Kripke and Identity Statements

From AC Grayling's An introduction to Philosophical Logic:

In Kripke's view, names are 'rigid designators', that is, terms which refer to the same individual in every possible world in which that individual exists. Because individuals will have different properties in different possible worlds -- their being different possible worlds will turn in in some cases just on the hypothesis that some selected individual answers to different descriptions in those worlds -- it cannot be the case that the name of that individual is synonymous with some set of descriptions. In other possible dispensations of things Aristotle may have been a hoplite, a physician, or whatever; but his name still rigidly designates him in all the worlds in which he exists. He will only possess in all possible worlds such properties as are essential to his being Aristotle. This allows what is surely true, that we can discover of individuals that certain descriptions fail to fit them. For example, suppose it is confirmed that Bacon did indeed write Othello, Hamlet, and the rest; nevertheless the name 'Shakespeare' will not cease to refer because the description 'the author of Hamlet' ceases to apply to that individual. For if we irreversibly identify whoever is designated by 'Shakespeare' with 'the author of Hamlet', it would be impossible to discover that he did not write Hamlet.

This then is the first important feature of the causal theory, that ordinary proper names are rigid designators and not abbreviations for clusters of descriptions. An interesting consequence of this relates to identity statements. It is commonly held that identity statements like 'Hesperus is Phosphorus' are contingent, because the fact that the two are one is something that had to be established a posteriori. But Kripke argues that if 'Hesperus is Phosphorus' is true, thens since both names are rigid designators and refer to the same entity in all possible worlds in which that entity exists, the identity statement is necessarily true. Philosophers had supposed this identity statement to be only contingently true because 'Hesperus is Phosphorus' is not analytic; but a failure to distinguish the metaphysical notion of necessity both from the epistemological notion of apriority and the semantic notion of analyticity makes for the muddle here. On Kripke's view, 'necessarily true' means 'true in all possible worlds'; so although 'Hesperus is Phosphorus' is a posteriori, it is necessary -- and if this is right, it establishes the existence of neceesary a posteriori truths, an exciting result.