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

On 3/26/2025 10:29 PM, Richard Damon wrote:

On 3/26/25 10:46 PM, olcott wrote:

On 3/26/2025 9:32 PM, Richard Damon wrote:

On 3/26/25 9:27 PM, olcott wrote:

On 3/26/2025 6:01 PM, Richard Damon wrote:

On 3/26/25 1:50 PM, olcott wrote:

On 3/26/2025 6:12 AM, Richard Damon wrote:

On 3/25/25 10:15 PM, olcott wrote:

On 3/25/2025 8:08 PM, Richard Damon wrote:

On 3/25/25 10:56 AM, olcott wrote:

On 3/25/2025 5:19 AM, Mikko wrote:

On 2025-03-22 17:53:28 +0000, olcott said:
 

On 3/22/2025 11:43 AM, Mikko wrote:

On 2025-03-21 12:49:06 +0000, olcott said:
 

On 3/21/2025 3:57 AM, Mikko wrote:

On 2025-03-20 15:02:42 +0000, olcott said:
 

On 3/20/2025 8:09 AM, Mikko wrote:

On 2025-03-20 02:42:53 +0000, olcott said:
 

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.

 A simple example is the first order group theory.
 

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.

 There is no computable predicate that tells whether a sentence
of the first order group theory can be proven.
 

 Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.

 However, it is possible that someone finds a proof of the conjecture
or its negation. Then the predicate True is no longer complete.
 

 The set of all human general knowledge that can
be expressed using language gets updated.
 

When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.

 However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable.
 

 When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.

 The set of human knowledge that can be expressed using language
is not a tautology.
 

 tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.

 And human knowledge is not.
 

 What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
 

 How do you DEFINE what is actually knowledge?
 

 *This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.

 SO that means that "Cats are Dogs" is part of Knowldedge?
 

 Try re-reading what I said as many times as needed
until you notice ALL of the words.

  I have, and you can't explain the difference.

 

 

How do we know what we think to be True is actually True?
 

 Stimulated relations between finite strings are necessarily
true. "cats" <are> "animals"

 Only if "cats" and "animals" have the appropriate definitions.
 

 Do think that anyone ever wrote these down?
Then they exist in the body of general knowledge expressed in language.

 So anything written down is true?
 Thus climare change must not be real, since THAT "fact" has been written down and accepted by a large number of peoplel
 

 

The trator down the street that is a "cat" isn't an animal, but sometimes the person that operates it can be a bit of one.
 

 General knowledge.

 But "cat" is a term for a type of tractor.
 

 

 

In FORMAL systems we can rigorously define what is true in that system, as we start with a defined set of given facts (which is why you can't change the definitions and stay in the system, as those definitions are what made the system).

 Almost the same idea as basic facts.

 Yes, but more than basic facts. Note,
 

 What formal system has an axiom that defines
ice cream as a diary product?

 Many,
 

 

 

When you talk about "Human Knowledge" for the "Real World" you run into the problem that we don't have a listing of the fundamental facts that define the system, but are trying to discover our best explainations by observation.
 

 Basic facts that cannot be derived from anything else.

 So what makes them true?

 What makes a dairy cow not a kind of rattlesnake.
Stipulated relations between finite strings that
provides their semantic meaning.

 No, stipulated relationships between concepts.
 

 OK, I will give you that and qualify my original statement.
Stipulated relations between concepts that are labeled by
finite strings, thus ultimately stipulated relations between
finite strings, the ultimate formalism.

 So, tho only thing you know to bo true are what you stipulated to be true.
 Sorry, that isn't a logic system.
 

 Actually it <is> a logic system because it only includes
relations between finite strings.
 I said the body of
(a) General knowledge (thus finite)
(b) Knowledge (thus true)
(c) Expressed in language (corrects analytic/synthetic distinction)
 

 So, what *ARE* your relationships. Logics systems are, by their definition, a system for DEDUCING things from rules of INFERENCE.

 As long as they are truth preserving any operation is permitted.