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

On 3/21/2025 6:49 PM, Richard Damon wrote:

On 3/21/25 8:43 AM, olcott wrote:

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.
 >
Because my system begins with basic facts and actual facts
can't contradict each other and no contradiction can be
formed by applying only truth preserving operations to these
basic facts there are no contradictions in the system.
>
>

 No, you system doesn't because you don't actually understand what you are trying to define.
 "Human Knowledge" is full of contradictions and incorrect statements.
 Adittedly, most of them can be resolved by properly putting the statements into context, but the problem is that for some statement, the context isn't precisely known or the statement is known to be an approximation of unknown accuracy, so doesn't actually specify a "fact".

It is self evidence that for every element of the set of human
knowledge that can be expressed using language that undecidability
cannot possibly exist.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer