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

On 11/11/24 8:55 AM, olcott wrote:

On 11/10/2024 10:03 PM, Richard Damon wrote:

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

On 11/10/2024 4:19 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

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.

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In other words you simply don't understand these
things well enough ....

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Not at all.  It's you that doesn't understand them well enough to make it
worthwhile trying to discuss things with you.
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.... to understand that when we change their basis the conclusion
changes.

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You're at too high a level of abstraction.  When your new basis has
counting numbers, it's either inconsistent, or Gödel's theorem applies to
it.
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Finally we are getting somewhere.
You know what levels of abstraction are.
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You are a learned-by-rote guy that accepts what you
memorized as infallible gospel.

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You're an uneducated boor.  So uneducated that you don't grasp that
learning by rote simply doesn't cut it at a university.
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Your ideas contradict that theorem.

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When we start with a different foundation then incompleteness
ceases to exist just like the different foundation of ZFC
eliminates Russell's Paradox.

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No.  You'd like it to, but it doesn't work that way.
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[ .... ]
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Therefore your ideas are incorrect.  Again, the precise details are
unimportant,

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So you have no clue how ZFC eliminated Russell's Paradox.
The details are unimportant and you never heard of ZFC
or Russell's Paradox anyway.

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Russell's paradox is a different thing from Gödel's theorem.  The latter
put to rest for ever the vainglorious falsehood that we could prove
everything that was true.
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Ah so you don't understand HOW ZFC eliminated Russell's Paradox.
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We can ALWAYS prove that any expression of language is true or not
on the basis of other expressions of language when we have a coherent
definition of True(L,x).

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No, we can't.
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We can sometimes prove it is true if we can find the sequence of steps that establish it.
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We can sometime prove it is false if we can find the sequence of steps that refute it.
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Since there are potentially an INFINITE number of possible proofs for either of these until we find one of them, we don't know if the statement IS provable or refutable.
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Your problem is you think that knowledge and truth are the same, but knowledge is only a subset of truth, and there are unknown truths, and even unknowable truths in any reasonably complicated system.
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Part of your issue is you seem to only think in very simple systems where exhaustive searching might actually be viable.
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That Gödel relies on True(meta-math, g) to mean True(PA, g)
is a stupid mistake that enables Incomplete(PA) to exist.
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Which just shows you don't understand how formal systems, and their meta-systems are constructed.
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 It does not matter how they are constructed the only
thing that matters is the functional end result.

OF course it does. If you don't understand the rules by which a system was constructed, you can't know what you can do in the system.
Yes, an ordinary user of a system may not need to know the gritty details of the system, but to claim it is not logical, requires going into the rules to find the error, otherwise the error is more apt to be in the "logic" that the user is trying to apply. (Like what WM has been doing).

 *When we construe True(L,x) this way*
When g is a necessary consequence of the Haskell Curry
elementary theorems of PA (Thus stipulated to be true in PA)
then and only then is g is True in PA.

But G *IS* a necessary consequence of the axioms of PA. Yes, it needs an infinite number of steps, but it is demonstrable by them.
That 0 does not satisfy the PRR, is a simple matter of the mathematics created by those axioms of PA.
That 1 does not satisfy the PRR, is a simple matter of the mathematics created by those axioms of PA.
That 2 does not satisfy the PRR, is a simple matter of the mathematics created by those axioms of PA.
That any given natural number g does not satisfy the PRR, is a simple matter of the mathematics created by those axioms of PA, but we have to evaluate this individually for each number g.
Thus, we have a chain of necessary consequences, infinite in length, that shows that the statement G is true, G being that there is no number g that satisfies that particular PRR.
The fact that we can prove, in MM, the fact that in general, no g can satisfy the PRR in a finite number of steps, doesn't negate that it is a necessary consequence in PA, it just takes longer there.
In MM, we can also prove that there is no finite sequence of steps in PA that would show it to be a necessary consequence, and the PRR was constructed in MM (using the operation available in PA) such that any finite proof in PA of that statement could be encoded into a number (which exist in PA) that would satisfy that PRR which can be processed in PA. Since the existance of such a number both proves that a number satisfing the PRR exists, and that no such number can exist, there can't be such a number.

 https://www.liarparadox.org/Haskell_Curry_45.pdf
(Haskell_Curry_Elementary_Theorems(PA) □ g) ≡ True(PA, g)
 If there is no sequence of truth preserving operations
in PA from its Haskell_Curry_Elementary_Theorems to g
then it can be construed that g is simply not true in PA.
Incorrect(PA,g) ≡ (True(PA, g) ∧ True(PA, ~g))

But I just showed it, AGAIN to you, so, you claim was refuted before you said it, so is just a lie.

 

Your ignorance doesn't make the claim not true, just shows that you are just stupid and a pathological liar.
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 That you say this without providing any supporting reasoning
indicates that you may not have an actual clue about these
thing and instead only have mere empty bluster.
 

The supporting reasoning is that you continually do things like this, bring up ideas that are false as disproven, shows your stupidity,
The fact you never try to find the step where an error was made, shows you don't understand how logic works.

I am not a liar and you are acting like a goofy nitwit.
 

No, your ARE a Liar, a pathological liar, that has stripped himself of the ability to undetstand what is truth because he has gaslighted and brainwashed himself (likely with the help of Satan) into beleiving your own lies, and stripped you of the ability to reason.