Why is "H2O = water" necessarily true while "water is transparent" is contingent? Kripke argued that identity statements between rigid designators are necessarily true if true at all, even when known a posteriori. This explains how empirical discoveries can establish necessities, revolutionizing philosophy's relationship to science and modal logic.
Begin with Kripke's distinction between epistemic and metaphysical necessity. "Water = H2O" is metaphysically necessary (true in all possible worlds) but epistemically contingent (we had to discover it empirically). Show why descriptivism makes this impossible: if "water" means "the clear liquid from lakes," then it could be false that water is clear. Work through Kripke's arguments that names are rigid designators and identity statements between rigid designators are always necessary.
You already know from Kripke's causal theory of naming that names are rigid designators: they pick out the same individual in every possible world. "Aristotle" refers to the same person whether we consider the actual world or a counterfactual world where he never taught Alexander. And you know from necessity and contingency that some truths hold across all possible worlds (necessary) while others hold only in some (contingent). This topic shows how these two ideas combine to produce a philosophically surprising result.
Consider the identity statement "Hesperus is Phosphorus"—the claim that the evening star and the morning star are the same object, namely Venus. This was an empirical discovery; ancient astronomers initially believed they were different celestial bodies. So there is a clear epistemic sense in which the statement is not a priori: we had to look at the sky over many nights to establish it. Yet once true, Kripke argues, it is necessarily true—true in every possible world. Why? Because "Hesperus" rigidly designates Venus, and "Phosphorus" rigidly designates Venus. In any possible world, these names pick out the same object, so the identity cannot fail. There is no possible world where Hesperus ≠ Phosphorus because there is no possible world where Hesperus fails to be Venus.
This severs a connection that philosophers had long assumed: that necessity and a prioricity go together. Kant treated them as nearly coextensive. Kripke showed they come apart in both directions. "Water is H₂O" is a posteriori necessary: we discovered it empirically, yet it is true in every world, because "water" rigidly designates the substance that is actually H₂O. Conversely, "I am in this room now" is a priori contingent: you can know it without investigation, yet it is false in many possible worlds. The old picture—necessary = a priori, contingent = a posteriori—is broken.
The deeper point returns to the contrast between epistemic and metaphysical modality. Epistemic possibility is about what is compatible with what we know; metaphysical possibility is about what could have been the case in reality. Before the discovery that Venus is both Hesperus and Phosphorus, it was *epistemically possible* that they differed—for all we knew, they might have been distinct. But it was never *metaphysically possible* for them to differ: in reality, there was always only one object. Once you distinguish these two senses of "possible," the puzzle dissolves. "Water = H₂O" feels contingent because it was epistemically open before the discovery; it is in fact necessary because in every possible world, the substance called water has whatever structure it actually has. This framework proves essential for analyzing theoretical identities in philosophy of mind—especially the identity theory's claim that pain = C-fiber firing, which faces exactly these modal pressures.
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