A nightmarishly difficult account of modal logic. The general idea is simple, though. What is a counterfactual? Df. = strict conditionals corresponding to an accessibility assignment determined by similarity of worlds–overall similarity, with respects of difference balanced off somehow against respects of similarity (Lewis 9). Lewis argues that the following modal operators obtain:
⃣ → means “if it were the case that x, then it would be the case…”
◇→ means “if it were the case that x, then it might be the case…”
The following two counterfactuals are interdefinable
Ф ◇→ ⃣ =
1.2 Strict Conditionals
⃣ (Ф ⊃ψ)
⃣ (Ф ⊃ψ) is true at i iff ψ is true at every accessible Ф world.
Entities that can be true or false at worlds, and (2) there are enough of them (46).
Sets of worlds are propositions. Lewis: A proposition P is true at a world i iff i belongs to the proposition–the set–P. (What if a person can also be defined as a possible world? In which case we have the following: A proposition (or maybe its set) = a Possible World = a person. Thus, a proposition (or its set) = a person. Gordon Clark?)
An impossible proposition is an empty set (47).
Section 4 is his famous chapter on Possible Worlds. The gist of it is quite similar (even if the particulars are not!). A possible world is simply the way things could have been. Lewis, however, seems committed to the idea that there are things that exist which aren’t actual, but he tries to shore up this problem by saying that actual worlds are indexical (here, now, I). See his discussion on realism on p. 87.
All maximal consistent sets are indices (125)