Re: How a True(X) predicate can be defined for the set of analytic knowledge

On 3/28/25 3:45 PM, olcott wrote:

On 3/28/2025 5:33 AM, joes wrote:

Am Thu, 27 Mar 2025 20:44:28 -0500 schrieb olcott:

On 3/27/2025 6:08 PM, Richard Damon wrote:

On 3/27/25 9:03 AM, olcott wrote:

On 3/27/2025 5:58 AM, Mikko wrote:

On 2025-03-26 18:01:14 +0000, olcott said:

On 3/26/2025 3:36 AM, Mikko wrote:

>

I am NOT referring to what is merely presented as the body of
general knowledge, I am referring to the actual body of general
knowledge. Within this hypothesis it is easy to see that True(X)
would be infallible.

>
In that case your True(X) is uncomputable and any theory that
contains it is incomplete.
>

The body of general knowledge that can be expressed using language is
defined to be complete. The moment that new knowledge that can be
expressed in language comes into existence it is added to the set.
>

No its not. We KNOW there are things we don't know yet, but hope to.
>

As soon as the first person knows new general knowledge and this
knowledge can be written down (unlike the actual direct physical
sensation of smelling a rose)
then this becomes an element of this set of knowledge.
>

And, the base of a logic system is STATIC and fixed.

The set of general knowledge that can be expressed in language has more
flexibility than that.
>

You just don't understand the meaning of the words you are using.
>

True(X) merely tests for membership in this set;
(a) Is X a Basic Fact? Then X is true.

Which makes it not a TRUTH test, but a KNOWLEDGE test, and thus not
names right.

The set of all general knowledge that can be expressed in language is a
subset of all truth and only excludes unknown and unknowable.

 

Exactly, it doesn't include the unknown truths and ought to be called
Known(X). It is also contradictory since it gives NO both for unknowns
and their negation.
>

 *The key defining aspect of knowledge is that it is true*

Which has been the eternal debate, how can we tell if some "fact" we have discovered is true.
In FORMAL LOGIC (which you just dismissed) truth has a solid definition, and we can formally PROVE some statements to be true and formally PROVE that some statements are just false, and thus such statements CAN become truely established knowledge. There may also be some statements we have not established yet (and maybe can never establish in the system) which will remain as "unknown". That doesn't mean the statements might not be true or false, just that we don't know the answer yet.

When LLM systems have all of the basic facts encoded and
are only allowed to perform truth preserving operations
on these basic facts:
(a) They won't be able to hallucinate
(b) They will have the basis to shut down the lies
     of liars before these lies have any effect.

Since LLM are only approximation machines, that is totally NOT the results.
And, only if the people you want to call liars have accepted your initial set of facts (which they won't), as almost all of the arguments are over interpretation of data, which is something that can not be logically difinitively proven.
Your problem has always been, it seems, that you just don't understand that fact, that basically ALL knowledge about the "real world" is either based on emperical observation, taken to be a "truth" because the vast majority accepts the conclusions from the observaitions, or is definitional based upon agreed upon terminology. (So "Cats are Animals" can be true based upon an agreed upon meaning of the words coupled with the observation of in the world that the thing we think of as those terms matches our definitions.)
Many big "breakthroughs" have been made when we realize a base assumption in our definitions about the world were incorrect.

 

(b) Can X be derived by applying truth preserving operations
      to Basic Facts? Then X is true.

But that isn't the membershop test you just mentioned, and it is that
op[eration which Tarski specifically showed can not be done.
The problem is TRUTH can be establish via an infinite set of truth
perserving operations, but knowledge can not.

None of this makes any actual difference in the world.
We won't be able to prevent nuclear Winter and the extinction of
humanity on the basis of knowing whether or not the Goldbach conjecture
is true.