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

On 3/22/2025 9:53 PM, Richard Damon wrote:

On 3/22/25 3:12 PM, olcott wrote:

On 3/22/2025 12:34 PM, Richard Damon wrote:

On 3/22/25 12:22 PM, olcott wrote:

On 3/22/2025 8:37 AM, Richard Damon wrote:

On 3/21/25 11:03 PM, olcott wrote:

On 3/21/2025 9:31 PM, Richard Damon wrote:

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.

>
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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>

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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.

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But Formal Logic proofs ARE just "syntactic"
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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.

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Yes, proof is a validatation of truth, but truth does not need to be able to be validated.
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True(X) ONLY validates that X is true and does nothing else.
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But can't do that, as Tarski shows, as it creates contradictions when the system is able to generate unprovable truths.
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Unless we do what ZFC did to redefine the foundations
of set theory and redefine the notion of a formal system.

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Not, that is NOT what ZFC did.
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ZFC defined a brand new version of Set Theory (called ZFC) and the community found it useful enough to change the meaning of the "generic" term of "Set Theory" to now mean that system.
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Which effectively replaces the erroneous foundation
of set theory wit one that is not erroneous.
>

 So, do that, define your own theory, fully and completely, and be honest that it isn't the old system, and that nothing done in the old has been impacted by your new system
 

If you can't possibly get the gist of the idea
how the Hell are you going to do better with much
more details?

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If a formal system only contains a finite set of basic
facts and facts are only derived by applying truth
preserving operations to elements of this set then
True(X) has already been implicitly defined for every
element of this set.
>

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No it hasn't, as the finite set of basic facts, if they are a good enough set of facts, allows the creation of an INFINITE set of ideas to look at, and True(x) hasn't been defined for all of them.

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Ideas that have a truth value that cannot be derived
from applying truth preserving operations to the set
of basic facts.

 But the problem is that there DO exist statements, that HAVE a truth value, because they CAN be derived by applying truth perserving operations (abet an infinite number of them) to the set of basic facts

Since you and I know that this does not derive knowledge
I can't understand why you keep bringing it up. (GKEUL)
will have a finite list of all unsolved problems as a
part of its basic facts.

exist. Such statements can not be proven, and the assumption of a Truth Predicate that answers for them causes a contradiction.
 You are just too stupid to understand that aspect of truth allowing infinite chains to establish things, one simple (in concept) is the idea that some statement may require checking every Natural Number individually to confirm a universal attribute (either ALL or NONE) for every one of them.
 That TRUTH can not be proved by trying to enumerate every case, as that enumeration can't be written out and shown, as those operation can only be done finitely, which is why proofs must be finite.
 

The set of all general knowledge that can be expressed
in language can have all basic facts that cannot be
derived from other facts finitely listed.
The infinite set of expressions of language of general
knowledge can be derived by applying truth preserving
operations to these basic facts.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer