1. Modality Counterfactuals

2. Possible Worlds A statement is something that is true or false. A set of statements is consistent iff all of the members could be true together. A set of statements is complete iff, for any statement S, either S or not-S is a member of the set. A possible world is a consistent and complete set of statements. The actual world (w a ) is the possible world consisting of all true statements.

3. Possible Worlds Predicates ‘W’ = ‘is a possible world’ ‘T’ = ‘is true in’ Definitions □ p = (  x) (Wx  Tpx) ◊ p = (  x) (Wx & Tpx) Colloquially Necessity is truth in all possible worlds Possibility is truth in some possible world

4. Indicatives and Subjunctives If Oswald didn’t shoot Kennedy, then somebody else did. If Oswald hadn’t shot Kennedy, then somebody else would have.

5. Indicatives and Subjunctives Indicative Conditionals (p  q) If I dropped the pen, it fell. If I’m standing outside, I’ve got a good tan. If I went to a different school than I actually did, then I didn’t meet my wife.

6. Indicatives and Subjunctives Subjunctive Conditionals (p □  q) If I had dropped the pen, then it would have fallen. If I had been standing outside, then I would have gotten a nice tan. If I had gone to a different school than I actually did, then I wouldn’t have met my wife.

7. Counterfactuals (p □  q) is true iff the closest possible world in which p is true is a world in which q is true (i.e., the closest p-world is a q-world). If I had dropped the pen, it would have fallen. If I had been standing outside, I would have gotten a nice tan. If I had gone to a different school than I actually did, then I wouldn’t have met my wife.

8. Counterfactuals If I had dropped the pen, I would have failed first grade. If I had dropped the pen, it would have floated up into the sky. If were in the Antarctic right now, I would be really cold.

9. Counterfactuals (1) It is of first importance to avoid big, widespread, diverse violations of law. (2) It is of second importance to maximize the spatio- temporal region throughout which perfect match of particular fact prevails. (3) It is of third importance to avoid even small, localized simple violations of law. (4) It is of little or no importance to secure approximate similarity of particular fact, even in matters that concern us greatly. David Lewis, “Counterfactual Dependence and Time’s Arrow,” pp.47-8

10. Counterfactuals (p □  q) is true iff the closest possible world in which p is true is a world in which q is true (i.e., the closest p-world is a q-world). The closest world is the one that does the best overall job of matching the actual laws of nature and particular matters of fact.

11. Causation If I hadn’t pushed the eraser, it wouldn’t have fallen. My pushing the eraser caused it to fall.