Rigidity and Necessity

Rigidity and Necessity

The idea of rigid designation was one of Kripke’s best ideas in Naming and Necessity, but he didn’t explore it in much depth. I will rectify that omission, putting rigidity in its proper place. It will turn out to be both more familiar and less well understood than we have been led to believe. The first point to be made is that rigidity is not really a property of words per se; it is a property of meanings—or better concepts. There could be rigid designation in thought independently of language, and in language the property is derivative from concepts. For, as we all know, words qua sounds and marks are only contingently connected to their meaning and reference, i.e., they are arbitrary signs. As Kripke is well aware, a word is rigid only relative to an interpretation of it—relative to a language (a term is “rigid-in-L”). It is really the sense that is rigid not the sign itself. There is no necessary connection between the syntactic or phonetic features of the term and its reference in a language; the connection obtains at the semantic level. No problem—but useful to bear in mind. A more substantial point is that rigidity is a type of necessity: it simply means that the designator necessarily designates its actual reference—in all possible worlds it designates the same object. A flexible (or flaccid) designator contingently designates its actual reference—in some possible worlds it designates other objects (e.g., “the teacher of Aristotle”). I don’t know why Kripke chose to use the word “rigid” in this connection, and he doesn’t say, but he could have left that word alone and stuck to “necessary”. It gives the impression that some other notion is being invoked, which is quickly belied by his actual use of the term “rigid” (ditto for “flexible”). We can simply define “rigid designation” as “necessary designation”—designating (denoting) the same object in all worlds (in which it exists). Again, no sweat, we just incorporate this point into our understanding.  It’s odd that Kripke didn’t make the point explicit, but the new term is certainly catchy; we would be living is a poorer possible world if it had never been invented. So, I will persist with it. We could equally have spoken of an invariable designator or a hard designator–or firm or fixed or stiff or inelastic or inflexible or unbending or locked-in; we would have meant that it couldn’t be otherwise, i.e., it is necessary.

Now we come to a less terminological point, indeed a metaphysical point. This is that rigid designation is a metaphysically necessary relation—a type of metaphysical necessity like other metaphysical necessities. It belongs to a family of modal theses. Other members of the family include: identity, origin, composition, instantiation, causation, succession (of numbers), and spatial and temporal relations. Thus: the identity of Hesperus with Phosphorus is a necessary relation; queen Elizabeth II being born of these particular parents is a necessary relation; this table being made of a particular piece of wood is a necessary relation; a cat instantiating the natural kind CAT is a necessary relation; 3 being the successor of 2 is a necessary relation; this event being caused by that event is a necessary relation; this region of space being next to this other region is a necessary relation; this moment in time following the prior moment is a necessary relation. And the name “Aristotle” (in the English language) designating a particular polymathic ancient Greek philosopher is a necessary relation (it designates Aristotle in all worlds, never Diogenes). This whole happy family of rigid (necessary) relations has name designation as one of its members (but not typical definite description designation). The name is invariably (necessarily) attached to a specific object in the way Elizabeth II is invariably (necessarily) attached to her actual parents (a couple of stiff Germans or some such). Or: the mental representation underlying the use of the name is non-contingently bound to its actual referent—unlike, say, “the inventor of bifocals”. That is the modal metaphysics of names (as understood by contemporary disciples of John Stuart Mill anyway). And just as anti-essentialists will question the list offered above, so description theorists of names will question Kripke’s claim about names. They might even reject the whole modal metaphysics being proposed, sternly insisting that nothing is metaphysically necessary. The point is that rigidity is of a piece with other claims of metaphysical necessity. Kripke could have cited the rigidity of names as another example of de re necessity along with identity, origin, composition, and natural kind. Why didn’t he? I don’t know; he seems not to have recognized the affinity between rigidity and other de re necessities. He didn’t see that semantic relations are a special case of modal facts (necessary or contingent). He could likewise have contended that the semantic relation between descriptions and their referents is contingent (non-rigid), like the relation between Elizabeth II and the palace in which she was born. It’s all a bunch of modal metaphysics, love it or hate it.

