Williams argues from premises about our desires to two conclusions: death is bad and immortality would (probably) be bad too.
The premise is that there is a distinction between two kinds of desires. The distinction turns on what it would be for desires to be satisfied.
Lucretius would be right if all of our desires fell into the first category: if the extinction of desire was as good as getting what we want, we might as well be dead. But most people have categorical desires: death is not a way of satisfying them so they give us a reason to live.
The problem with immortality, according to Williams, is that it would lead to the extinction of categorical desires and thus the reason we have for continuing to live.
There’s a dilemma, according to Williams. If the immortal person’s character doesn’t change in the light of her experiences, she will become bored with life, having done all that she can do with the character she has. But if the immortal person’s character can change, the distant future version of a person will have little interest in the categorical desires of the present person, such that the present person has little reason to value the distant person’s life.
We were split on this. Dhruv, Selma and others thought that Williams had a good point. Rob and others thought he was too pessimistic. The world is a dynamic, rich place that is full of interesting things. I believe their optimism was more closely tied to the possibility of a changing character. It may be true that my distant successor will be unintelligible to me. But, as Nick pointed out, I am now unintelligible to my six year old self: why would that be worse?
Williams ends with a discussion of Unamuno’s views. I put the relevant part on a handout.