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

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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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.

If you gave some actual formal basis for your reasoning, then perhaps a formal reply could be made.
Since your arguement starts with mis-interpreatations of what Godel's proof does, you start off in error.

 

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
 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

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.
Thus, YOU are the one disagreeing with yourself.

 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.
 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/
 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.

But you aren't allowed to CHANGE those meanings.
Sorry, but until you actually and formally fully define your logic system, you can't start using it.
And, if you want to talk in your logic system, you can't say it refutes arguments built in other logic system.
At best you can show those proofs can't be built in your system, but first you will need to show that your idea of a logic system can be used to build formal systems with the power described as the prerequisites of those proofs, which for Godel says you need to first show that your equivalent of PA that can be built in your system supports the needed properties.
My guesss is that will take you 10-20 years, if you can even do it, my guess is it is actually beyond your ability to understand the processes.

 Mathworld
is correct yet fails to provide enough details.
 The principle of explosion
is incorrect because its conclusion is not a necessary
consequence of applying truth preserving operations.
It fails to require semantic relevance.

What step in the proof was wrong?
Your failure means you accept that your logic is just inconsistant.

 Validity and Soundness
is incorrect because its conclusion is not a necessary
consequence of applying truth preserving operations.
It fails to require semantic relevance.

I don't think you understand what "semantics" are in formal logic.
It semms you really do need to start by throwing out EVERYTHING from the existing logic systems, and fully define what you mean, and see what you can prove with that.
Something on the order of Euclid's geometry.

 

-- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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