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

Am Sun, 23 Mar 2025 16:33:27 -0500 schrieb olcott:

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:

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.

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.

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

What about them?

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.

I want to dispute the notion that there are only finitely many unsolved
problems.

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.

Any reason for that?

The infinite set of expressions of language of general knowledge can be
derived by applying truth preserving operations to these basic facts.

Not sure of that either.

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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.