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On 8/18/2024 5:14 AM, Mikko wrote:No, it requrires re-proving EVERYTHING that was possibly derived from the axioms you are changing to do this, and if that is something fundamental like the definiton of how we do implications, that means EVERYTHING.On 2024-08-16 18:11:46 +0000, olcott said:I am redefining the notion of a formal system to get
>On 8/16/2024 11:32 AM, Richard Damon wrote:>On 8/16/24 7:02 AM, olcott wrote:>>>
*This abolishes the notion of undecidability*
As with all math and logic we have expressions of language
that are true on the basis of their meaning expressed
in this same language. Unless expression x has a connection
(through a sequence of true preserving operations) in system
F to its semantic meanings expressed in language L of F
x is simply untrue in F.
But you clearly don't understand the meaning of "undecidability"
Not at all. I am doing the same sort thing that ZFC
did to conquer Russell's Paradox.
Zermelo constructed a new formal theory that does not have that paradox.
Note that the paradox was not present in Cantor's original theory as
Cantor did not promise that Russell's set exists. But Cantor's original
presentation was not fully formal so it was not clear that Russell's
set does not exist.
>
rid of undecidability. This requires few changes.
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