Notes on Sklar, 
"Up and Down, Left and Right, Past and Future"

The idea that Sklar is considering is the intriguing idea that the direction of time can be explained (somehow) in terms of the direction of entropy. There are lots of tricky details to how this idea might be worked out, but there are also fundamental philosophical worries or questions about it.

Notice that Sklar says that the entropic theory "presupposes . . . the full topology of time" with the sole exception of "the past-future asymmetry."

What does that mean? I think we can understand it like this: the entropic theory is designed to be an explanation of how to get from McTaggart's C-series to his B-series. The B-series, recall, relates events solely in terms of simultaneity and between-ness. (And in fact I think we could define Simultaneous(x,y) in terms of Between(x,y,z). Simultaneous(x,y) if and only if there is no z such that Between(x, y, z).)

So the question can be understood to be: what do we need to add to the C-series in order to get the B-series?

C-series + direction → B-series

B-series + now → A-series

(It might seem that adding direction amounts to adding "earlier" and "later," which amounts to adding all there is to the B-series, in which case the stuff about the C-series seems unnecessary! But that's misleading. The significance of starting with the C-series already in place is that we can use that structure to extend the results of entropic considerations. In fact it seems that in a sense we would only need to be able to determine, for two events, which was earlier, in order to be able to extend the earlier/later sequence to every event.)

Left- and right-orientation seem like basic geometric notions. It may well be (in fact it seems to be) that there are basic physical laws that are sensitive to this distinction. (Sklar mentions "the familiar examples of the parity non-conservation of weak interactions," though, I blush to admit, these are not familiar to me, at least under this description.) I think he has in mind chemical bonding, where many compounds have both left- and right-handed versions (e.g. dextrose and levulose). In some cases these are equally possible, and if one is found more commonly than the other, this is just an empirical accident. But in other cases, it seems that nature permits a compound with one orientation but not with the other.

Sklar's point is that even if this turns out to be a fundamental feature of the most basic physical laws, we still would not say that left/right orientation had turned out to be somehow identical with this asymmetry of the physical laws. Instead, we would simply say that 

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