Rigid designators

In modal logic and the philosophy of language, a term is said to be a rigid designator or absolute substantial term when it designates (picks out, denotes, refers to) the same thing in all possible worlds in which that thing exists and does not designate anything else in those possible worlds in which that thing does not exist. A designator is persistently rigid if it designates the same thing in every possible world in which that thing exists and designates nothing in all other possible worlds. A designator is obstinately rigid if it designates the same thing in every possible world, period, whether or not that thing exists in that world. Rigid designators are contrasted with connotative terms, non-rigid or flaccid designators, which may designate different things in different possible worlds.

The Scholastic philosophers in the Middle Ages developed a theory of properties of terms in which different classifications of concepts feature prominently.

Concepts, and the terms that signify them, can be divided into absolute or connotative, according to the mode in which they signify. If they signify something absolutely, that is, after the manner of substance, they are absolute, for example rock, lion, man, whiteness, wisdom, tallness. If they signify something connotatively, that is, with reference to a subject of inherence, i.e., after the manner of accidents, they are connotative, for example, white, wise, tall.

Both connotative and absolute concepts can be used to signify accidents, but since connotative concepts signify with a reference to a subject of inherence, they can refer to object with different definitions and properties (i.e. with different essences). For example, large, as a connotative concept, can signify objects with many distinct essences: a man, a lion, a triangle can be large.

On the other hand, absolute concepts signify objects that have the same definitions and properties. For example, the concept of gold, as an absolute concept, can signify only objects with the same definitions and properties (i.e. with the same essence).

The notion of absolute concepts was then revived by Saul Kripke, with the name “rigid designation”, in the lectures that became Naming and Necessity, in the course of his argument against descriptivist theories of reference, building on the work of Ruth Barcan Marcus. At the time of Kripke's lectures, the dominant theory of reference in analytic philosophy (associated with the theories of Gottlob Frege and Bertrand Russell) was that the meaning of sentences involving proper names could be given by substituting a contextually appropriate description for the name. Russell, for example, famously held that someone who had never met Otto von Bismarck might know of him as the first Chancellor of the German Empire, and if so, his statement that (say) "Bismarck was a ruthless politician" should be understood to mean "The first Chancellor of the German Empire was a ruthless politician" (which could in turn be analysed into a series of more basic statements according to the method Russell introduced in his theory of definite descriptions). Kripke argued—against both the Russellian analysis and several attempted refinements of it—that such descriptions could not possibly mean the same thing as the name "Bismarck," on the grounds that proper names such as "Bismarck" always designate rigidly, whereas descriptions such as "the first Chancellor of the German Empire" do not. Thus, for example, it might have been the case that Bismarck died in infancy. If so, he would not have ever satisfied the description "the first Chancellor of the German Empire," and (indeed) someone else probably would have. It does not follow that the first Chancellor of the German Empire may not have been the first Chancellor of the German Empire—that is (at least according to its surface-structure) a contradiction. Kripke argues that the way that proper names work is that when we make statements about what might or might not have been true of Bismarck, we are talking about what might or might not have been true of that particular person in various situations, whereas when we make statements about what might or might not have been true of, say, the first Chancellor of the German Empire we could be talking about what might or might not have been true of whoever would have happened to fill that office in those situations.

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