Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable

On 2025-05-06 17:14:04 +0000, olcott said:

On 5/6/2025 5:04 AM, joes wrote:

Am Mon, 05 May 2025 14:22:58 -0500 schrieb olcott:

On 5/5/2025 1:52 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 5/5/2025 1:19 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 5/5/2025 11:05 AM, Alan Mackenzie wrote:

 

Follow the details of the proof of Gödel's Incompleteness Theorem,
and apply them to your "system".  That will give you your counter
example.

 

My system does not do "provable" instead it does "provably true".

 

I don't know anything about your "system" and I don't care.  If it's
a formal system with anything above minimal capabilities, Gödel's
Theorem applies to it, and the "system" will be incomplete (in
Gödel's sense).

 

I reformulate the entire notion of "formal system"
so that undecidability ceases to be possible.

 Liar.  That is impossible.
 

When you start with truth and only apply truth preserving operations
then you necessarily end up with truth.

Truth such as Gödel's undecidability theorem, but not all truths.

 The entire body of all general knowledge that can be
expressed using language is included in the system
that I propose.

Whether something can be expressed in a system is constant in time
but all general knowledge is not. Therefore the two cannot be the
same.
--
Mikko