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

On 3/20/25 10:57 AM, olcott wrote:

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.

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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.
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 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.
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 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.

And thus it will be wrong when we ask it about statements which are known to have a truth value, because they belong to a field for which the law of the excluded middle holds, but whose value is not know.
For instance if x is a statement about the truth of the Collatz Conjecture being true, then by your definition:
True(x) is False and True(~x) is False, and thus we have a contradiction since we know one of them must be true,

 

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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.
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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.
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 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*

Nope, because that is just built on OPINION and you are just a liar for saying otherwise.
Please show an actual LOGICAL PROOF of your statements, based on sound axiomatic logic, and not just a perdonderance of the evidence.
Your problem is you just don't understand what Truth means, or even what Knowledge means.

 

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

And thus you admit that you logic system FAILS to meet the requirement, mostly because you are too stupid to understand the logic of the requirements because you world is just built on the foundation of the right to LIE.

 

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.

Nope. Not until your FIND the induction.
Note, there is not such thing (in standard logic) of an "Infinite Proof", that is like you example of a square circle, a contradiction inherent in the terminology.
You are still just proving that you are just too stupid to se your ignorance of what you talk about.

 

while knowledge requires a finite chain (since we are finite, we can't 'know' something only learnable via an infinite path).
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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.

I don't know which, but I do know that either there exist an even number that can be proved to not be representable as the sum of two primes, or there is no such number. Mathematics is definite, so there can't be a number that "sort of" exists to get us into a middle ground.
So, it is quite possible to know that a statement must have a truth value, while having no idea which value it has, something your "logic" is incapable of handling.

 Any TRUTH that can only be resolved by an infinite number
of inference steps remains forever unknown and outside
the scope of human knowledge.
 

Right, but not outside the scope of Truth.
That is your problem, you don't understand the difference of that.
Truth is unchanging, a logically True statement will ALWAYS be true, as long as the logic system that established it is still in force.
Knowledge changes, as we discover new things to be "true". (or think we discover things to be true when we run into erroneous knowledge, a big problem in the establishment of what is knowledge).
Thus they are different, and you make a category error trying to equate tehm.