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

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.
 There are additional axioms in MM, but the rules are built specifically

One single level of indirect reference CHANGES EVERYTHING.
PA speaks PA. Meta-math speaks ABOUT PA.
The liar paradox is nonsense gibberish except when applied
to itself, then it becomes true.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer