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

On 11/15/24 6:41 PM, olcott wrote:

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.

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Logic DEFINES how "Truth" works in the system.
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 Logic inherits its notion of truth from the foundation
of truth itself.

Depends on what you call the "foundations of truth itself".
It the physical universe, Truth is what actually is.
In Logic, "Truth" is what follows from the stipulations put into the system, so "what is" is what derives from those.
I can stipulate in my logical system that the sky is green, and in the system, the sky *IS* green, even though in reality it isn't.

 

You don't seem to understand that Formal Logic Systems are really independent universes with their own rules.
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 That is *NOT* the way that truth really works.

Sure it is, there is nothing that forces a tie to the stipulation that make up a given Formal Logic System to anything outside of it.

 

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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.

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Of course there is, that is what a stipulated axiom is.
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 The stipulation *IS NOT NOTHING*

There is nothing *IN* the system that supports the stipulation. So, there is NOTHING in the system that makes the stipulations true, except that they ARE the stipulations, and the stipulation is OUTSIDE the system to build it. IN the system we just have that they HAVE BEEN stipulated, and thus are true without any other basis.

 

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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.
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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.

So?
Your problem is that you keep on claiming that statements, that have HAD there connection to the stiputed axioms of the system PROVEN, to be untrue.
I will explain two of your instances.
Godel: You look at the off-hand comment that we could use any other antinomy to develop a similar proof, which IS a true statement, but by that you ASSUME (INCORRECTLY) that he somehow use the "truth" of the Liar's Paradox to build his arguement. He didn't. He used they strutural SYNTAX, with a transformation, which changes its semantic meaning, as a foundation. He build a statement which shows (not just states) that his statement, rather than the liar which asserts its own falsehood, asserts its on unprovability in the original system. That altered statement is no longer an contradiction, and can have a truth value, just one that requires an infinite amount of work in the original syatem.
Tarski: Tarski SHOWS that with this meta-logic system, that if you have in the system a "Truth Predicate", that returns True for all true statements, and False for all statements that are either False, or are not a Truth-Bearer in L, you can create a statement that asserts that in L, x is not a member of the set of True Statements in L. Yes, this sounds like the Liar's Paradox, but he didn't START with it as an assumption, but as a statement that can be PROVEN TO EXIST in the system, and when we appy that assumed truth predicate, we hit a contradiction.
So, your strawman that "Nothing Shows that if X is true that X is untrue" is not actually used in Godel, and is in fact the final logical step of Tarski, as he shows that the existance of a Truth Predicate leads to that sort of statement, which can not be, and thus there can not be a Truth Predicate (something I don't think you understand what it is).

 There is NOTHING that shows the Liar Paradox is
TRUE or FALSE therefore it is not a truth bearer.

Right, but no one has used the truth bearing of the Liar's Paradox in there arguement, as I just showed.

 It has been 2000 freaking years and the world's greatest
experts STILL DO NOT UNDERSTAND THIS SIMPLE POINT.
 

No, YOU still are too stupid to understand that your OVERSIMPLIFICATION of the arguements is just invalid.