After an introduction that introduces the question of numerical identity of persons over time, Parfit's paper is divided into two sections. The first (which ends in the first column of p. 658) outlines a variety of positions, most of them some form of reductionism. Many of these will be analogous to positions you've seen but it's worth remembering that these are positions concerning the nature of persons rather than the nature of minds.

The remainder of the paper concerns certain examples and their implications, principally what Parfit calls the Physicial Spectrum. It may not be clear immediately what Parfit takes the implications of these examples to be but, by the end of the paper, he will connect various responses to these examples to some of the reductionist and anti-reductionist positions he has described earlier.

Do you agree that his imaginary problem cases reveal "some of our deepest assumptions about ourselves" (p. 660, col. 2)?