## McGee conditionals vs SDA

Has it been noted that McGee conditionals seem to clash with the Simplification of Disjunctive Antecedents (SDA)?

Consider the following conditional, inspired by McGee (1985).

(1) If a Republican had won then if it hadn't been Reagan then it would have been Andersen.

For context, imagine a scenario in which there were exactly two Republican candidates for the office in question, called Reagan and Andersen. Neither won. In this kind of context, (1) seems fine. So does (2).

(2) If Reagan or Andersen had won then if Reagan hadn't won then Andersen would have won.

Now, SDA (in its strong form) is the hypothesis that a conditional of the form 'if A or B then C' is equivalent to the conjunction of 'if A then C' and 'if B then C'. Applying this to (2), we would predict that (2) is equivalent to the conjunction of (3) and (4).

(3) If Reagan had won then if Reagan hadn't won then Andersen would have won.
(4) If Andersen had won then if Reagan hadn't won then Andersen would have won.

But these both sound terrible, and their conjunction doesn't seem equivalent to (1) or (2).

Let's compare this apparent counterexample to the standard counterexample from McKay and Van Inwagen (1977):

(5) If Spain had fought on one side or the other in World War II, it would have fought on the Axis side.

As McKay and van Inwagen note, this does not seem to imply (6):

(6) If Spain had fought on the Allied side in World War II, it would have fought on the Axis side.

Friends of SDA have a response to this kind of case (see, e.g., Warmbrod (1981), Fine (2012), Starr (2014), Willer (2018)). (5), they say, is only appropriate if there's no way that Spain would have fought with the allies. In that case, (6) is actually true, because its antecedent is necessarily false. It's just unassertable, for obvious Gricean reasons.

Could one say the same about (2)? Does (2) convey that there's no way Andersen could have won? I don't think so. Don't worry about any actual historical context. Imagine that Reagan and Andersen were neck and neck in the polls, and either could easily have won. In fact, they narrowly lost to the Libertarian candidate (say). (2) still seems fine. But clearly it doesn't convey or presuppose that one of the disjuncts is impossible.

The problem is, of course, quite general. It's not specific to the example, or to subjunctive conditionals. It arises whenever we want to distinguish between the different disjuncts in the consequent. Some more examples:

(7) If you draw a coloured ball [or: a red or blue ball], you get 5 points if it's red and 3 if it's blue.
(8) If you had drawn a coloured [red or blue] ball, you would have got 5 points if it had been red and 3 if it had been blue.
(9) If you run into Alice or Aaron, say hi and if it's Aaron tell him I'll call him back.

(Friends of SDA should probably say that (3) and (4) together really are equivalent to (2), due to the validity of Import/Export, and that both are merely unassertable. Not sure what they should say if they reject Import/Export.)

Fine, Kit. 2012. “Counterfactuals Without Possible Worlds.” Journal of Philosophy 109: 221–46.
McGee, Vann. 1985. “A Counterexample to Modus Ponens.” The Journal of Philosophy 82 (9): 462. doi.org/10.2307/2026276.
McKay, Thomas, and Peter Van Inwagen. 1977. “Counterfactuals with Disjunctive Antecedents.” Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition 31 (5): 353–56. doi.org/10.1007/BF01873862.
Starr, William B. 2014. “A Uniform Theory of Conditionals.” Journal of Philosophical Logic 43 (6): 1019–64. doi.org/10.1007/s10992-013-9300-8.
Warmbrod, Ken. 1981. “Counterfactuals and Substitution of Equivalent Antecedents.” Journal of Philosophical Logic 10 (2): 267–89. doi.org/10.1007/bf00248853.
Willer, Malte. 2018. “Simplifying with Free Choice.” Topoi 37 (3): 379–92. doi.org/10.1007/s11245-016-9437-5.