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

On 2/10/25 6:48 AM, olcott wrote:

On 2/10/2025 2:55 AM, Mikko wrote:

On 2025-02-09 13:10:37 +0000, Richard Damon said:
>

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.
>
It is far from clear that a theory of that kind can express all arithmetic
truths that Peano arithmetic can and avoid its incompletness.

>
WHich, it seems, are the only type of logic system that Peter can understand.
>
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.

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

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

So you think.
So, what *IS* the answer to True(L, x) where x is !True(L, x)
"Reject" is not an option unless you admit that your system can't handle the properties of the Natural Numbers, proving you are just a liar.

 On 2/8/2025 9:51 AM, Ross Finlayson wrote:
 > then there's a Comenius language of it that only
 > truisms are well-formed formulas...
 We can easily extend the Comenius language to evaluate
FALSE as well as TRUE by allowing True(L, x) to also
evaluate True(L, ~x).