I interpret “$SITUATION is logically possible” to mean “$SITUATION can be modeled without any necessary contradictions”; thus, it’s logically possible for energy not to be conserved (if we allow to change whatever laws need to change), but not for 21 to be a prime number (within any system of arithmetic like the ones we’re used to, but then, if we used another system the relevant object/predicate wouldn’t be what we mean by “21″/”prime”) - or, more significantly, only one of P=NP and P≠NP is logically possible, even though with my knowledge I can conceive of both.
I interpret “$SITUATION is logically possible” to mean “$SITUATION can be modeled without any necessary contradictions”; thus, it’s logically possible for energy not to be conserved (if we allow to change whatever laws need to change), but not for 21 to be a prime number (within any system of arithmetic like the ones we’re used to, but then, if we used another system the relevant object/predicate wouldn’t be what we mean by “21″/”prime”) - or, more significantly, only one of P=NP and P≠NP is logically possible, even though with my knowledge I can conceive of both.