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

On 3/20/2025 6:00 AM, Richard Damon wrote:

On 3/19/25 10:42 PM, olcott wrote:

It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.

 Which just means that you have stipulated yourself out of all classical logic, since Truth is different than Knowledge. In a good logic system, Knowledge will be a subset of Truth, but you have defined that in your system, Truth is a subset of Knowledge, so you have it backwards.
 

True(X) always returns TRUE for every element in the set
of general knowledge that can be expressed using language.
It never gets confused by paradoxes.

In fact, your definition impllies a possibility that there may be some Knowledge that isn't True, depending on how you parse your definition.
 

Knowledge is defined to be TRUE.
The set of human general knowledge is defined as elements
derived by applying truth preserving operations to basic facts.

 

>
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.
>

 Only because you have defined Truth to be limited to knowledge, and thus made your "Logic System" worthless, as it can be used to find out something new.
 

It is not at all worthless. It can prove that climate change is
real and everyone saying otherwise is a liar. It can prove
that there never was any actual evidence of election fraud
that could have possibly changed the outcome of the 2020
presidential election and everyone saying otherwise is a liar.
*True(X) can save the planet and save Democracy*

This has always been your problem, you confuse the concept of actual Truth, with includes statements which might not be know, or can even be unknowable, with the limited concept of what is known.
 

Unknown things are outside of the scope of any True(X)
predicate that can possibly exist.

Note, in REAL logic systems, Truth can be established via infinite length chains of reasoning steps,

All of these otherwise infinite proofs are compressed using
something like mathematical induction. When they are compressed
then they become elements of the set of knowledge.

while knowledge requires a finite chain (since we are finite, we can't 'know' something only learnable via an infinite path).
 Sorry, you are just proving how stupid you actually are.

Show me how you actually know right now how the Goldbach
Conjecture is true or false, which it is TRUE or FALSE
and show ALL of your steps.
Any TRUTH that can only be resolved by an infinite number
of inference steps remains forever unknown and outside
the scope of human knowledge.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer