Re: Mathematical incompleteness has always been a misconception

On 2025-02-05 16:03:21 +0000, olcott said:

On 2/5/2025 1:44 AM, Mikko wrote:

On 2025-02-04 16:11:08 +0000, olcott said:
 

On 2/4/2025 3:22 AM, Mikko wrote:

On 2025-02-03 16:54:08 +0000, olcott said:
 

On 2/3/2025 9:07 AM, Mikko wrote:

On 2025-02-03 03:30:46 +0000, olcott said:
 

On 2/2/2025 3:27 AM, Mikko wrote:

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

 The fundamental base meaning of Truth[0] itself remains the same
no matter what idiomatic meanings say.

 Irrelevant as the subject line does not mention truth.
Therefore, no need to revise my initial comment.

 The notion of truth is entailed by the subject line:
misconception means ~True.

 The title line means that something is misunderstood but that something
is not the meaning of "true".

 It is untrue because it is misunderstood.

 Mathematical incompleteness is not a claim so it cannot be untrue.

 That mathematical incompleteness coherently exists <is> claim.

Yes, but you didn't claim that.

The closest that it can possibly be interpreted as true would
be that because key elements of proof[0] have been specified
as not existing in proof[math] math is intentionally made less
than complete.

Math is not intentionally incomplete. Many theories are incomplete,
intertionally or otherwise, but they don't restrict the rest of math.
But there are areas of matheimatics that are not yet studied.

When-so-ever any expression of formal or natural language X lacks
a connection to its truthmaker X remains untrue.

An expresion can be true in one interpretation and false in another.
--
Mikko