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Naming and Necessity

A simple descriptivist theory of names can be thought of as follows: for every proper name p, there is some collection of descriptions D associated with p that constitute the meaning of p. For example, the descriptivist may hold that the proper name Saul Kripke is synonymous with the collection of descriptions such as "the man who wrote Naming and Necessity", "a person who was born on November 13, 1940 in Bay Shore, New York","the son of a leader of Beth El Synagogue in Omaha, Nebraska",etc ...

The descriptivist takes the meaning of the name Saul Kripke to be that collection of descriptions and takes the referent of the name to be the thing that satisfies all or most of those descriptions. A simple descriptivist theory may further hold that the meaning of a sentence S that contains p is given by the collection of sentences produced by replacing each instance of p in S with one of the descriptions in D. So, the sentence such as "Saul Kripke stands next to a table" has the same meaning as the following collection of sentences: "The man who wrote Naming and Necessity stands next to a table","A person who was born on November 13, 1940 in Bay Shore, New York stands next to a table","The son of a leader of Beth El Synagogue in Omaha, Nebraska stands next to a table",etc ...

A type of simple descriptivism was originally formulated by Frege in reaction to problems that confronted the predominant theory of names of the 19th century by John Stuart Mill. Mill's theory suggests that the meaning of a proper name is simply its bearer in the external world (its direct referent, as we would say now). There are several significant problems with this proposal, however. First, it does not explain how and why names without bearers can still be meaningful even though they have no reference. Take the following two examples: "There is no Santa Claus" and "Santa Claus does not exist". According to Mill's theory, these sentences must be meaningless.

Frege set about to resolve this problem, among others, with his famous distinction between sense and reference. In the case of proper names, the sense (or Sinn) of a term consists in the (usually) definite description that speakers associate with it. Thus, the sense of the proper name Santa Claus may be something like “The benevolent, bearded elf that brings gifts to children at Christmas time.” However, a proper name can have more than one sense associated with it. The name Santa Claus could be associated with “The benevolent, bearded elf…” as well as with the description “The fat, old gentleman with the red cape…” In Frege, the relationship between sense and representation is one of determination: the references of names are determined by their senses as modes of presentation. If referents are objects in the external world, then senses are simply different ways of grasping the same object through different means. An object need not necessarily have a referent either in the external world or in the realm of abstract objects but it will always have a sense in the objective realm of thought for Frege.

The three lectures that form Naming and Necessity constitute an attack on descriptivist theory of names. He gives several examples purporting to render descriptivism implausible as a theory of how names get their references determined. Kripke argued that in order to use a name successfully to refer to something, you do not have to be acquainted with a uniquely identifying description of that thing. Rather, your use of the name need only be caused (in an appropriate way) by the naming of that thing. (For example, a speaker can talk about Phillie Sophik even if one only knows him as 'some poet'.) Moreover, we can successfully refer to individuals for whom the only identifying descriptions we have fail to refer as we believe them to. (Many speakers have no identifying beliefs about Christopher Columbus other than 'the first European in North America' or 'the first person to believe that the earth was round'. Both of these beliefs are incorrect. Nevertheless, when such a person says 'Christopher Columbus', we acknowledge that they are referring to Christopher Columbus, not to whatever individual satisfies one of those descriptions). Also we use names to speak hypothetically about what could have happened to a person and those statments surly don't satisfy in descriptions in our world, yet they are possible in another world.

As an alternative, Kripke outlined a causal theory of reference that avoids these difficulties, according to which a name refers to an object by virtue of a causal connection with the object as mediated through communities of people who have used the name. A name's referent is fixed by an original act of naming (also called a "dubbing" or, by Saul Kripke, an "initial baptism") and later uses of the name succeed in referring to the referent by being linked to that original act via a causal chain. Such a causal process might proceed as follows: the parents of a newborn baby name it, pointing to the child and saying "we'll call her 'Jane'." Henceforth everyone calls her 'Jane'. With that act, the parents give the girl her name. The assembled family and friends now know that 'Jane' is a name which refers to Jane. This is referred to as Jane's dubbing, naming, or initial baptism. However, not everyone who knows Jane and uses the name 'Jane' to refer to her was present at this naming. So how is it that when they use the name 'Jane', they are referring to Jane? The answer provided by causal theories is that there is a causal chain that passes from the original observers of Jane's naming to everyone else who uses her name. For example, maybe Jill was not at the naming, but Jill learns about Jane, and learns that her name is 'Jane', from Jane's mother, who was there. She then uses the name 'Jane' with the intention of referring to the child Jane's mother referred to. Jill can now use the name, and her use of it can in turn transmit the ability to refer to Jane to other speakers.

