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

Am Sat, 29 Mar 2025 09:14:36 -0500 schrieb olcott:

On 3/29/2025 5:52 AM, Richard Damon wrote:

On 3/28/25 11:19 PM, olcott wrote:

On 3/28/2025 4:18 PM, Richard Damon wrote:

On 3/28/25 4:07 PM, olcott wrote:

On 3/28/2025 8:46 AM, Richard Damon wrote:

On 3/27/25 10:18 PM, olcott wrote:

On 3/27/2025 8:54 PM, Richard Damon wrote:

On 3/27/25 9:04 PM, olcott wrote:

On 3/27/2025 5:48 AM, Mikko wrote:

On 2025-03-26 17:58:10 +0000, olcott said:

On 3/26/2025 3:39 AM, Mikko wrote:

On 2025-03-26 02:15:26 +0000, olcott said:

On 3/25/2025 8:08 PM, Richard Damon wrote:

On 3/25/25 10:56 AM, olcott wrote:

On 3/25/2025 5:19 AM, Mikko wrote:

On 2025-03-22 17:53:28 +0000, olcott said:

On 3/22/2025 11:43 AM, Mikko wrote:

On 2025-03-21 12:49:06 +0000, olcott said:

On 3/21/2025 3:57 AM, Mikko wrote:

On 2025-03-20 15:02:42 +0000, olcott said:

On 3/20/2025 8:09 AM, Mikko wrote:

On 2025-03-20 02:42:53 +0000, olcott said:

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.

There is no computable predicate that tells whether
a sentence of the first order group theory can be
proven.

Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.

No, it is either true or not.

However, it is possible (and, for sufficiently
powerful sysems, certain)
that the provability is not computable.

Ok, so therefore it includes all the "laws of mathematics" and the
"rules of inference" and thus, the system is capable of creating
the rules and properties of the Natural Numbers, so it supports the
proofs of Godel and Tarski, and thus there are statements in that
sytstem that are True but unprovable and no definition of the Truth
Predicate can handle those,
>

Yes it will showed the formal system can be defined that have all
kinds of issues because they were defined incoherently.

Where is there an incoherent definition?

When any formal logic system begins with stipulated set of basic facts
and is only allowed to apply truth preserving operations to these
facts and expressions derived from these facts then undecidability
cannot possibly occur.

 
Sure it can, as Godel and Turing Proved.
 

When full semantics is directly integrated into the formal system, the
system begins with an list of basic facts, the only inference step is
semantic logical entailment applying truth preserving operations
Tarski's proof fails.

Where, at which step, how, why?

We are no longer seeking mere provability we are seeking provably true
at the semantic level. At the semantic level incoherent nonsense such as
"This sentence is not true" is screened out.

How?

--
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.