"Hesperus (the evening star) is Phosphorus (the morning star)" is one of Kripke's examples of necessary aposteriori, statements that are true necessarily if true at all, even if their truth can only be established empirically. Since this is a path from is to ought there is a catch. According to Kripke (in Soames's phrasing), "being non-identical is a relation that holds essentially of any pair it relates. So, we know apriori that if any objects... stand in this relation, then they have, or stand in, them in any genuinely possible circumstance in which they exist". "Water is H20" necessarily for the same reason, although here identity is applied not to singular objects but to "natural kind" of objects.
I understand the reasoning, what I do not understand is what drives it. What makes some properties/relations essential and others not? what do we gain by attaching "essential" to them, and "necessarily" to statements? For example, is "inertial mass=gravitational mass" necessarily? Like Hesperus and Phosphorus they appear in two ostensibly different situations, when measuring inertia and attractive force respectively, however every measurement to date produced identical results. It is as empirically solid as the identity of Venus's manifestations, and a postulate of general relativity. But is it necessary? and what does that mean in practice? What about "green is extended" that Quine puzzled over, certainly every manifestation of green we met or imagined was extended in space?
Generally, when we discover some persistent empirical coincidence, how are we to decide if it is necessary or just true? I can think of two possible approaches, a testing principle or a guiding principle, perhaps their is a third or they can be mixed.
1) Testing: necessity is relative to a set of presuppositions to be tested. We heuristically designate some relations as essential, and see what distribution of necessities/contingents obtains, then we test if it works. Obviously we can not test it directly, since possible worlds are empirically inaccessible, but perhaps attaching modal logic to scientific theories may prove fruitful/unhelpful in some ways. This is not the impression I get from Kripke, he seems to envision some absolute intuitions about essential and necessary, but were there any concrete proposals for testing them, from others perhaps?
2) Guiding: there is some methodological principle or a speculative model about how the world works that motivate essentialness. Perhaps, not a cut and dry prescription but solid enough to specify broad classes of properties/relations as definitely essential, and others as definitely not. If so, what is this principle, and why is it plausible?