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

On 2025-03-25 14:40:26 +0000, olcott said:

On 3/22/2025 11:32 AM, Mikko wrote:

On 2025-03-21 12:43:39 +0000, olcott said:
 

On 3/21/2025 3:41 AM, Mikko wrote:

On 2025-03-20 14:57:16 +0000, olcott said:
 

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.

 Not useful unless it returns TRUE for no X that contradicts anything
that can be inferred from the set of general knowledge.

 I can't parse that.
 > (a) Not useful unless
 > (b) it returns TRUE for
 > (c) no X that contradicts anything
 > (d) that can be inferred from the set of general knowledge.

 Can you parse "It might be useful if it would return something else that
TRUE for some X, especially if that X contradicts something that can be
inferred from the set of general knowledge." ?

 Before we can get into these details it must first be
acknowledged that True(X) would necessarily work correctly
for the set of actual knowledge that can be expressed in
language.

Unlikely to work correctly for any other knowledge than what is included
in its construction. Before it is published some new knowledge will be
already known.

True(X) for this set proves Tarski was wrong that no True(X)
can ever be consistently defined.

Tarski did not say "no True(X)". But he did prove that one that can
correctly answer about all arithmetic sentences cannot be constructed.
About many useful and much used theories it is also proven that there are
no computable or constructible predicate that tells whether a sentence
can be proven.
--
Mikko