The next point that needs badly to be made (it’s aching to be made) is that rigidity has nothing essentially to do with names; it is a general feature of natural languages (and conceptual schemes).[1] First, it applies to (some) definite descriptions (“the actual inventor of bifocals”, “the successor of 2”); so, it is not the same property as what is called “direct reference” or “Millianism”. Nor is it confined to singular terms: predicates, too, rigidly refer to the properties or attributes they “express”—in all possible worlds “red” refers to redness (never to blueness). Logical connectives rigidly designate (mean, express) particular truth functions: “and” refers to conjunction in all worlds, never to disjunction—that is its contribution to truth conditions in all worlds. The concept of conjunction is inextricably linked to a particular truth function; it can’t be pulled apart from this function and used flexibly to refer to other truth functions in the manner of flexible definite descriptions. Quantifiers likewise rigidly designate specific second-level functions; they can’t vary their reference across other such functions—as if “all” could refer to the existential quantifier function in some possible worlds. We can even say that a necessarily true sentence rigidly designates its actual truth-value, since it has no other truth-value in any possible world. Rigidity (the de jure kind) is thus the rule not the exception; names are by no means uniquelyrigid. Language is generally rigid in its referential propensities. Senses are generally tied inelastically to their references—firm, fixed, invariable. There is a necessary relation between the two semantic levels. What else would you expect? Why would all aboutness in thought and language depend on knowledge of contingent properties? Haven’t we got enough to think about? Rigidity is predictable and banal not remarkable and exotic. Rigidity in language is as commonplace as solidity in the physical world—or, we might say, physical rigidity (most physical objects are rigid).

Kripke is rightly celebrated for distinguishing metaphysical from epistemic necessity, and for clarifying the distinction. He is particularly good on articulating what epistemic necessity amounts to: the impossibility of an identical epistemic situation correlated with a different fact. Most things turn out to be epistemically contingent—anything that is not certain, basically. “I exist” is epistemically necessary, but not “I am in Miami”. Strange, then, that he says nothing about epistemic rigidity: is it epistemically necessary that “Aristotle” designates Aristotle (that guy)—is this a cast-iron certainty? No, because I might be a brain in a vat and designate nobody by this name; and no, because I might have made a mistake about its reference—maybe the name really refers to Aristotle’s assistant and then got mistakenly applied to the great philosopher. If you ask me who “Aristotle” names, I will say the great Greek philosopher who wrote such and such books, but in fact it refers to his bookless assistant. It might turn out that many names I use refer to people other than the people I think they refer to—I am fallible that way. I don’t always know who my names refer to; skepticism applies. Yet my names do refer metaphysically rigidly—just not epistemically. I can be wrong about whether a table is made of wood and yet it necessarily is (if it is); and I can be wrong about whether a name refers to the person I think it does, though it necessarily does (if it does). So, names are epistemically non-rigid, i.e., it could turn out that they have a different bearer from the one I think they have. This is exactly the same as other metaphysically necessities for which metaphysical necessity does not imply epistemic necessity. The only way to inject epistemic necessity into a name is by stipulating that it refers to oneself: I say “Let the name ‘Colin McGinn’ refer to the same person as ‘I’ refers to when I say it”; then it will be certain that “Colin McGinn” designates me, since that is guaranteed by my knowledge that I am myself, about which I cannot be wrong.

Returning to metaphysical rigidity, we can observe that it does raise metaphysical questions. First, it brings up the issue of metaphysical necessity in general: we can only make sense of rigid reference if we can make sense of metaphysical necessity in general (is this why Kripke gave it another name?). There is the vexing question of how we know that names rigidly designate their bearers, given that necessity is not an empirical property of things—like the necessity of origin or kind. We just have a modal intuition to this effect; so, the epistemology of modality is an issue. Second, there is something peculiar about the necessary link between language and the world: how do meanings hook up necessarily with objects?  How is what is in the mind necessarily conjoined with something existing outside my mind? How does meaning entail reality?[2] The sense of “Aristotle” ensures that in all worlds Aristotle is denoted, but how does it do that? Is it because sense and reference are identical (as Mill maintained) or is the sense somehow glued to the reference? Necessary relations are already puzzling, but the puzzle intensifies if it crosses ontological categories: the name in my head somehow contrives to take the same reference in every possible world—by what magical power does it do that? Rigid designation may be common and banal, but that doesn’t mean it isn’t philosophically puzzling. Call this the “rigidity puzzle”: Kripke could have written a paper entitled “A Puzzle About Rigidity”. What is the meaning of a name such that rigid designation holds of it? How can we avoid collapsing sense into reference if rigidity holds? Not easy questions.[3]

[1] I discuss this more fully in my old paper “Rigid Designation and Semantic Value”, published in Philosophical Quarterly (1982).

[2] Here we see the concerns of Kripke’s Wittgenstein on Rules and Private Language intersecting with the doctrines of Naming and Necessity: what would the semantic skeptic say about the concept of rigid designation? What kind of fact is that? How does “+” rigidly mean addition?

[3] In Naming and Necessity Kripke manages to make the whole subject seem commonsensical and straightforward, but it raises thorny philosophical questions. I have always wished he would have gone back to that seminal text, especially with respect to metaphysical necessity. Did he really have nothing more to say about it? I discussed it in “Modal Reality” (1981), and David Lewis made a living out of it, but Kripke was cryptically silent on the subject.