More significantly, only one of P=NP and P≠NP is logically possible, even though with my knowledge I can conceive of both.
Couldn’t P=NP and P≠NP both be consistent with the standard axioms of complexity theory (whatever they happen to be right now), in the same way that, say, the different parallel postulates are all consistent with the rest of the commonly accepted axioms of geometry, or the way that the continuum hypothesis is independent of Zermelo–Fraenkel set theory with the axiom of choice?
More significantly, only one of P=NP and P≠NP is logically possible, even though with my knowledge I can conceive of both.
Couldn’t P=NP and P≠NP both be consistent with the standard axioms of complexity theory (whatever they happen to be right now), in the same way that, say, the different parallel postulates are all consistent with the rest of the commonly accepted axioms of geometry, or the way that the continuum hypothesis is independent of Zermelo–Fraenkel set theory with the axiom of choice?