“My view is that ‘Aristotle’ in (1) is rigid, but ‘the last great philosopher of antiquity’ in (2) is not. No hypothesis about scope conventions for modal contexts expresses this view […] it is a doctrine about the truth conditions, with respect to counterfactual situations, of (the propositions expressed by) all sentences, including simple sentences.”

Kripke refutes the objection that rigidity is merely an effect of giving names a wide scope in sentences containing modal operators. He counters that the distinction between rigid and nonrigid designators applies even to simple, non-modal sentences where scope conventions are irrelevant. This establishes rigidity as a fundamental semantic property of names concerning how they refer, not a syntactic feature of how they behave in complex sentences.

“The thirty-six possibilities, the one that is actual included, are (abstract) states of the dice, not complex physical entities. Nor should any school pupil receive high marks for the question ‘How do we know, in the state where die A is six and die B is five, whether it is die A or die B which is six? Don’t we need a “criterion of transstate identity”…?’”

Using an analogy from probability theory, Kripke demystifies the concept of “possible worlds” and critiques the problem of “transworld identification.” Just as one can stipulate that a specific die shows a six in a possible outcome, one can stipulate reference to a specific person in a counterfactual situation. This strategy argues that possible worlds are stipulated and that reference to individuals within them does not require a set of qualitative criteria for identification.

“The first topic in the pair of topics is naming. By a name here I will mean a proper name, i.e., the name of a person, a city, a country, etc. […] We will use the term ‘name’ so that it does not include definite descriptions of that sort, but only those things which in ordinary language would be called ‘proper names.’”

At the outset of the lectures, Kripke establishes a crucial terminological distinction that structures his argument. By separating “proper names” from “definite descriptions,” he frames his project as a direct challenge to the Frege-Russell tradition, which treats names as abbreviated descriptions. This foundational move allows him to argue that these two types of designators function in fundamentally different ways.

“The terms ‘necessary’ and ‘a priori,’ then, as applied to statements, are not obvious synonyms. […] I will argue below that in fact they are not even coextensive—that necessary a posteriori truths, and probably contingent a priori truths, both exist.”

This passage makes a distinction between metaphysics and epistemology, separating the concept of “necessity” (what could not be otherwise) from the concept of the “a priori” (what is knowable independent of experience). Kripke argues that philosophers have erroneously treated these distinct concepts as interchangeable. The second sentence serves as a thesis statement, forecasting his claim that these categories are not coextensive and setting up his later arguments for truths that are both necessary and discoverable only through experience (a posteriori).

“If someone thinks that the notion of a necessary or contingent property […] is a philosopher’s notion with no intuitive content, he is wrong. Of course, some philosophers think that something’s having intuitive content is very inconclusive evidence in favor of it. I think it is very heavy evidence in favor of anything, myself.”

Kripke defends essentialism, or the view that objects have necessary properties, by appealing to intuition and ordinary language. He argues that the idea of an individual having a property contingently is a natural thought, not an obscure philosophical doctrine. This statement of methodological principle reveals his reliance on common linguistic practice as primary evidence for philosophical claims, a strategy he employs to counter more abstract, theoretical views.

“Let’s call something a rigid designator if in every possible world it designates the same object, a nonrigid or accidental designator if that is not the case. […] One of the intuitive theses I will maintain in these talks is that names are rigid designators.”

Here, Kripke provides the explicit definition for the central technical concept of his lectures. By coining the term “rigid designator,” he gives a name to the semantic property he has been illustrating through examples. This definition establishes his core thesis that proper names, unlike definite descriptions, function to pick out the very same object in any counterfactual situation in which that object exists.

“Even if this is the only standard of length that he uses, there is an intuitive difference between the phrase ‘one meter’ and the phrase ‘the length of S at t₀.’ The first phrase is meant to designate rigidly a certain length in all possible worlds […] On the other hand ‘the length of S at t₀’ does not designate anything rigidly.”

Using the example of the standard meter stick (S), Kripke illustrates the distinction between fixing a reference and giving a synonym. The description “the length of S at t₀” is used to fix the reference of the term “one meter,” but it is not its meaning. Because “one meter” is a rigid designator and “the length of S” is not, one can assert the contingent truth that the stick, S, might not have been one meter long, establishing a model for contingent a priori truths.

“For any successful theory, the account must not be circular. The properties which are used in the vote must not themselves involve the notion of reference in a way that it is ultimately impossible to eliminate.”

In setting up his refutation of the cluster-concept theory of names, Kripke articulates a key condition for any adequate theory of reference. The non-circularity condition holds that a theory cannot explain how a name refers by using a description that itself presupposes reference. He uses this principle to dismiss theories where “Socrates” means “the man called ‘Socrates’” as begging the question, clearing the way for his own causal-historical account.

