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

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.

(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.

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.