Counterfactuals (also known as subjunctive conditionals)

1. Counterfactuals(also known as subjunctive conditionals) Dorothy Edgington Paris 2019 Lecture 3

2. Unionism or Separatism? • A fundamentally unified theory of both, or two radically different theories? • For unity: ‘If you go in you will get hurt’, ‘We’ll be home by 10 if the train is on time’, and ‘If you had gone in you would have got hurt’, ‘We would have been home by 10 if the train had been on time’. You seem to be essentially saying the same thing, but from a different perspective.

3. For separatism • If Oswald didn’t kill Kennedy someone else did • If Oswald hadn’t killed Kennedy someone else would have • Or the other way round: • If Oswald didn’t kill Kennedy no one else did • If Oswald hadn’t killed Kennedy no one else would have.

4. Large variety of views Lewis: the t-f account for indicatives. For counterfactuals, roughly, all close A-worlds are B-worlds. Gibbardand Bennett: even bigger difference. Suppositional, probabilistic account for indicatives; Lewis-like account for counterfactuals. Stalnaker and Lycan: unified account, only pragmatic differences between them Adams: the suppositional account applies to counterfactuals too.

5. Early theories of counterfactuals • Closely linked to laws of nature. • Goodman: a counterfactual AC is true iff there is a conjunction of truths T which include a law of nature, and are cotenable with A, such that A&T entails C. • B is cotenable with A iff it’s not the case that if A had been true, B would not have been true. • Circularity (as Goodman saw)

6. Circularity: the match • Struck (S)  Lit (L) √ • Struck (S)  ¬Dry (¬D) x • Why the difference? Because D is cotenable with S; ¬L is not cotenable with S. • i.e. ¬(S¬D); and SL

7. Other problems • We don’t always need a law of nature: • If I’d known you were coming I’d have baked a cake • If you had asked me yesterday, I would have accepted. • If you had tossed this (fair) coin ten times, it would have landed heads at least once [almost certain]

8. Lewis (1973), opening sentence • If kangaroos had no tails they would topple over seems to me to mean something like this: in any possible state of affairs in which kangaroos have no tails, and which resembles the actual state of affairs as much as kangaroos having no tails permits it to, the kangaroos topple over.

9. Lewis • i.e. a counterfactual AC is true iff in all the ‘closest’—most similar to actuality—worlds in which the antecedent is true, the consequent is true, • i.e. ‘it takes less of a departure from actuality to make the consequent true along with the antecedent, than it does to make the antecedent true without the consequent’.

10. Problem • Many examples suggest that these two question can get different answers: what would have happened if A were true? And what is true in the most similar A-worlds to the actual world? Any example of the form: ‘if A, things would have been very, very different’, cause problems.

11. e.g. (Fine’s Nixon example) If Nixon had pressed the button in 1973, there would have been a nuclear holocaust. That may well be true. But: in the most similar world to the actual world in which Nixon pressed the button, there was no disaster. Or: if Hitler had died in infancy, things would have been very different in the 1930s. But in the world most like the actual world in which Hitler died in infancy, some other infant grew up to play an almost identical Hitler-like role.

12. Lewis’s refined account (1979) • of the respects of similarity that (standardly) matter: • (1) It is of the first importance to avoid big, widespread, diverse violations of law. • (2) It is of the second importance to maximize the spatio-temporal region throughout which perfect match of particular fact prevails. • (3) It is of the 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 which concern us greatly.

13. Comments • 1. Much more ad hoc than the original idea. • 2. Much closer to Goodman’s—as (a) laws are written in to the account, and (b), what matters is what you hold constant, rather than what is similar. • 3. Many problems of detail still remain.

14. A different problem Set aside problems about closeness. There is still this problem for Lewis as well as Goodman: If almost all, but not all the relevant A-worlds are B-worlds, for Lewis the conditional is false, whereas you should be close to certainthat, e.g., she would have been cured if she had had the operation; or the dog would have bitten if I had approached, or if you had tossed the coin ten times you would have got at least one heads.

