In modern logic, the existential import is removed from universal statements. So All S is P may still be true if there is no S at all.
Contradictory statements must have opposite truth values.
Why is the contradictory relationship between "All S is P" and "Some S is not P" in modern logic?
There are 2 cases, one where there is at least one object that is S, one where there isn't.
If there isn't an object that is S, then "Some S is not P" must be false, because it implies the existence of at least one object that is S and not P. But in a world without S, "All S is P" doesn't have to be true. It is conceivable that it is false too. Doesn't this mean there is one case where both statements are false?