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

On 2/17/25 10:59 PM, olcott wrote:

On 2/12/2025 4:21 AM, Mikko wrote:

On 2025-02-11 14:07:11 +0000, olcott said:
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On 2/11/2025 3:50 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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When the essence of the change is to simply reject expressions
that specify semantic nonsense there is no reduction in the
expressive power of such a system.

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The essence of the change is not sufficient to determine that.

 In the same way that 3 > 2 is stipulated the essence of the
change is that semantically incorrect expressions are rejected.
Disagreeing with this is the same as disagreeing that 3 > 2.

But your logic needs to reject some of the results of your logic as semantically incorrect, and thus your logic is itself semantically incorrect.
Sorry, the problem is you don't understand what you are talking about, but only understand "toy" level logic, and not the subtleties that happen when you logic needs to handle real problems.

 

The
result depends on all of the change. But as long as we don't even
know whether that kind of change is possible at all the details are
impossible to determine.
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 LP := ~True(LP) has never been more than nonsense.
Tarski (although otherwise quite brilliant) had a blind spot.