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

Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:

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:

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.

The liar sentence is contradictory.

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.

Not self-evident was Gödel's disproof of that.

SO, you admit you don't know what it means to prove something.
>

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.

True(X) ONLY validates that X is true and does nothing else.

Not if X is unknown (but still true).

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.