Williams is a little difficult to read until you get the hang of it. Go slow. These notes should help. (Sorry, they're a little late. But better late than never).
Very basic outlines
Most of the first article ("Personal Identity and Individuation") is concerned with showing that memory doesn't have any special role to play in identifying persons. The arguments are all very interesting, but we're going to focus on just a few of them, specifically, those concerning Charles, Robert, and Guy Fawkes (pp. 7-10). If you're having trouble with the article, focus on this part first.
The second Williams piece, "Are Persons Bodies?" falls into two parts. In the first part, Williams develops the reduplication argument, specifically, by addressing the objection that it applies to the bodily criterion just as well as it applies to the psychological criterion: if you divide a brain in half and transplant each half into a different body, haven't you "reduplicated" the physical person? Williams says no. We should return to this when we talk about Parfit -- so if it seems obscure now, don't worry.
The second part contrasts what Williams calls person types and person tokens. We will talk about this because it is a point of conflict between Williams and Quinton: each thinks his favored criterion of personal identity best explains why it makes sense to care about particular persons.
Vocabulary: what are types and tokens?
Since it's important, what is the distinction between a type of person and a token person? Read that as a distinction between a kind of person (tall people are a kind of person, for example) and a particular person. Do the same for references to "tokens" of other things like actions or thoughts -- a token action is a single, particular action.
Here's an example that may help illustrate the distinction.
I was at Safeway last week in the express lane. The man in front of me had forty cans in his cart. I objected that he was only allowed nine items. He indignantly replied that he only had four items: beans, tomatoes, soup, and juice. That is, ten cans of beans, ten cans of tomatoes, ten cans of soup, and ten cans of juice.
He was saying that he had four types of items. I was saying that he had forty tokens, that is, forty individual cans.
We were both correct. Whether he was breaking the rule or not depends on whether the store allows people into the express line with nine types of food or nine tokens.
References: who is Miss Beauchamp? What about the Tichborne claimant?
Finally, you may wonder about his references to "Miss Beauchamp." This was an early case of dissociation or multiple personality disorder. You can read more about Miss Beauchamp's case, and the development of study in this area in general, in Nancy Burnett's essay on the history of multiple personality disorder, published by the Mining Company.
You might also wonder about the "Tichborne claimant" (Quinton mentions this). This is a reference to a famous English legal case in which a man claiming to be the lost Baron Tichborne was put on trial for perjury. Obviously what was at issue was a question of personal identity: was the claimant the same person as the Baron?
The trial lasted for 188 days, featured 400 witnesses and the judge's instructions to the jury lasted for 18 days. It was sort of the OJ trial of its day. All of which goes to show that questions about personal identity can be very hard to settle. Mark Twain had a reasonably good line about it:
"I had forgotten that I was a member of this club -- it is so long ago. But now I remember that I was here five-and-twenty years ago, and that I was then at a dinner of the Whitefriars Club, and it was in those old days when you had just made two great finds. All London was talking about nothing else than that they had found Livingstone, and that the lost Sir Roger Tichborne had been found -- and they were trying him for it. "
If you want, you can even watch a Tichborne movie (this page gives a brief synopsis of the case).
Logically sufficient conditions
What I mean by saying "X is a logically sufficient condition for Y" is that if you have X then you are guaranteed to have Y.
The proposal that psychological continuity is logically sufficient for personal identity means that if A is psychologically continuous with B then A is guaranteed to be the same person as B, no exceptions.
The proposal that having a particular set of psychological characteristics is logically sufficient to make one a particular person means that only one person can have these, no exceptions.
Williams found the exceptions (he claims): he described logically possible cases in which the putative logically sufficient conditions of personal identity (or being a unique, singular person) don't, in fact, guarantee personal identity (or uniqueness).
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