Re: Mathematical incompleteness has always been a misconception

On 2025-02-01 14:09:54 +0000, olcott said:

On 2/1/2025 3:19 AM, Mikko wrote:

On 2025-01-31 13:57:02 +0000, olcott said:
 

On 1/31/2025 3:24 AM, Mikko wrote:

On 2025-01-30 23:10:18 +0000, olcott said:
 

Within the entire body of analytical truth any expression of language that has no sequence of formalized semantic deductive inference steps from the formalized semantic foundational truths of this system are simply untrue in this system. (Isomorphic to provable from axioms).

 If there is a misconception then you have misconceived something. It is well
known that it is possible to construct a formal theory where some formulas
are neither provble nor disprovable.

 This is well known.

 And well undeerstood. The claim on the subject line is false.

 a fact or piece of information that shows that something
exists or is true:
https://dictionary.cambridge.org/us/dictionary/english/proof

We require that terms of art are used with their term-of-art meaning and
that the same word is not used for any other meaning. Dictionaries that
are not deictionaries of the particular art are not relevant.
Consequently, there is no reason to revise my initial comment.
--
Mikko