“Hitler might have spent all his days in quiet in Linz. In that case we would not say that then this man would not have been Hitler, for we use the name ‘Hitler’ just as the name of that man, even in describing other possible worlds.”

This thought experiment illustrates the concept of a rigid designator. Kripke argues that the name “Hitler” picks out a specific individual across all possible scenarios, even ones where that individual lacks the properties we commonly associate with him. He uses this counterfactual to attack the descriptivist thesis that a name’s meaning is equivalent to a cluster of descriptions, showing that a name’s referential function is distinct from the contingent properties of its bearer.

“When I say that a designator is rigid, and designates the same thing in all possible worlds, I mean that, as used in our language, it stands for that thing, when we talk about counterfactual situations. I don’t mean, of course, that there mightn’t be counterfactual situations in which in the other possible worlds people actually spoke a different language.”

Here, Kripke offers a clarification of his central technical term, the “rigid designator,” to preempt a common misunderstanding. He specifies that rigidity is a semantic property of terms as they are used in our actual language to describe alternative possibilities. The distinction between using our language to describe a counterfactual world and the language spoken within that world is a key methodological point.

“Consider Richard Feynman, to whom many of us are able to refer. […] However, the man in the street, not possessing these abilities, may still use the name ‘Feynman.’ When asked he will say: well he’s a physicist or something. He may not think that this picks out anyone uniquely. I still think he uses the name ‘Feynman’ as a name for Feynman.”

This passage uses the example of a real public figure to mount an empirical attack on the descriptivist thesis that a speaker must possess a uniquely identifying description to refer. Kripke appeals to the common linguistic practice of referring to individuals about whom one has only vague or non-unique information. The argument demonstrates that reference can be successful even when the speaker’s associated beliefs are insufficient to satisfy the conditions of the cluster-description theory.

“Suppose that Gödel was not in fact the author of this theorem. A man named ‘Schmidt’ […] actually did the work in question. His friend Gödel somehow got hold of the manuscript and it was thereafter attributed to Gödel. On the view in question, then, when our ordinary man uses the name ‘Gödel,’ he really means to refer to Schmidt […] But it seems to me that we are not. We simply are not.”

This thought experiment is a central argument against the description theory of names. Kripke constructs a fictional scenario where the primary description associated with “Gödel” is satisfied by someone else entirely. The intuitive force of the example rests on the shared linguistic intuition that the name “Gödel” would still refer to Gödel, not Schmidt, demonstrating that reference tracks a historical person rather than whoever happens to fit a description.

“Columbus was the first man to realize that the earth was round. He was also the first European to land in the western hemisphere. Probably none of these things are true, and therefore, when people use the term ‘Columbus’ they really refer to some Greek if they use the roundness of the earth, or to some Norseman, perhaps, if they use the ‘discovery of America.’ But they don’t.”

Following the fictional Gödel-Schmidt case, this quote applies the same logic to a real historical figure, showing that widespread misinformation does not redirect the reference of a name. By listing common but false beliefs about Columbus, Kripke argues that the descriptivist theory would wrongly predict that speakers are referring to other historical individuals. This example reinforces the idea that reference is determined by a causal-historical link, not by the accuracy of the speaker’s beliefs, a key part of the theme of Rigid Designation as an Alternative to Descriptivism.

“Someone, let’s say, a baby, is born; his parents call him by a certain name. […] Through various sorts of talk the name is spread from link to link as if by a chain. A speaker who is on the far end of this chain […] may be referring to Richard Feynman even though he can’t remember from whom he first heard of Feynman or from whom he ever heard of Feynman.”

After dismantling the descriptivist view, Kripke introduces his alternative account, the “causal-historical picture” of reference. The metaphor of a “chain” illustrates how a name’s reference is preserved and transmitted through a community of speakers, originating from an initial act of “baptism.” This model contrasts sharply with the descriptivist picture by grounding reference in a social and historical practice.

“A rough statement of a theory might be the following: An initial ‘baptism’ takes place. Here the object may be named by ostension, or the reference of the name may be fixed by a description. When the name is ‘passed from link to link,’ the receiver of the name must, I think, intend when he learns it to use it with the same reference as the man from whom he heard it.”

This passage offers a concise, provisional formulation of the causal-historical theory of reference. It breaks the process down into two key components: an initial act of naming (a baptism) and a subsequent chain of transmission. The condition for the transmission is the speaker’s intention to preserve the reference, which introduces an element of psychological continuity into the otherwise external causal chain.

“We may tag the planet Venus, some fine evening, with the proper name ‘Hesperus.’ We may tag the same planet again, some day before sunrise, with the proper name ‘Phosphorus.’ When we discover that we have tagged the same planet twice our discovery is empirical. And not because the proper names were descriptions.”

