I would suggest you read all of Lecture I for this meeting, but we will focus on pp. 22-53. You do not need to read the Preface, which considers some objections that were made after the lectures were originally published.
For a review of the literature on rigidity, see Jason Stanley, "Names and Rigid Designation", in B. Hale and C. Wright, eds., A Companion to the Philosophy of Language (Oxford: Blackwell, 1997), pp. 555-85 (PDF).
There are four crucial things to understand in this lecture:
- The distinction between necessity and a priority
- The distinction between rigid and non-rigid designators
- The distinction between a description's "giving the meaning" of a name and its merely "fixing the reference" of that name
- The argument Kripke gives against the description theory of names
I'd suggest writing, just for yourself, a couple sentences about each of these. We will focus on the first two for this meeting.
On pp. 22-34, Kripke quickly summarizes a lot of the history we have just studied. Is there anything about this description that strikes you as wrong? or perhaps as biased? (I'm not necessarily saying there is anything wrong or biased. But I might be implying that there is.)
On pp. 34-9, Kripke introduces the distinction between what is a priori and what is necessary. As he notes, these had largely been conflated. The key point here, really, is that the two notions apply to two diferent things. The term "a priori" should be regarded as an epistemic adverb: It describes a way of believing or knowing something and has to do with the sort of justification one has. So we can say that someone knows a priori that 2+2=4, say, but doesn't know a priori that they have hands. What is necessary, by contrast, is a proposition (or something along those lines), and whether a proposition is necessary does not depend upon what anyone knows.
To tease these apart, Kripke gives a few examples. He remarks that one could know a certain mathematical fact becaue it has been proven by a computer. But that knowledge would not, he claims, be a priori, though the mathematical fact, if true, would, like any mathematical fact, be necessary. More strongly, if Goldbach's conjecture is true, it is necessary; but perhaps there is no possible proof of it, and it is not even possible (for a person at least) to know it a priori.
It is not obvious that one does not know mathematical facts that are proven by computers a priori, and Tyler Burge has argued the opposite, in "Computer Proof, A Priori Knowledge, and Other Minds" (PhilPapers). But there are better examples. Can you come up with a case in which someone might have empirical verification even for what turns out to be a logical truth?
As Kripke notes, this does not by itself show that there isn't some connection between a priority and necessity. It does show that these are different notions and that, if there is such a connection, it needs to be established by argument.
Kripke then turns to the sorts of issues raised by Quine about de dicto and de re necessity. He first argues that the notion of an essential property (a property an object necessarily has) is well-grounded intuitively (pp. 41-2). For example, it seems obvious that Barack Obama might not ever have been the US President—that, as Kripke keeps saying, he might not have been—even though, if we describe him as "the first black President", then it's equally obvious that it's a necessary truth that the first black President was at some time the President.
The sentence "The first black President might not have been the President" exhibits a scope ambiguity. How could it be represented? Why does pointing this out not help Quine? (Hint: At which grade of modal involvement would that put us?)
Kripke then turns, on pp. 42-53, to a set of questions about the nature of possible worlds and our cognitive access to them. (These issues will not be our focus, but it is important to understand what is going on here.) Kripke's main target is David Lewis, who holds an extreme form of "modal realism" (see his Plurality of Worlds) according to which (i) possible worlds are something like "alternative universes", containing real people, e.g., just like you and me, and (ii) for every way things might have been, there is a possible world (an alternative universe) in which things are that way. So, according to Lewis, there is a possible world in which Mitt Romney won the 2012 US election and is now President of the US, and another in which he won but was assassinated by a crazed former president who went insane after his affair with an intern was revealed.
But note that, in these worlds, it isn't really Mitt Romney who wins. That's because Mitt lives in our universe, not in some alternative universe, and that raises the question of "transworld identity": How do we know which of these other people in this other universe is Mitt's "counterpart"? It is hard to see what other sort of answer might be given than one that involves some sort of qualitative similarity. (There is a large literature on "counterpart theory".)
If transworld identity has to be explained in terms of qualitative similarity, then that might suggest that every proper name must be associated with "purely qualitative necessary and sufficient conditions for being" its referent (p. 46). And that seems, at least, to be very friendly to the description theory of names. Why?
It's against this view that Kripke argues. His central claim is that we should not think of possible worlds as "alternative universes", so that we have to figure out who is playing the Mitt Romney character in one. Rather, we should think of them simply as situations we imagine and that include Mitt Romney by stipulation. (It might be better if we called these possible situations, since they are usually just fragments of complete worlds. And whether imagination is the right faculty is not obvious, but it helps to fix ideas.) So, contra Quine, again, Kripke claims we can simply consider Mitt himself and ask: Could he have won the 2012 election? Note that this question is not supposed to be epistemic: Could it turn out that Romney actually won? We're assuming he lost and asking if it's possible that he could have won.
Kripke then introduces the second really important distinction in this lecture: between rigid and non-rigid designators. A rigid designator, he says, is one that always denotes the same object in every possible world. So, he says, "9" always picks out the same thing in every possible situation, namely, the number 9, whereas "the number of planets" could pick out different numbers in different situations. Note that the claim here is not that "9" couldn't have meant something different and that, as it would have been used in some different situation, it couldn't have referred to something else. Rather, Kripke's claim is that when we use "9" to describe a possible situation, it always refers to 9; whereas we can use "the number of planets" in describing a possible situation and use it to refer to the number of planets in that situation, which need not be 9.
When Kripke introduces the notion of rigid designation on p. 48, he does so with reference to Quine's example about the number of planets. But Kripke does not really explain how might one use the distinction to respond to Quine. How might one?
There's an important distinction here that emerged later between a designator that is rigid by nature and one that, so to speak, just happens to be rigid. An example of the latter would be "the square of 3". This is a description, and descriptons are not rigid by nature; but since "3" is rigid", and since being the square of something is a mathematical and therefore necessary property of a thing, this particular description is rigid. Names, by contrast, are supposed to be rigid because of what kind of meaning they have. They are, as is said nowadays, rigid de jure and not just rigid de facto. (See also the example of π, on p. 60.)
There is then a brief return to questions about transworld identity, which elaborates some of the earlier themes.