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From Lecture I

Kripke is concerned with proper names. He will use the term "designator" for both proper names and definite descriptions, and call proper names "names" but never call definite descriptions "names."

The referent of a description is the thing which satisfies (makes true) that description.

Kripke considers the "cluster theory." We'll discuss this theory more when we read Searle -- but the idea is simple, and Kripke cites Wittgenstein as his source. Instead of a claiming a name is a single description, we'll claim a name is a cluster of descriptions.

Kripke points out there is an ambiguity here: the cluster theory might be that the name "Abe Lincoln" means the man who such and such and such.... Or the theory might instead be that the name "Abe Lincoln" has its reference determined by the description the man who such and such and such....

It is not clear whether the second interpretation solves the puzzles of negative existentials or names without a referent.

Kripke will distinguish a priori from necessary. He will make a priori refer to what is given prior to experience for some particular person. Thus, For example, a mathematical claim that has not yet been proved or disproved is either necessarily true or necessarily false, but it is not a priori, since no one knows yet how to check.

A rigid designator is a name or phrase that designates the same thing in every world. Note that the object need not exist in every world. It is not necessary that Nixon existed, but (Kripke claims) the name "Nixon" is a rigid designator. Thus, there are some worlds where the rigid designator does not designate anything. On the other hand, a rigid designator for a necessary object is to be called a "strongly rigid designator."

Claim: "Nixon" is a rigid designator. But "U. S. President in 1970" is not -- someone else might have won that election. So, a rigid designator is not the same as a description.

Note: some complain that you cannot determine what a thing is in every world. How do you identify Nixon in every possible world? But Kripke says that question is backwards. You must first have a rigid designator before you can ask the question. When we ask, "could Nixon have lost the election," Kripke claims, we implicitly assume that "Nixon" is a rigid designator. (I worry that though this is plausible, it does hide a certain problem: surely at some point claims become incoherent because they are descriptions that are unreasonable. Like, "Nixon could have been a kangaroo." Could he have been? Wouldn't he at some point stop being enough like Nixon that we would call him "Nixon"? Kripke can answer this concern with a certain theory of possibility, but it is not trivial and is glossed in this work.)

From Lecture II

Kripke puts a sophisticated/cluster version of Russellian names as stating:

1. There are a cluster of properties for each name that the speaker believes are true of the thing designated by the name.
2. The speaker believes some of the properties pick out one thing.
3. Anything having most of the cluster properties is the referent of the name.
4. If there is no thing with the properties, then the name does not refer.
5. The speaker knows a priori that if the thing named exists then it has most of those properties.
6. It is necessary that the thing, if it exists, it has most of the cluster properties.

He adds also that the properties cannot be circular and refer to reference (e.g., "Socrates is the proper referent of 'Socrates'").

Kripke rejects most of these theses!

Thesis #1 he interprets as a definition, and so not something you can disprove. Rather, one will offer a different definition that may be better.

Thesis #2: what does "Cicero" mean to most people? Kripke claims that to most people it just means, famous Roman orator. And, of course, these people know that "famous Roman orator" is not a unique description! Or, say, what do "Feynman" or "Fermi" mean to most people? Famous physicists. Of course, we know that is not a unique description!

Thesis #3: suppose conditions of thesis two were met. Suppose someone can state Godel's incompleteness theorem, and says, "'Godel' means the man who discovered the incompleteness theorem. Now, isn't it possible that we could read in the newspaper that someone else actually wrote the incompleteness theorem, and Godel stole it and published it under his own name? If that's possible, we would say "Godel did not discover the incompleteness theorem!" But that would be incoherent if we take it to mean "The man who discovered the incompleteness theorem did not discover the incompleteness theorem."

Note also that people often profess false descriptions. They say that Einstein was the inventor of the atomic bomb, or that Columbus was the first man to think that the Earth was round, or that Newton discovered gravity.

Thesis #4: isn't it possible that there was a Jonah, but he was not swallowed by a whale? Then the description fails but the thing refered to does not fail to exist.

Thesis #5: when the conditions described in theses 2-4 are satisfied by accident, it still does not follow that I know these things a priori. I cannot be certain about these things, such as that Godel wrote the incompleteness theorem.

Kripke rejects #6 because it could have been, for example, that Aristotle was not the tutor of Alexander, and lacked any other likely candidate for an identifying property.

Kripke's Theory

Kripke proposes a causal chain linking the naming event and the thing named, down to all causally related uses of the name.

A name is given in a naming or baptism. There is a causal chain linking from that point on all the people who use that name to the initial naming ceremony. The referent of this name is now the thing baptized (metaphorically or literally) with this name and which has a causal chain from that naming ceremony down to this instance of the use.

Kripke recognizes that there are some problems with this theory. One is that maybe "Santa Claus" has a causal chain linking back to a particular man -- but that's perhaps not at all what children mean to refer to when they use the term.