A posteriori necessity

A posteriori necessity is a concept in metaphysics and the philosophy of language. This prospect says that some knowledge gained a posteriori can also be 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.^[1]

Causal theory of reference

Kripke’s causal theory of reference is a necessary component of a posteriori necessity.

The causal theory of reference is an explanation of how terms acquire specific referents. Referring terms that it may include are proper names, natural kinds, and logical terms. A causal theory of reference claims that the referent of a name is fixed by the original act of naming. Future uses of the name continue to successfully refer to the referent via a causal chain. The chain can then, in principle, be traced back to the original act of naming. Kripke indicates that this explanation is more appealing than the descriptive theory of names developed by Bertrand Russell and Gottlob Frege. The descriptive theory says that names are attached to a uniquely identifying description of that thing. A name’s semantic contents are identical to the descriptions associated with them.

Consider these two theories’ approach to the following question: To whom does the name “Richard Nixon” refer?

The causal/ historical theory could proceed thusly: Suppose the parents of a newborn baby boy gesture to their child and declare “We shall name him Richard Nixon!” From that time onward, that person is referred to as “Richard Nixon”. When someone uses the name “Richard Nixon”, that act can be traced back to the initial baptism of the child by his parents. The name refers to the object originally designated as “Richard Nixon”.

According to the descriptivist theory of names, the referent might be fixed like so: the name “Richard Nixon” refers to the man who won the 1968 election, the 37th President of the United States, etc. Only one person satisfies this description and that is “Richard Nixon”. This could be true for a number of different unique descriptions that identify “Richard Nixon”. So the name “Richard Nixon” would refer to whoever satisfies the particular unique description.

Rigidity

Rigidity is also a key component of necessary a posteriori knowledge.

A term is a rigid designator when it designates the same object in all possible worlds in which that object exists. When a name’s referent is fixed by the original act of naming (via Kripke’s causal theory of reference, see above) it becomes a rigid designator. Some examples of rigid designators include proper names (i.e. ‘Richard Nixon’), natural kind terms ( i.e. ‘gold’ or ‘H2O’) and some descriptions.

Rigid designation is a property of the way that names are used. So we can speak of “Richard Nixon” referring to the same person in all possible worlds, but the description “the man who won the 1968 election” could refer to many different people. According to Kripke, the proper name “Richard Nixon” can only be used rigidly, but the description “the man who won the 1968 election” can be used non-rigidly.

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. They pick out the same thing in all possible worlds in which the thing exists.

(P2) Hesperus is Phosphorus. They are, in reality, two different names that refer to the same thing: Venus. This is necessarily true.

(P3) The fact that Hesperus is Phosphorus was discovered by empirical observation. So it is a posteriori knowledge.

(C) Therefore, it is possible for knowledge obtained a posteriori to be necessary.

Premise (1): According to the causal theory of reference, the names Hesperus and Phosphorus are causally linked to the initial act of giving them their respective referents, respectively. Therefore, they must also be rigid designators. So they each will pick out the same object in all possible worlds, if the thing exists.

Premise (2): But Hesperus is the same thing as Phosphorus. Regardless of which name is being used, they both refer to the same thing all possible worlds. So it is the case that in all possible worlds the identity claim “Hesperus is Phosphorus” is true. Therefore it is necessary.

Premise (3): 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) So Hesperus is Phosphorus has been shown to be both necessary, because they 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".

Significance

Naming and necessity is among the most important philosophical works of the 20th century.^[2] 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:^[3]

(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” ^[4]

See also

• Descriptivist theory of names
• Causal theory of reference
• Rigid designator
• Modality
• Necessity

References