rigid designation

Definition and Origin

Rigid designation is a technical term in contemporary analytic philosophy of language, introduced and made prominent by Saul Kripke in his lectures published as Naming and Necessity (1972/1980). Kripke sought to explain how words, especially proper names and natural kind terms, refer to objects and kinds not only in the actual world but across possible worlds.

A rigid designator is, in Kripke’s canonical formulation, an expression that designates the same object in every possible world in which that object exists, and designates nothing else in worlds in which that object does not exist. Thus, “Aristotle” (as the name of the historical individual) rigidly designates that very person in all worlds where he exists; it does not pick out any other individual in any counterfactual scenario.

By contrast, Kripke argued, many traditional descriptions are not rigid. The description “the teacher of Alexander the Great” might refer to Aristotle in the actual world but could refer to another person—or to no one—under different counterfactual suppositions.

Kripke’s term “rigid designation” emerged against the backdrop of earlier descriptivist theories of names associated with Frege and Russell, which treated names as semantically equivalent to definite descriptions. Kripke’s account aimed to capture the intuition that names and certain kind terms hold their reference fixed across modal contexts independently of descriptive information speakers associate with them.

Rigid vs Non-Rigid Designators

The distinction between rigid and non-rigid (sometimes called “flaccid”) designators plays a central role in modal semantics.

• Rigid designators:

  • Proper names such as “Aristotle,” “Marie Curie,” or “Barack Obama” are standard examples.
  • Many philosophers, following Kripke, also treat natural kind terms like “water,” “gold,” or “tiger” as rigid, assuming they refer to underlying essences or microstructural kinds across possible worlds. For instance, if water is in fact H₂O, then “water” rigidly designates H₂O in every possible world, even in a world where most watery-looking stuff is another compound (e.g., XYZ).
  • Some indexicals and demonstratives (“I,” “here,” “this”) are considered rigid relative to a context, especially in the work of David Kaplan. Once the context fixes that “I” refers to a particular speaker, it refers to that individual in all worlds considered from that context.

• Non-rigid (flaccid) designators:

  • Definite descriptions such as “the president of the United States in 2020” or “the inventor of bifocals” typically vary their reference across possible worlds. In one world, the president in 2020 is one person; in another, it could be someone else.
  • These expressions are often called designators of whoever or whatever fits a certain description in each world, rather than terms that follow a single individual or kind across worlds.

Kripke also introduced refinements:

• Strongly rigid designators designate the same individual in all possible worlds, including those in which the individual does not exist (where they then designate “nothing”). Proper names are usually treated as strongly rigid.
• Weakly rigid designators designate the same individual in all worlds in which that individual exists, but may not have a determinate non-referring status in worlds where the individual does not exist. These refinements are sometimes used to clarify edge cases in modal reasoning.

The rigid/non-rigid contrast helps explain the modal behavior of identity statements. For example, Kripke contended that if “Hesperus” and “Phosphorus” both rigidly designate Venus, then the identity statement “Hesperus is Phosphorus” is necessarily true if true at all, even though it was discovered empirically and is not knowable a priori.

Philosophical Significance and Debates

1. Against descriptivism about names

Kripke used rigid designation to challenge descriptivist theories of proper names, which had claimed that a name is equivalent in meaning to some associated description (e.g., “Aristotle” = “the greatest student of Plato and teacher of Alexander”). If this were correct, then names, like descriptions, would be non-rigid; their reference would shift with the truth of the associated description in different possible worlds.

Kripke argued instead that names are rigid designators fixed by an initial “baptism” and preserved through a causal-historical chain of communication. The descriptive information speakers associate with a name may help them identify its bearer but does not constitute the name’s semantic content. This distinction between semantic reference and associated descriptions became a cornerstone of later theories of reference.

2. Necessary a posteriori and contingent a priori

Rigid designation underpins Kripke’s celebrated distinction between:

• Necessary a posteriori truths, such as “Water is H₂O” or “Hesperus is Phosphorus.” Given rigidity of both sides of the identity, such statements, if true, are true in all possible worlds, yet they are known only through empirical investigation, not a priori.
• Contingent a priori truths, like certain stipulative identifications (e.g., fixing a meter stick as a standard of length). These may be known a priori in virtue of stipulation, while their truth remains contingent.

Rigid designation thus separates modal status (necessary/contingent) from epistemic status (a priori/a posteriori), challenging earlier assumptions that identified necessity with a priority.

3. Natural kinds and essentialism

Applied to natural kinds, rigidity has fueled debates about essentialism. If “water” rigidly designates H₂O and not just “the clear, drinkable liquid in rivers and lakes,” then the essence of water is its microstructural composition. A liquid that is not H₂O, even if indistinguishable in ordinary experience, would not be water but a different substance.

Proponents argue this supports a robust metaphysical picture where objects and kinds have essential properties that determine their identity across possible worlds. Critics question whether such essences are metaphysically required or whether rigidity can be explained in more deflationary or pragmatic terms.

4. Indexicals, demonstratives, and two-dimensional semantics

Later work, particularly by David Kaplan, extended the notion of rigidity to context-sensitive expressions like “I,” “here,” and “now.” Once the context of utterance is fixed, these expressions can behave rigidly across modal space. At the same time, their context dependence motivated more complex semantic frameworks.

In two-dimensional semantics (associated with thinkers such as Frank Jackson and David Chalmers), a distinction is drawn between:

• A primary intension (roughly, how a term’s reference is fixed given a scenario thought of as actual), and
• A secondary intension (how it tracks the same object or kind across counterfactual worlds once the actual reference is fixed).

On this view, rigidity is primarily a feature of the secondary intension: once “water” is fixed in the actual world as H₂O, it designates H₂O in all counterfactual worlds considered as counterfactuals, even though its primary intension might pick out different stuff in different scenarios considered as actual.

5. Criticisms and alternative perspectives

Critics of rigid designation raise several concerns:

• Some argue that the intuitive rigidity of names can be captured by more sophisticated descriptivist or information-theoretic accounts, without positing a separate metaphysical notion of essences.
• Others question the reliance on possible-world semantics, suggesting that talk of the “same object in different worlds” is metaphorical or dispensable.
• There are also debates about whether all names and natural kind terms are rigid in the same way, and whether the rigid/non-rigid distinction is sharp or admits grey areas.

Despite these controversies, rigid designation remains a standard tool in analytic philosophy for analyzing reference, modal discourse, and identity. It continues to inform contemporary work in metaphysics, philosophy of language, and the philosophy of mind, especially in discussions of physicalism, mind–body identity, and the semantics of thought and talk about possibility.