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

On 5/6/25 1:14 PM, olcott wrote:

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.

Nope. because that can not be expressed as a finite list by what you say is your logic operations.
The problem is you claim to have all the mathematics, so all the statements of x + y = (x+y), but your "logic" seems to reject the operations that allow this to be reduced to a finite number of axioms.

 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.

Only because your system doesn't do what you claim. if it can support Mathematics, it has Godel's proof and thus true statements that can not be proven, as truth can come from infinite sequences, but Proof and decidability can not.

 LP = "This sentence is not true."
True(LP) == FALSE
True(~LP) == FALSE
Proves that LP is not a valid proposition with a truth value.
 

So?
You keep on bringing this up which just shows you don't know what you are talking about.