One of Kripke's principal themes in Naming and Necessity and elsewhere is the distinction between the metaphysical status of a statement and its epistemic status. In Chapter 4 we considered the status of identity statements involving ordinary proper names and Kripke's arguments that such claims are examples of necessary a posteriori truths. In this chapter we continue Kripke's theme of the importance of separating the epistemic status of a statement from its metaphysical status by first considering the claim that there are contingent a priori truths; then we consider Kripke's views on theoretical identifications. Kripke argues for a version of what is now called scientific realism. We conclude with his argument against materialism.

Kripke provides us with a number of examples of contingent a priori statements based on a single idea. One example comes from Wittgenstein. Wittgenstein remarks that the bar in Paris that (at that time) was the standard for the length of one metre cannot itself be a metre long. It is not completely clear why Wittgenstein thought the standard for something cannot have the property that it is the standard for. In any case, Kripke makes the following remarks about this example (where ‘S’ is the standard metre bar):