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

On 4/1/25 1:56 PM, olcott wrote:

On 4/1/2025 1:33 AM, Mikko wrote:

On 2025-03-31 18:33:26 +0000, olcott said:
>

>
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.

>
Anything that follows from true sentences by a truth preserving
transformations is true. If you can prove that a true sentence
is false your system is unsound.
>

 Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
 

No, the proof is that it is impossible to prove that a system is consistant. (sort of the opposite of what you are thinking of).
Proving inconsistancy is easy, you just need one example.
Proving the non-existance isn't as easy, and for a complicated enough system, can't be done, as you need to search an infinite space for the problem, which we can't be sure we have finished,
Sort of like we can easily prove that a machine halts, but simulating it to that point (like a real emulator can do for DDD), but showing that a machine is non-halting can be more of a problem. Sometimes we can find an induction property to let us prove it, but not always.