Abstract:

Imagine that a secret toss of a fair coin will decide whether someone is to be awakened either a larger or a smaller number of times. Add to this that at the end of any awakening he will be made to forget it, so that he'll never have any memories of how many awakenings there have been. But when he does awaken, it seems, he could infer the greater probability that he is being awakened the larger number of times because that would have made more probable the occurrence of the awakening he is in.

The Sleeping Beauty problem is that just before he is first made to sleep, and before the coin has even been tossed, he could infer nothing and yet he knew then that in his very next episode of thought he would be properly inferring the greater probability of the many awakenings. It is as though he already knew both what he would see when he opened a door and what he would conclude on the basis of seeing it but somehow could not yet arrive at that conclusion.

In the paper that sparked the great interest in this problem, Adam Elga said that Robert Stalnaker (who named it), 'first learned of examples of this kind in unpublished work by Arnold Zuboff'. In the work thus credited as the source of the problem, I was arguing for an application of probability to metaphysics. And in the first sections of this dissertation I show that the solution of the Sleeping Beauty problem requires getting clear not just about probability but also about metaphysics.

I argue that the problem arises from an inconsistency in the way we are individuating experiences in relation to time.

After presenting the solution of the problem, I show that probability reasoning can establish which of two rival ways of individuating experiences is correct. Parallel reasoning is then applied to the individuation of experiences in relation to the identity of the experiencer. And that reasoning forces us into a radical solution of the problem of personal identity.

There are six appendices. In one I argue that this same style of probability reasoning is the justifiable basis of all empirical inference. In another appendix, I use this sort of reasoning to solve the problem in physics of the anthropic principle. Three of the appendices are published papers, including both a later published version of that unpublished work in which Stalnaker 'first learned of examples of this kind' and 'The Story of a Brain', first published in Hoffstadter and Dennet's anthology, The Mind's I .