Re: Mathematical incompleteness has always been a misconception --- Tarski

On 02/11/2025 01:50 AM, Mikko wrote:

On 2025-02-10 11:48:16 +0000, olcott said:
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On 2/10/2025 2:55 AM, Mikko wrote:

On 2025-02-09 13:10:37 +0000, Richard Damon said:
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On 2/9/25 5:33 AM, Mikko wrote:

Of course, completness can be achieved if language is sufficiently
restricted so that sufficiently many arithemtic truths become
inexpressible.
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It is far from clear that a theory of that kind can express all
arithmetic
truths that Peano arithmetic can and avoid its incompletness.

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WHich, it seems, are the only type of logic system that Peter can
understand.
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He can only think in primitive logic systems that can't reach the
complexity needed for the proofs he talks about, but can't see the
problem, as he just doesn't understand the needed concepts.

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That would be OK if he wouldn't try to solve problems that cannot even
exist in those systems.

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There are no problems than cannot be solved in a system
that can also reject semantically incorrect expressions.

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The topic of the discussion is completeness. Is there a complete system
that can solve all solvable problems?
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There are various notions about arithmetic that
there's no standard model of integers anyways,
so that there are though fragments and extensions,
so there are at least three laws of large numbers,
and at least three models of linear continua,
so that thusly at least there can be the
more "replete" than the standard's, "complete".
Don't forget Goedel's completeness theorems while
you're at it, though, they're ordinary, and it's
quite telling that Goedel repeats Mirimanoff in
simply showing the extra-ordinary is a simple
consequence of quantification.
Or, your "GITs" was already a "MITs".