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

On 4/3/2025 2:08 AM, Mikko wrote:

On 2025-04-03 01:30:28 +0000, olcott said:
 

On 4/2/2025 5:05 PM, Richard Damon wrote:

On 4/2/25 11:59 AM, olcott wrote:

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 you can't do that unless you limit the system to only have a finite number of statements expressible in it, and thus it can't handle most real problems
 

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

 Sure it can.
 The problem is you need to be very careful about what you allow as your "Basic Facts", and if you allow the system to create the concept of the Natural Numbers, you can't verify that you don't actually have a contradition in it.
 

 It never has been that natural numbers have
ever actually had any inconsistency themselves

 That is generally believed but not actually proven.
 

they are essentially nothing more than an ordered
set of finite strings of digits.

 The "nothing more" part cannot be proven.

 It is a stipulated basic fact.