15. Extending the suppositional/probabilistic theory to counterfactuals • Just as good a case can be made for treating antecedents as suppositions: suppose you had had the operation; then your back pain would have improved. Just as good a case for treating uncertainty seriously, and treating it as a conditional probability. Start with the indicative: it’s likely that you will be cured if you have the operation. You decline. It’s likely that you would have been cured if you had had the operation.

16. An unhappy combination • Take someone like Bennett who is an Adams fan about indicatives but a Lewis fan about counterfactuals. The former are assessed by conditional probability. ‘It’s 90% likely that if you pick a red ball it will have a black spot.’ The latter are true only if all relevant A-worlds are B-worlds. So it is 0% likely that if you had picked a red ball it would have had a black spot. This is wrong! It should still be 90%. • (NB it is genuinely indeterminate which red ball you would have picked it you had done so.)

17. The relevant worlds • Specify the relevant A-worlds (as Lewis does). Instead of asking whether C is true in all of them, take a probability distribution over the relevant A-worlds and see how likely it is that C is true. The difference between the indicative and the counterfactual is that for the latter, a shift in perspective is needed—they are (typically) not the probabilities rooted in your present belief state, but (often) those you think were appropriate at an earlier time.

18. No problem about the Oswald-Kennedy pairs. Different temporal perspectives are involved. It’s now very probable, indeed certain, that if Oswald didn’t someone else did. That leaves us free to believe that back in 1963, there was a low probability that someone else would have if Oswald hadn’t.

19. What are counterfactuals for? • The play an indispensable role in non-demonstrative inferences to conclusions about what is actually the case. • (1) You are driving, at night, close to the house of friends and consider paying a visit. ‘They’re not at home’, you say, ‘for the lights are off. And if they had been at home the lights would have been on’

20. Second example (Anderson) • A patient is brought to hospital in a coma. ‘I think he has taken arsenic’, says the doctor, ‘for he has [such-and-such] symptoms; and these are just the symptoms he would have if he had taken arsenic’. • Even in this case, the counterfactual form is needed because the doctor is distancing himself from his present belief state when he says ‘and if he had taken arsenic he would have these symptoms. • Both examples are defeasible inferences.

21. Context-dependence I’ve been focusing on the most common type of counterfactual—forward-looking, typically broadly causal: ‘If you had had the operation you would have been cured’, ‘If you had approached the dog would have bitten’. But there is a much wider class that are permissible in context. Any indicative conditional can translate into a counterfactual if and when it is discovered that the antecedent is false.

22. Even this one, back in 1963 • The police are asked: ‘You already had Oswald; why did you arrest all those others from that part of the crowd?’ Answer: ‘We didn’t know it was Oswald: if it hadn’t been Oswald it would have been one of them’. • Or take any indicative conditional you believe, ‘If A, B’. Then you discover ¬B. So you conclude ¬A, for if it had been that A, it would have been that B, and it’s not’. In both these cases you are simply reporting the conditional belief you had, before you found out that the antecedent was false.

23. Two lessons • which will be relevant in the next lecture. • (1) It is often indeterminate what would have happened if A were true, but we assess them probabilistically nevertheless.

24. Examples • If I pick a red ball it will have a black spot (90%) • If I had picked a red ball it would have had a black sport. • If you approach the dog will bit (v. likely) • If you had approached the dog would have bitten. • If you have the operation you will be cured (90%) • If you had ha the operation you would have been cured.

25. Reasons for no determinate truth value • 1. Indeterminism • 2. Determinism but still no saying exactly what my hand movements would have been • 3. Determinism but vocabulary of conditional not suited to subsumption under deterministic laws. • 4. Determinism but antecedent highly general: ‘If I had had another child it would have been a girl’

26. Second lesson • Any indicative conditional has a counterfactual counterpart, should the antecedent prove false. Often this is very natural, as in the above examples. Sometimes it is not the standard was to evaluate the counterfactual, but it is a permissible way. That is, if I think that B if A, and then A proves false, I can always capture my earlier belief by saying B would have happened if A had.

27. Thanks!