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

On 5/5/2025 2:34 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

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.

 

[ Irrelevant nonsense snipped. ]

 

When you start with truth and only apply truth preserving
operations then you necessarily end up with truth.
Is that too difficult for you?

 Not at all.  One of the truths you inescapably end up with is Gödel's
Theorem.  Either that, or the system is self-contradictory or too weak to
do anything at all.
 

Gödel's theorem cannot possibly be recreated when
True(x) is defined to apply truth preserving
operations to basic facts.
LP = "This sentence is not true"
is unreachable by applying truth preserving
operations to basic facts thus:
True(LP) == FALSE
True(~LP) == FALSE.
Everything is decidable as True(x) or ~True(x).
Every expression e such that True(e) == FALSE
and True(~e) == FALSE is rejected as not a
semantically sound proposition.

That would appear to be well beyond your level of understanding.  You
ought to show some respect towards those who do understand these things.
 

I have spent 22 years focusing on pathological self-reference.
My understanding really is deeper.

-- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

 

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer