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

On 11/10/24 3:07 PM, olcott wrote:

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:

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[ .... ]
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Gödel understood mathematical logic full well (indeed, played a
significant part in its development),

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He utterly failed to understand that his understanding
of provable in meta-math cannot mean true in PA unless
also provable in PA according to the deductive inference
foundation of all logic.

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You're lying in your usual fashion, namely by lack of expertise. It is
entirely your lack of understanding.  If Gödel's proof was not rigorously
correct, his result would have been long discarded.  It is correct.

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Even if every other detail is 100% correct without
"true and unprovable" (the heart of incompleteness)
it utterly fails to make its incompleteness conclusion.

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You are, of course, wrong here.  You are too ignorant to make such a
judgment.  I believe you've never even read through and verified a proof
of Gödel's theorem.
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If you had a basis in reasoning to show that I was wrong
on this specific point you could provide it. You have no
basis in reasoning on this specific point all you have is
presumption.

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If you gave some actual formal basis for your reasoning, then perhaps a formal reply could be made.
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Since your arguement starts with mis-interpreatations of what Godel's proof does, you start off in error.
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Perhaps you simply don't understand it at that level
thus will never have any idea that I proved I am correct.

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More lies.  You don't even understand what the word "proved" means.
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Here is what Mathworld construes as proof
A rigorous mathematical argument which unequivocally
demonstrates the truth of a given proposition. A
mathematical statement that has been proven is called
a theorem. https://mathworld.wolfram.com/Proof.html
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the principle of explosion is the law according to which any statement can be proven from a contradiction.
https://en.wikipedia.org/wiki/Principle_of_explosion

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Right, and I have shown your that proof, and you haven't shown what statement in that proof is wrong, so you have accepted it.
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Thus, YOU are the one disagreeing with yourself.
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Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. Otherwise, a deductive argument is said
to be invalid.
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A deductive argument is sound if and only if it is
both valid, and all of its premises are actually true.
Otherwise, a deductive argument is unsound.
https://iep.utm.edu/val-snd/
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Here is the PL Olcott correction / clarification of all of
them. A proof begins with a set of expressions of language
known to be true (true premises) and derives a conclusion
that is a necessary consequence by applying truth preserving
operations to the true premises.

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But you aren't allowed to CHANGE those meanings.
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 Within the philosophy of logic assumptions
can be changed to see where t that lead.

But the theories you are talking about aren't in the "Phiosophy of Logic" but in Formal Logic systems, where you can't change them.

 

Sorry, but until you actually and formally fully define your logic system, you can't start using it.
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 We don't really have a symbols for truth preserving operations.

So, I guess you are just admitting that you can't define what you are talking about.

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.
https://www.liarparadox.org/Haskell_Curry_45.pdf

And "Necessary Consequence" in formal logic means that if follows from a (potentailly infinite) series of the defined operation on the defined stipulated truths.
Godel did exactly that, showing that his statement G, which is that there does not exist a number g that satisfies a particular primative recursive relationship, MUST be true, and can not be proven in that system, as the only sequence in the system that establishes the necessary consequence is one of infinite length, namely being the testing of every possible natural number, and seeing that it does not meet the requirements.

 (Haskell_Curry_Elementary_Theorems(L) □ C) ≡ True(L, C)
 This simple change does get rid of incompleteness because
Incomplete(L) is superseded and replaced by Incorrect(L,x).

Nope, just proves that you are too stupid to understand what you are talking about.

 

And, if you want to talk in your logic system, you can't say it refutes arguments built in other logic system.
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 ZFC proves that naive set theory was incoherent.
Russell's paradox still exists in incoherent naive set theory.
 

No, Russels's paradox proved that naive set theory was incoherent.
ZFC was an alternate system proposed to fix the issue, and is immune to Russell's paradox, as it doesn't allow the logic of Russell's paradox to be formed.
Note, in some senses ZFC is weaker than Naive Set Theory, as there are concepts in Naive Set Theory that can't be mapped to ZFC, and thus there are other Set Theories used in some applications.
As has been pointed out, you are free to try to define your alternate system of logic, but if you want to do that, you need to actually do the work to create it, and not just have a concept of a plan.
You can perhaps talk about your ideas, and what they might or might not be able to do, but until you actually build the system, and show what it can do, and PROVE that it can meet the needed requirements, you can't say that you can "solve" the problems that you are trying to refute.
A lot of what you talk about is actually old and has been tried before (but of course since you don't know history, you are doomed to repeat it) and while sometimes the results are interesting, they inverably result in systems much "weaker" than classical logic, and I don't think anyone has gotten a system to the point of support a good equivalent of the full set of properties of the Natural Numbers, as it seems there is something in the power to define that, which leads to things like incompleteness.