 There are stronger and weaker brands of necessity corresponding to the possible notions of rigidity. Kripke argues that a sentence like ‘Hesperus = Phosphorus’ is at least “weakly” necessary (1971, p. 137): true in all those possible worlds in which Hesperus exists and Phosphorus exists. The statement may enjoy a stronger necessity, too, which would render it true in all worlds,  period.[2]  In this entry, “necessity” is to be understood as weak necessity (at least).