itself.

You don't seem to understand that Formal Logic Systems are really independent universes with their own rules.
 

That is *NOT* the way that truth really works.

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Logic confused itself by not breaking things down to
their barest essence. There is no such thing as any
analytic expression of language that is true having
nothing that shows it is true.

 Of course there is, that is what a stipulated axiom is.
 

The stipulation *IS NOT NOTHING*

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If Goldbach conjecture is true then there is some
finite or infinite sequence of truth preserving
operations that shows this, otherwise it is not true.
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 Right, but there may not be a finite sequence to allow that results to be proven.
 You seem very unclear on the difference between Truth and Knowledge

If there is literally NOTHING that shows that X is
true then X is untrue.
There is NOTHING that shows the Liar Paradox is
TRUE or FALSE therefore it is not a truth bearer.
It has been 2000 freaking years and the world's greatest
experts STILL DO NOT UNDERSTAND THIS SIMPLE POINT.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer