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

On 4/3/2025 2:03 AM, Mikko wrote:

On 2025-04-02 15:59:47 +0000, olcott said:
 

On 4/2/2025 4:20 AM, Mikko wrote:

On 2025-04-01 17:51:29 +0000, olcott said:
>

>
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.

>
There already are programs that check proofs. But you can make your own
if you think the logic used by the existing ones is not correct.
>
If the your logic system is sufficiently weak there may also be a way to
make a C program that can construct the proof or determine that there is
none.

>
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.

 But a proof of paraconsistency is required.
 

When it is stipulated that {cats} <are> {Animals}
When it is stipulated that {Animals} <are> {Living Things}
Then the complete proof of those is their stipulation.
AND {Cats} <are> {Living Things} is semantically entailed.

A system entirely comprised of Basic Facts and Semantic logical entailment cannot possibly be inconsistent.

 It can if the set of basic facts is inconsistent or if the logical
entailment sematics is not sufficiently weak. Inconsistencies are
avoided if your system has no way to express logical negations
(which incudes negative quantification).
 

Stipulated basic facts + semantic logical entailment
guarantees True(X). When the basic facts do not contradict
each other then undecidability is impossible.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer