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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 complied and assembled into his seminal book, Naming and Necessity.
Here is an overview of the argument:
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”
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