A posteriori necessity
A posteriori necessity is a thesis in metaphysics and the philosophy of language, that some statements of which we must acquire knowledge a posteriori are also necessarily true. It challenges previously widespread belief that only a priori knowledge can be necessary. It draws on a number of philosophical concepts such as necessity, the causal theory of reference, rigidity, and the a priori a posteriori distinction.
It was first introduced by philosopher Saul Kripke in his 1970 series of lectures at Princeton University. The transcript of these lectures was then compiled and assembled into his seminal book, Naming and Necessity.
Main argument for a posteriori necessity
Here is an overview of the argument:
- (P1) 'Hesperus' is a proper name that refers to the evening star. 'Phosphorus' is also a proper name and it refers to the morning star. But the evening star and the morning star are the same planetary body (Venus). So both names designate Venus
- (P2) If both names designate rigidly, they designate the same object (Venus) in every possible world. Therefore (by the definition of 'necessary') 'Hesperus = Phosphorus' is necessarily true. If it is the case that in all possible worlds the identity claim “Hesperus is Phosphorus” is true, the statement is necessary
- (P3) The fact that Hesperus is Phosphorus was discovered by empirical observation. So it is a posteriori knowledge. Knowing that Hesperus is Phosphorus cannot have been discovered a priori. Using scientific instruments and empirical research, it was concluded that both Hesperus and Phosphorus are the same object. This is a posteriori knowledge.
- (C) Therefore, it is possible for knowledge obtained a posteriori to be necessary. That Hesperus is Phosphorus has been shown to be both necessary, because the names pick out the same thing in all possible worlds, and a posteriori, because this claim was discovered by empirical research.
Other instances of a posteriori necessary truths include: "H2O is water".
Naming and necessity is among the most important philosophical works of the 20th century. The prospect of a posteriori necessity also makes the distinction between a prioricity, analyticity, and necessity harder to discern because they were previously thought to be largely separated from the a posteriori, the synthetic, and the contingent. With the example “Hesperus is Phosphorus”, Kripke seems to have provided a successful counter-example to the Kantian claims:
(a) P is a priori iff P is necessary.
(b) P is a posteriori iff P is contingent.
Hilary Putnam comments on the significance of Kripke’s counter-examples, "Since Kant there has been a big split between philosophers who thought that all necessary truths were analytic and philosophers who thought that some necessary truths were synthetic a priori. But none of these philosophers thought that a (metaphysically) necessary truth could fail to be a priori.” 
- Necessity of identity
- Descriptivist theory of names
- Causal theory of reference
- Rigid designator
- Kripke, Saul A. (1980). Naming and Necessity. Cambridge, Mass.: Harvard University Press.
- LaPorte, Joseph (24 October 2006). "Rigid Designators". The Stanford Encyclopedia of Philosophy. Retrieved 5 August 2016.
- Vaidya, Anand (5 December 2007). "The Epistemology of Modality". The Stanford Encyclopedia of Philosophy. Retrieved 5 August 2016.
- Putnam, Hilary (1975). "The Meaning of 'Meaning'". Minnesota Studies in the Philosophy of Science. 7: 131–193.