He points out that proper names, in contrast to most descriptions, are rigid designators. That is, a proper name refers to the named object regardless of any particular facts about the bearer, and in all possible worlds in which the object exists, while most descriptions designate different objects in different possible worlds. For example, Aristotle could have died at age two in a different possible world and so hasn't satisfied any of the descriptions we associate with his name, and yet it would seem wrong to deny that he was Aristotle. So, the link between the property of being a murderer and the person referred to is contingent (depends on the world) rather than necessary or essential.

Kripke argued identity is not a relation that holds between names. It is a relation that holds between an object and itself. So when someone accurately claims that two names refer to the same object, the claim is necessarily true, even though it may be known a posteriori (can be known only through empirical investigation). For example, the proposition that water is H2O (if it is true). According to Kripke, this statement is necessarily true (since water and H2O are the same thing, they are identical in every possible world, and truths of identity are logically necessary) and a posteriori (since it is known only through empirical investigation). Also it is analytic because analysis of H20 says that it is water. Kripke's controversial analysis of naming as contingent and a priori would best fit into Kant's epistemological framework by calling it "analytic a posteriori".

Another example is the sentence, "the evening star" (Hesperus) is "the morning star" (Phosphorus). 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.
(P4) Therefore, it is possible for knowledge obtained a posteriori to be necessary.
(P5) It is analytic because the predicate concept is contained in its subject concept.

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.

And also he provided a counter example to Quine's claim that the terms analyticity, synonymy, necessity are circularly definable, so have to be rejected. Because now A prioricity, analyticity, and necessity have since been more clearly separated from each other. Although some truths are both necessary and apriori, there are many examples of each that are not examples of the other. Thus, the relationship between aprioricity, necessity, and analyticity is not easy to discern. the a priori/a posteriori distinction is epistemological, the analytic/synthetic distinction is linguistic, and the necessary/contingent distinction is metaphysical.

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”.

Wittgenstein on Rules and Private Language

The obvious objection to rule following is that the addition function is not defined by a number of examples, but by a general rule or algorithm. But then the algorithm itself will contain terms that are susceptible to different and incompatible interpretations, and the skeptical problem simply resurfaces at a higher level. In short, rules for interpreting rules provide no help, because they themselves can be interpreted in different ways. Or, as Wittgenstein himself puts it, "any interpretation still hangs in the air along with what it interprets, and cannot give it any support. Interpretations by themselves do not determine meaning" (PI 198a).

Kripke, following David Hume, distinguishes between two types of solution to skeptical paradoxes. Straight solutions dissolve paradoxes by rejecting one (or more) of the premises that lead to them. Skeptical solutions accept the truth of the paradox, but argue that it does not undermine our ordinary beliefs and practices in the way it seems to. Kripke thinks that Wittgenstein endorses the skeptical paradox.

Kripke's skeptical solution is this: A language-user's following a rule correctly is not justified by any fact that obtains about the relationship between his candidate application of a rule in a particular case, and the putative rule itself (as for Hume the causal link between two events a and b is not determined by any particular fact obtaining between them taken in isolation), but rather the assertion that the rule is being followed is justified by the fact that the behaviors surrounding the candidate instance of rule-following (by the candidate rule-follower) meet the expectations of other language users. That the solution is not based on a fact about a particular instance of putative rule-following-- as it would be if it were based on some mental state of meaning, interpretation, or intention-- shows that this solution is skeptical in the sense Kripke specifies. He says that the work should not be read as an attempt to give an accurate statement of Wittgenstein's views, but rather as an account of Wittgenstein's argument "as it struck Kripke, as it presented a problem for him"

In contrast to the kind of solution offered by Kripke, John McDowell interprets Wittgenstein as correctly (by McDowell's lights) offering a "straight solution". McDowell argues that Wittgenstein does present the paradox (as Kripke argues), but he argues further that Wittgenstein rejects the paradox on the grounds that it assimilates understanding and interpretation. Meaning that in order to understand something, we must have an interpretation. That is, to understand what is meant by "plus," we must first have an interpretation of what "plus" means. This leads one to either skepticism - how do you know your interpretation is the correct interpretation?- or relativity whereby our understandings, and thus interpretations, are only so determined in so far as we have used them. McDowell writes further, in his interpretation of Wittgenstein, that to understand rule-following we should understand it as resulting from inculcation into a custom or practice. Thus, to understand addition, is simply to have been inculcated into a practice of adding.