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

On 3/20/25 10:14 PM, olcott wrote:

On 3/20/2025 8:31 PM, Richard Damon wrote:

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.
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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.

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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.
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For instance if x is a statement about the truth of the Collatz Conjecture being true, then by your definition:
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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*

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Nope, because that is just built on OPINION and you are just a liar for saying otherwise.
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 I got on an Elon Musk page and dared anyone to point
to any actual evidence what-so-ever that election
fraud changed the outcome of the 2020 presidential
election and they didn't even have double talk and
weasel words to back their position after many
hundreds of exchanges.
 

But that isn't proof.
That is part of your problme, you don't understand what truth actually means.
Most of what we consider to be Human Knowledge is our agreed upon opinion of the best solution that represents our observations, or the agreed upon naming/classification of things.
The knowledge that comes from Formal Logic is the one segment which is actually truth, and all of that is still just conditionally true, the conditions being that you are in looking in a system based on the same axioms.

Please show an actual LOGICAL PROOF of your statements, based on sound axiomatic logic, and not just a perdonderance of the evidence.
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Your problem is you just don't understand what Truth means, or even what Knowledge means.
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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.

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And thus you admit that you logic system FAILS to meet the requirement,

 It is stupid that you require the set of knowledge to
contain unknown things.

I don't, because unknown things can't be known.
What I require is that TRUTH includes unknown things, because it has been shown that it does.
You just seem to have a memtal block on the difference between our knowledge, and the actaul existance of a truth.

 

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

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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.

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Nope. Not until your FIND the induction.
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Right and until, then they are outside of the set
of knowledge. True(X) works for the set of knowledge
thus Tarski was WRONG.

But the set of knowledge isn't a logic system that meets Tarski's criteria for a system.

 

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.
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 SET OF KNOWLEDGE DOOFUS
SET OF KNOWLEDGE DOOFUS
SET OF KNOWLEDGE DOOFUS
SET OF KNOWLEDGE DOOFUS

Still not a logc, and thus not applicable to what you claim.

 

You are still just proving that you are just too stupid to se your ignorance of what you talk about.
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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.

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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.

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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.
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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.
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 Knowing what is unknown is an aspect of knowledge doofus
Knowing what is unknown is an aspect of knowledge doofus
Knowing what is unknown is an aspect of knowledge doofus

Right, So by your logic, we can have a statement x that is neither True or False (because we don't know which it is) but you still admit that it can be a fact that it must be True or False.

 

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Any TRUTH that can only be resolved by an infinite number
of inference steps remains forever unknown and outside
the scope of human knowledge.
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Right, but not outside the scope of Truth.
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That is your problem, you don't understand the difference of that.
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 It is flat out stupid to require the set of all knowledge
to contain all the answers to every unknown.

But I never said that knowledge need to contain that.
Only that Truth does, ad thus it is stupid to think that Truth can be equated or defined by Knowledge.

 I am taking your dishonest dodge to be a flat out
admission that you know that True(X) will always
be correct for every element of the set of knowledge
that can be expressed in language.

But not for every statement of the language.
After all, if your system has all the current mathematical knowledge, and your definition of truth, then as Tarski shows (in the part you don't look at) that there exists a statement x, such that x will be accepted by the Truth Predicate, if and only if the statement that x will be accepted is false.
Thus, your system is inconsistant.

 

Truth is unchanging, a logically True statement will ALWAYS be true, as long as the logic system that established it is still in force.
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 My system would contain a superset of logical truths.
The whole idea is to give it the basis to become a
human mind.

Which just shows you don't understand what you are talking about.

 

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).
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 True(X) will always work correctly on the basis of
its encoded basic facts.

And fails when it needs to look at something that hasn't been encoded, as we look at a new idea that hasn't been decided on yet, or needs the infinite sequence to make it true.

 

Thus they are different, and you make a category error trying to equate tehm.