Chapter 19 Subjunctive Conditionals
And Time’s Arrow
(Plus Antecedent Relativity)
§ 114 Explaining the Arrow of Time
Bennett’s account of subjunctive conditionals is based on Lewis’s. However, there are
differences. This is the topic of Chapter 19.
Lewis wants his account of subjunctive conditionals to help explain temporal asymmetry,
the difference between past and future. Although Bennett uses the blanket term “time’s
arrow” for the direction of time, there are a few different categories of temporal
asymmetry, e.g. entropic processes, expanding light spheres, consciousness, and the
dependency of the future on the past. Lewis’s account deals with the last of these.
Lewis wants his analysis of subjunctive conditionals to explain our sense that the past is
fixed and that there are many possible futures, which he terms the Asymmetry of
Openness (AO). He also wants it to explain the Asymmetry of Causation (AC), the fact
that causes predate their effects.
Neither the future nor the past can change. Logically, whatever happens at a future time
Tf will be whatever happens at time Tf. However, we can say that the past affects the
A affects C : A is true, C is true, (A>(C is true.
Lewis then says that C counter-factually depends on A.
Earlier times affect later times because most true counterfactuals have an antecedent
which concerns a time which is earlier than the time of the consequent. This is all there
is to openness. A causes C if there is a chain of counter-factual dependencies of this sort
which connects A and C. Bennett adds that for Lewis, causation only holds between
Lewis thinks that it makes sense to speak of the future affecting the past in exotic
situations such as sci-fi time travel, precognition, Godel topologies, etc. Presumably, in
such scenarios there is a true counterfactual (A>(C, where A is later than C, and,
intuitively, we judge that A causes C.
The problem is that Lewis’s analysis seems to imply that the future affects the past in
ordinary, everyday situations. There are true, backwards counterfactuals which we do
not think involve backwards causation. These are conditionals which say that if it were
the case that A, then C would have to have obtained. We covered these last week.