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

On 3/21/25 9:24 PM, olcott wrote:

On 3/21/2025 7:50 PM, Richard Damon wrote:

On 3/21/25 8:40 PM, olcott wrote:

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:
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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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Not useful unless it returns TRUE for no X that contradicts anything
that can be inferred from the set of general knowledge.
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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.
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No, you system doesn't because you don't actually understand what you are trying to define.
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"Human Knowledge" is full of contradictions and incorrect statements.
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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".

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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.
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SO, you admit you don't know what it means to prove something.
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 When the proof is only syntactic then it isn't directly
connected to any meaning.

But Formal Logic proofs ARE just "syntactic"

 When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.

Yes, proof is a validatation of truth, but truth does not need to be able to be validated.
In any reasonable system, a proof is the validation of a statement being true (if you can proof a false statement to be true, your system is inconsistant). The issue is it doesn't work in reverse, not every truth can necessarily be validated by a proof in the system. (or any system)
You think so, but you are wrong, and you can't find the error in the proof that says you are wrong, so you need to accept it or keep looking.
Just trying to define that it can't be just breaks your system.

 When G is connected to every detail of all of its
semantics then a walk through the tree of knowledge
proves that it is true (if it was ever true).

Nope, because if it WAS true, and could be proven, then that proof can be encoded into a numerical value, which would then satisfy the Relationship, making G false.
What Godel proved is that it is possible to design in the metalanguage, a theorem prover that can work in the language to detect if something is a valid proof.
Thus, if your system COULD prove it, that proof becomes the counter-example that shows the statement is not true, and thus you just showed your system is inconsistant.
The problem is your idea that every true statement is provable is just a false statement in any system with the required expressiveness.

 

It is clearly not "self-evidently true", since I just listed a problem that it couldn't decide on.
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Your problem is your system doesn't have a valid definition of "Truth" in the first place.
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Sorry, you are just proving your stupidity.