It may help to think of constraints on attributes as being either static or dynamic (I'm just making up these terms). Those that only take into account the attribute itself and don't rely on external values are static; numbers being non-negative, strings being non-empty, that sort of thing.
By contrast, requiring that the lower bound of an interval does not exceed its upper bound is a dynamic constraint: you can't know whether the constraint is violated without actually checking the upper bound, i.e. accessing the interval object.
It may thus help to use public attributes only when you can be sure that all constraints are static in nature. If you need dynamic constraints, use methods so you have the language's full power at your disposal for verification.
