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

On 11/8/24 8:03 PM, olcott wrote:

On 11/8/2024 6:58 PM, Richard Damon wrote:

On 11/8/24 7:39 PM, olcott wrote:

On 11/8/2024 6:33 PM, Richard Damon wrote:

On 11/8/24 6:36 PM, olcott wrote:

On 11/8/2024 3:59 PM, Richard Damon wrote:

On 11/8/24 4:17 PM, olcott wrote:

On 11/8/2024 12:31 PM, Richard Damon wrote:

On 11/8/24 1:08 PM, olcott wrote:

On 11/8/2024 12:02 PM, Richard Damon wrote:

On 11/8/24 12:25 PM, olcott wrote:
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That formal systems that only apply truth preserving
operations to expressions of their formal language
that have been stipulated to be true cannot possibly
be undecidable is proven to be over-your-head on the
basis that you have no actual reasoning as a rebuttal.
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No, all you have done is shown that you don't undertstand what you are talking about.
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Godel PROVED that the FORMAL SYSTEM that his proof started in, is unable to PROVE that the statement G, being "that no Natural Number g, that satifies a particularly designed Primitive Recursive Relationship" is true, but also shows (using the Meta- Mathematics that derived the PRR for the original Formal System) that no such number can exist.
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The equivocation of switching formal systems from PA to meta-math.
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No, it just shows you don't understand how meta-systems work.
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IT SHOWS THAT I KNOW IT IS STUPID TO
CONSTRUE TRUE IN META-MATH AS TRUE IN PA.
THAT YOU DON'T UNDERSTAND THIS IS STUPID IS YOUR ERROR.

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But, as I pointed out, the way Meta-Math is derived from PA,

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Meta-math <IS NOT> PA.
Meta-math <IS NOT> PA.
Meta-math <IS NOT> PA.
Meta-math <IS NOT> PA.
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True in meta-math <IS NOT> True in PA.
True in meta-math <IS NOT> True in PA.
True in meta-math <IS NOT> True in PA.
True in meta-math <IS NOT> True in PA.
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This sentence is not true: "This sentence is not true"
is only true because the inner sentence is bullshit gibberish.
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But MM has exactly the same axioms and rules as PA, so anything established by that set of axioms and rules in MM is established in PA too.
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There are additional axioms in MM, but the rules are built specifically

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One single level of indirect reference CHANGES EVERYTHING.
PA speaks PA. Meta-math speaks ABOUT PA.
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The liar paradox is nonsense gibberish except when applied
to itself, then it becomes true.
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No, Meta-Math speaks PA, because is includes ALL the axioms and rules of PA, so it can speak PA.
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You just don't understand what a meta-system is.
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 In C we can have a pointer to a character string
and a pointer to a pointer to a character string.
 

But we are not talking about C.

The pointer to pointer is one level of indirect
reference away form the pointer to the character string.

But the meta-math is not restricted to nust talking about PA, it can talk in the language of PA.

 I know exactly what a meta-system is. It is a system that
refers to the underlying system by one level of indirect
reference. PA talks PA meta-math talks ABOUT PA.
 

Nope, you THINK you know about what a meta-system is, but you don't.
You are using a definition from another context which isn't applicable.
The "meta" systems, are system that FULLY INHERET the base system, and then ADD information about that system, in a way they can still talk the original language.
Sorry, you are just proving your ignorance.
Read the papers and where they talk about how the meta-systems are built.