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In modal logic and the philosophy of language, a term is said to be a rigid designator when it picks out the same thing in all possible worlds in which that thing exists (and picks out nothing in those possible worlds in which it does not exist). Rigid designators are contrasted with non-rigid or flaccid designators, which may pick out different things in different possible worlds.

The notion of rigid designation was first introduced by Saul Kripke in the lectures that became Naming and Necessity , in the course of his argument against descriptivist theories of reference. At the time of Kripke's lectures, the dominant theories of reference in Analytic philosophy (associated with the theories of Frege and Russell) held that the meaning of sentences involving proper names could be analysed by substituting a contextually appropriate description for the name. Thus, for example, Russell 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 analysed as "The first Chancellor of the German Empire was a ruthless politician" (which in turn could be analysed into a series of more basic logical statements according to the method Russell introduced in his theory of definite descriptions). Against the Russellian analysis (and several attempted refinements of it), Kripke argued that such descriptions could not possibly mean the same thing as the name "Bismarck," because (Kripke argued) proper names such as "Bismarck" always designate rigidly, whereas descriptions such as "the first Chancellor of the German Empire" sometimes 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. But that is not to utter the contradictory sentence that it might have been the case that Bismarck died before he became Bismarck, or that someone else probably would have become Bismarck. 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.

1 Essentialism

In Naming and Necessity, Kripke argues that proper names and certain natural kind terms—including biological taxa and types of natural substances (most famously, "water" and "H₂O") designate rigidly. He argues for a form of scientific essentialism not unlike Aristotelian essentialism. Essential properties are common to an object in all possible worlds, and so they pick out the same objects in all possible worlds - they rigidly designate.

2 Causal-Historical Theory of Reference

Proper names rigidly designate for reasons that differ from natural kinds terms. The reason 'Johnny Depp' refers to one particular person in all possible worlds is because some person initially gave the name to him by saying something like "Let's call our baby 'Johnny Depp'". This is called the initial baptism. This usage of 'Johnny Depp' for referring to some particular baby got passed on from person-to-person in a giant causal and historical chain of events. That is why everybody calls Johnny Depp 'Johnny Depp'. Johnny's mother passed it onto her friends who passed it onto their friends who passed it onto their friends, and so on.