I would suggest you read all of Lecture II for this meeting, but we will focus on pp. 71-90. You should read Lecture III at some point. We will not be discussing it in class, however.
Recall that the cluster theory consists of six theses:
- The "cluster" that a speaker S associates with a name 'N' is the family of properties φ such that S believes 'φ(N)'.
- One of the properties, or some conjointly, are believed by S to pick out some individual uniquely.
- If most, or a weighted most, of the φ's are satisfied by one unique object y, then y is the referent of 'N'.
- If the vote yields no unique object, 'N' does not refer.
- The statement, 'If N exists, then N has most of the φs' is known a priori by the speaker.
- The statement, 'If N exists, then N has most of the φs' expresses a necessary truth (in S's language).
Thesis (6) is part of the theory only if one thinks that the cluster "gives the meaning" of the name.
Kripke begins Lecture II by re-emphasizing the importance of the additional condition, (C), that specifies that the account must not be circular. He then summarizes the arguments given against thesis (6) in the first lecture, remarking that it seems to be contingent that Aristotle has any of the properties commonly attributed to him. This is clearly too strong, since being human is such a property, and Kripke himself regards this as an essential property. (This is not argued until Lecture III.) But this does not really matter: If thesis (6) is to be true, then it has to be necessary that Aristotle enough properties to individuate him uniquely, and properties like being human are not likely to do that.
With thesis (6) disposed of, then, Kripke turns to the remaining theses, which constitute the cluster theory of reference-fixing. And Kripke allows that, for some names (Neptune, Jack the Ripper, St Anne), it may be a good account. But he claims that it does not give a good account of how reference is fixed for most names.
Kripke gives two main arguments against the cluster theory. So far as I know, there are no standard names for these, but I call them the argument from ignorance and the argument from error. (Collectively, these are sometimes called the epistemological arguments, to distinguish them from the modal arguments given in Lecture I.)
In the argument from ignorance (pp. 81-2), Kripke claims that people can refer to an object even if they do not have enough information about that object to individuate it. Kripke uses the example of "Richard Feynmann", noting that many people who understand this name know little more about Feynmann than that he is a physicist, and do not know enough about him to distinguish him from many other physicists. And, indeed, this seems quite common.
Can you give some other examples like Kripke's "Feynmann" example?
Kripke presents this as an argument against thesis (2): that speakers generally believe that they have enough information to individuate an object. In fact, however, it seems better directed at thesis (4): that if the information a speaker has does not pick out a unique object, the name does not refer. What speakers believe about this sort of thing does not seem terribly interesting, let alone crucial.
In the argument from error (pp. 82-5), Kripke claims that people can refer to an object even if the information they have about that object fails to apply to anyone, or applies to someone else. Here, the central example is the Gödel–Schmidt example. Most people, Kripke says, probably believe no more about Gödel than that he proved the incompleteness theorem. But, he insists, even if that were not true—if someone else proved the theorem and Gödel stole it from them—they would still use the name "Gödel" to refer to Gödel.
Kripke also mentions some real-life examples, involving Peano (who did not discover the so-called Peano axioms); Columbus (who was not the first Eurpoean to visit the Americas); and Einstein (who did not invent the atomic bomb). Can you think of other such examples?
When we make the judgement that someone who knew nothing else about Gödel than that he proved the incompleteness theorem could still refer to Gödel in the circumstances described, what kind of judgement are we making? On what basis do we make it? Is this a case where we are relying upon "intuition"? Do the real-life examples seem somehow different from the invented example about Gödel and Schmidt?
This argument is directed primarily against thesis (3): The information the speaker has does pick out an object uniquely, but it is the wrong one. It also constitutes an argument against thesis (5): Even if it is true that Gödel proved the incompleteness theorem, it is not a priori that he did so; and, Kripke claims, that is true even for a speaker who knows nothing more about Gödel than that he proved the incompleteness theorem.
Note that this is a stronger claim than the one made in Lecture I: Kripke is not just saying that it is not a necessary truth that Gödel proved the incompleteness theorem, i.e., that there are other possible worlds in which he did not prove it; he is claiming that we can at least make sense of the suggestion that Gödel did not in fact prove the incompleteness theorem in the actual world.
One of the things that makes these arguments difficult to evaluate is that they depend, in a way the "modal" argument does not, upon exactly what sorts of descriptions one thinks ought to form part of the "cluster". The sort of view Kripke spends most of his time discussing is sometimes called "famous deeds" descriptivism, since the descriptions all seem to concern the "famous deeds" of the referent. On pp. 87-90, then, Kripke considers some other suggestions about what the descriptions ought to be. Do any of these seem promising?