Kripke uses the classic Hesperus/Phosphorus example to frame the puzzle of identity statements. The example highlights the tension between the empirical nature of the discovery that two names refer to the same object and the philosophical intuition that identity is a necessary relation. This establishes the problem that Kripke’s concept of necessary a posteriori truths is designed to solve, setting the stage for his argument that the statement “Hesperus is Phosphorus,” though discovered empirically, expresses a necessary truth.

“[I]n a counterfactual world in which ‘Hesperus’ and ‘Phosphorus’ were not used in the way that we use them, as names of this planet, but as names of some other objects, one could have had qualitatively identical evidence and concluded that ‘Hesperus’ and ‘Phosphorus’ named two different objects. But we, using the names as we do right now, can say in advance, that if Hesperus and Phosphorus are one and the same, then in no other possible world can they be different.”

Kripke resolves the apparent paradox of contingent identity by distinguishing between epistemic and metaphysical possibility. He explains that the feeling of contingency arises because we can imagine a qualitatively identical evidential situation leading to a different discovery. This imagined situation, however, is not one in which Hesperus is not Phosphorus but one where the names “Hesperus” and “Phosphorus” refer to different things, thus upholding the theme of Identity Truths as Necessary A Posteriori.

“[L]et’s suppose we gave him his account. Suppose identity were a relation in English between the names. I shall introduce an artificial relation called ‘schmidentity’ (not a word of English) which I now stipulate to hold only between an object and itself.”

In this passage, Kripke invents a new term, “schmidentity,” to perform a reductio ad absurdum on the theory that identity is a relation between names. By stipulating that “schmidentity” holds between an object and itself, he shows that all the philosophical puzzles thought to motivate the name-relation theory would re-emerge for this new relation. The argument’s structure forces the conclusion that identity should be understood as a relation an object has to itself.

“How could a person originating from different parents, from a totally different sperm and egg, be this very woman? […] It seems to me that anything coming from a different origin would not be this object.”

Using a thought experiment centered on Queen Elizabeth II, this quote articulates the theme of Essence and the Necessity of Origin. Kripke distinguishes between an individual’s contingent properties and essential properties, like biological parentage. He argues through an appeal to intuition that an individual’s origin is a necessary condition for their identity; a person from a different sperm and egg would be a different person, not the same person with a different history.

“Suppose there were an optical illusion which made the substance appear to be yellow; but, in fact, once the peculiar properties of the atmosphere were removed, we would see that it is actually blue. […] Would there on this basis be an announcement in the newspapers: ‘It has turned out that there is no gold. Gold does not exist.’?”

This quote presents a hypothetical scenario to challenge the descriptivist theory that a word’s meaning is a set of associated properties. Kripke argues that “gold” is a rigid designator for a specific substance, not a shorthand for “the yellow metal.” The thought experiment demonstrates that if the identifying properties of gold were discovered to be illusory, one would conclude that gold has a different color, not that it does not exist, thereby separating the term’s reference from the contingent properties used to identify it.

“Even though we don’t know the internal structure of tigers, we suppose—and let us suppose that we are right—that tigers form a certain species or natural kind. We then can imagine that there should be a creature which, though having all the external appearance of tigers, differs from them internally enough that we should say that it is not the same kind of thing.”

Kripke extends his theory of rigid designation from proper names to natural kind terms like “tiger.” He argues that such terms refer to a species with a presumed, underlying essential nature, independent of our knowledge of that nature or of its superficial identifying marks. This introduces the idea of a “division of linguistic labor,” where a term’s reference is fixed to a scientific kind, even before that kind’s essence is fully discovered.

“So if this consideration is right, it tends to show that such statements representing scientific discoveries about what this stuff is are not contingent truths but necessary truths in the strictest possible sense. […] Given that gold is this element, any other substance, even though it looks like gold […] would not be gold.”

This passage states a central thesis of the book, exemplifying the theme of Identity Truths as Necessary A Posteriori. Kripke concludes that once science discovers the essential nature of a substance, such as gold’s atomic number, that identity holds necessarily across all possible worlds. This recasts scientific discoveries as the uncovering of metaphysical necessities.

“What characteristically goes on in these cases of, let’s say, ‘heat is molecular motion’? There is a certain referent which we have fixed, for the real world and for all possible worlds, by a contingent property of it, namely the property that it’s able to produce such and such sensations in us.”

This quote articulates the core mechanism that explains the apparent contingency of necessary a posteriori truths. Kripke draws a distinction between a rigid designator (“heat”) and the contingent property used to fix its reference (its effect on our senses). The statement “[H]eat is molecular motion” is necessary because both terms rigidly designate the same phenomenon, while the illusion of contingency arises from the fact that we could imagine that same sensation being caused by something else.