That's fine. The law of excluded middle already encodes this.commonsense wrote: ↑Fri Sep 15, 2023 1:23 pm Sorry, but what you pose as the excluded middle overlooks something. When each premise is evaluated, P may be true or false and not P may be true or false, leaving both indeterminate.
P means "I accept P as true"
-P means "I accept the negation of P as true"
If you accept neither as true (e.g you are still busy evaluating) then shut up.
There is simply no fence for skeptics in Classical logic.
You can't reject P but refuse to accept not-P.
You can't reject not-P but refuse to accept P.
The law compels you.
The only thing to note while doing evaluations. P and not-P are complementary - evaluating one determines the other.
It may be much much easier to evaluate P.
It may be much much easier to evaluate not-P.
As is the case here. Evaluating not-P (negation of impossibility) requires a single counter-example
Whereas evaluating P (impossibility) requires simply observing the lack of a counter-example.