Kripke opens his lecture series at Princeton by introducing the topics of naming and necessity, noting their wide-ranging implications for other philosophical problems such as the mind-body problem, though he is not sure if he will have time to discuss all implications.

Kripke suggests that we cannot say under what circumstances unicorns would have existed and that even discovering fossils matching the myth would not prove they existed. He defines “name” to mean proper name, distinguished from definite descriptions like “the man who corrupted Hadleyburg” (24), with “designator” as a cover term for both. He acknowledges Donnellan’s distinction between semantic reference and speaker’s reference but uses “referent” to mean the thing to which the designator refers.

Kripke presents John Stuart Mill’s view that names have denotation but not connotation, illustrated by “Dartmouth,” which could still name the town even if it no longer lay at the mouth of the Dart, meaning “river.” He contrasts this with the Frege-Russell theory that a proper name is a disguise for a definite description providing the name’s sense or meaning. The Frege-Russell view accounts for how reference is determined; why identity statements like “Hesperus is Phosphorus” (20), both terms for Venus, are informative; and how to make sense of questions of whether something exists. Despite these advantages, Kripke asserts that the view is false.

He introduces the modern cluster concept theory, associated with Ludwig Wittgenstein and John R. Searle, which holds that a name’s reference is determined by a family of descriptions rather than a single one, identifying a referent as the thing that meets enough of the descriptions. Kripke distinguishes two interpretations of description theories: theories of meaning (where the description gives a synonym) or of reference-fixing (where it picks out the referent without giving the meaning).

Kripke then undertakes a methodological clarification, distinguishing several categories. “A priori” is an epistemological concept, meaning the truth is knowable independently of experience. “Necessary” is a metaphysical concept, meaning that the truth could not have been otherwise. Kripke asserts that these are not synonymous. The Goldbach conjecture, that every even integer greater than two can be expressed as the sum of two prime numbers, if true, is necessarily true (since mathematical truths cannot be contingent), yet we cannot know it a priori. “Analytic” truths are true by virtue of meaning and are both necessary and a priori by stipulation. “Certainty” is another epistemological notion, meaning a truth can be known a priori without being certain.

Kripke challenges the view, famously associated with Willard Van Orman Quine, that whether a property is necessary depends on how an object is described. Against this, the ordinary intuition is clear: Richard Nixon might have lost the election, regardless of whether we describe him as “Nixon” or “the winner.” The distinction between necessary and accidental properties reflects common sense.

He asserts that possible worlds are not foreign countries requiring qualitative “criteria of transworld identity” (49). Possible worlds are not discovered through observation but are stipulated by descriptive conditions. We can stipulate that a counterfactual situation contains Nixon and ask what would have happened to him. Kripke criticizes philosopher David Lewis’s counterpart theory as an extreme version of this mistake. He acknowledges that “transworld identification” can be a real issue when we ask about the identity of complex objects in terms of their constituent parts, but even here, we can often refer directly to the object in question.

Kripke defines a rigid designator as a term that designates the same object in every possible world where that object exists. Proper names are rigid designators. While someone other than Nixon might have been president in 1970, no one other than Nixon could have been Nixon. This intuition makes transworld identification unproblematic for names. Kripke denies that his view commits him to “bare particulars”; he simply rejects that a particular is nothing but a bundle of qualities.

To illustrate the distinction between synonymy and reference-fixing, Kripke examines the standard meter in Paris. He rejects Wittgenstein’s claim that the meter stick is neither one meter long nor not one meter long, maintaining that it is one meter long. Even if “one meter” is defined as “the length of stick S at time t₀,” the statement “S is one meter long at t₀” is contingent, not necessary (63). This is because “one meter” rigidly designates a particular length, while “the length of S at t₀” does not rigidly designate (S might have had a different length under different conditions). The person who fixed the reference this way can know a priori that S is one meter long at t₀, yet this is a contingent truth, giving an example of the contingent a priori. The description fixes the reference without giving the meaning.

This distinction applies to names. A description can either give a name’s meaning (making the name non-rigid, like abbreviating a description) or merely fix its reference (making the name rigid). Kripke states that names are always rigid. Frege conflated two senses of “sense”: meaning and reference-fixer.

Returning to the cluster concept theory, Kripke cites Searle’s view that it is necessary that Aristotle has the disjunction of his commonly attributed properties. Kripke argues that this is false since most such properties are contingent. He breaks the cluster theory into six theses. Thesis 1 defines the cluster of properties the speaker associates with a name. Kripke argues that theses 2-6 are substantive but false: 2. the speaker believes some properties uniquely pick out the referent; 3. if most (or a weighted most) of these properties are satisfied by a unique object, that object is the referent; 4. if no unique object satisfies them, the name fails to refer; 5. the speaker knows a priori that if X exists, X has most of these properties; 6. if X exists, it is a necessary truth that X has most of these properties.

Kripke argues that the properties typically chosen for such clusters are often wrong. Wittgenstein’s example of Moses suggests that if the biblical stories are largely false, Moses did not exist. However, Kripke distinguishes between a legend about no one and a legend about a real person. Biblical scholars believe that Jonah existed even though they regard the stories about him as almost entirely false and note that his name may not have been “Jonah” by the common pronunciation. This shows that we can refer to a person even when most of our associated descriptions are mistaken.

Finally, Kripke introduces a non-circularity condition: The properties used to fix reference must not themselves presuppose the notion of a required reference. He criticizes philosopher William Kneale’s theory that “Socrates” means “[t]he individual called ‘Socrates’” as a blatant violation (68). This theory is circular since it requires that we must already know to whom “Socrates” refers. If this were the only content of a name, reference could never begin.