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

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.
Undecidability cannot possibly occur in any system
that ONLY derives True(x) by applying truth preserving
operations to basic facts that are stipulated to be true.
LP = "This sentence is not true."
True(LP) == FALSE
True(~LP) == FALSE
Proves that LP is not a valid proposition with a truth value.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer