Let me explain. A and B are alternative “trains” on the shift to reductionism. To make it more precise, consider two relations R1 and S1 as in this diagram:

Diagram. Trains A and B.

me at later times

// R1

-----me now

\\ S1

you at later times

When I shift my beliefs to reductionism, I may come to believe that the relations R1 and S1 are more alike than I had been assuming prior to the shift. This may not happen, and indeed the question whether it should happen, given the attitudes I tend to have, needs to be investigated. But it is plausible that it will and should happen insofar as it can be shown that the relations R1 and S1 are more alike in important respects given nondensity than they would be if we were dense. Given density, Liddy argues, R1 is simply identity of a dense entity (a simple, indivisible thing, etc.) whereas S1 is a social relation of some type between two distinct dense entities. Given nondensity, while R1 is again identity, there is no simple, indivisible entity, and the psychological connections between me now and me later play a significant role (e.g. it is not necessarily all-or-nothing, hence the possibility of indeterminacy, as even non-reductionists like McDowell can and do acknowledge). These psychological relations may be similar to the social relations that hold between me now and you later. If so, R1 is more like S1 given nondensity than it would be given density. By the way, the reason Liddy talks about the “switch to nondensity” rather than (like Parfit) the “shift to reductionism” is to include nonreductionists like McDowell in the discussion. McD is not a “reductionist” because he denies that the relations that constitute R (such as memory and intention) can be given a non-circular “identity-free” analysis. But nonetheless, insofar as he rejects aspects of density he also can ponder the Rams. --But I digress.

The two distinct “trains” on the shift to non-density are views about what should happen, concerning my attitudes about R1 and S1, given that the relations become more alike when we make the shift:

TRAIN A: My attitudes about INTRApersonal R1 should become more like my antecedent attitudes about INTERpersonal S1.

TRAIN B: My attitudes about INTERpersonal S1 should become more like my antecedent attitudes about INTRApersonal R1.

On A, my attitudes about my own future or past should become more like my antecedent attitudes about the futures and pasts of others, whereas on B my attitudes about the futures and pasts of others should become more like my antecedent attitudes toward my own future and past. To see the difference between the two Trains on the shift to nondensity, let us consider an example.

Consider death. There will be a time later when I do not exist. On train A on the shift to nondensity, my attitudes become more like my antecdent attitudes about the deaths of others. Even when I have cared a great deal about them, I still have tended to be less concerned about their deaths than about mine. Shifting to nondensity via Train A, one comes to care less about one's own death: one may have more equanimity of the the type which Parfit expresses when he says that what my death means is simply that at later times there will be no events or states R-related to mine now. One cares less about one's own death. The Train B effect is different: instead one comes to care more about the deaths of others insofar as one's attitudes shift to become more like one's antecedent attitudes towards one's own death. Liddy points out that if one adopts both Train A and B, which is possible, one develops more equanimity about one's own death while also coming to care more about the deaths of others. Similar points can be made about injuries or harms that one or others suffer. On a Train A shift to nondensity, one comes to care less about harms to oneself, whereas on B one comes to care more about harms to others.

Or look at the case where I survive another's death (perhaps we were in a serious accident together where I survive but she did not). On Train A there may be no effect at all in making the shift. Of course my joy in surviving may be tempered by her not being around anymore --but only because I may miss her, perhaps feel guilty in some way, and so forth. The shift to nondensity itself via Train A wouldn't change anything (since it pertains only to my attitudes about me now and me later). But on Train B there is an interesting change because my attitude towards her death becomes more like my antecedent attitude towards my own death. My joy is tempered not only because I miss her but because her death becomes to me more like my own death. Similarly, adopting Train B on another's surviving my death, my attitude towards her survival becomes more like my attitudes toward my own. Her surviving becomes to me more like my own surviving.

There. That's it. Liddy says much more, BUT IF YOU WANT INTERESTING AND SIGNIFICANT RAMIFICATIONS OF THE SHIFT TO REDUCTIONISM, LOOK NO FURTHER. If one shifts to reductionism via both Trains A and B then one will be less likely to harm others in situations in which some type of self sacrifice is required in order to avoid harming. Perhaps the effect would be small. It is intended to be a modest claim. (Incidentally, Scully, the real Branch Parfitians are characterized by their riding on the B Train in contrast with Parfit's taking the A Train.)

Scully: That is interesting, Mulder. You explained that nicely, and it is interesting. Thanks. I really mean that. And once you see the distinction it is quite evident that Parfit takes the A train almost exclusively in discussing “the Rams.” -- By the way, why are you so sure that Zoe Alexander stole it from J. Gordon Liddy rather than vice versa?--