EL GENERADOR

I would like to avoid the impression that the atomic change semantics by itself offers a comprehensive semantics of counterfactuals. It does not. This section

is devoted to one feature of our counterfactual imagination: our openness to considering hypothetical contexts beyond those explicitly raised by a counter- factual antecedent. For it seems the imagination is highly suggestible, open to bringing extra hypothetical contexts to bear on counterfactuals that do not explicitly mention them.2

As an illustration, consider the following dialogue between Jenny and Bob. (44) [jennyflips a coin and hides it in her hands.]

j: Heads or tails?

b: Heads.

j: [Reveals the coin.] It’s heads: you win! Well done! (45) Ending 1.

b: Yay! If I had bet tails, I would have lost.

We have a strong feeling that what Bob said is true: if Bob had bet tails he would have lost. But consider the following alternate ending to their dialogue. (46) Ending 2.

b: Well, it was all down to luck. The coin could have just as easily landed tails.

j: Yes, but you could have just as easily bet tails.

b: True. If I had bet tails, well, the coin might have landed tails and I would have won anyway.

j: Right! So it’s false to say: if you had bet tails, you would have lost. For if you had bet tails, you might have still won!

In the dialogue with the first ending, it seems we fix the fact that the coin landed heads. But in the dialogue with the second ending, Bob invites us to stretch our imagination by unfixing the fact that the coin landed heads, a suggestion Jenny goes along with. Now, the truth of(47)all depends on whether we fix the result of the coin flip.

(47) If Bob had bet tails, he would have lost.

Fixing that the coin landed heads,(47)is true. But allowing that the coin might have landed tails, if Bob had bet tails then still the coin might have landed tails, and Bob would have won, making(47)false. So what is the truth of the matter? I do not think there is one. Each truth value of(47)seems appropriate to the ending in which it is uttered. Nonetheless, default interpretations can act in 2_{This section was inspired in particular by the discussion of a background parameter byCiardelli}

et al.(2018b,§4), though as their discussion makes use of inquisitive propositions, their account undesirably makes semantically equivalent some counterfactuals that, as we saw in section1.2, ought to receive distinct interpretations.

place of authoritative ones. Ending 2 requires more interpretative work to get

(47)to come out false: Bob had tounfixthe result of the coin flip, implying that it began fixed. So(47)is true by default. At least in this instance, we assume the default interpretation is to keep things fixed.

It may be helpful to understand the falsity of(47)after the second dialogue as an instance of the failure of antecedent strengthening—of the kind we know and love fromGoodman(1947) andLewis(1973b, 10)—but where the part that does the strengthening is implicit rather than part of the counterfactual itself. (48) a. If Bob had bet tails, he would have lost.

b. But if Bob had bet tails [and the coin had landed tails], he would have won.

Even though the possibility of the coin landing heads is not mentioned explic- itly by(47), we can formally represent its semantic role in the interpretation of that counterfactual within the second dialogue(46). We simply introduce a set implicit-hyp of implicit hypotheticals, where each ‘implicit hypothetical’ is a set of imaginative contents. In our illustration, let↑and↓be the imaginative con- tents of the coin landing heads and tails, respectively; that is,ι(heads) =↑and

ι(tails) =↓. In(45), our dialogue with the first ending, the sole implicit hypo- thetical is the default interpretation, to take an alternative with no imaginative content: implicit-hyp1={∅}. But in(46), our dialogue with the second ending, implicit-hyp2={{↑},{↓}}.

The two endings show how implicit hypotheticals can come to bear on our counterfactual evaluation. We take it that implicit hypotheticals achieve this by introducing counterfactual possibilities. In our modal framework this amounts to implicit hypotheticals altering the accessibility relations. We therefore rein- terpret the accessibility relations as follows.

Definition 51(Adding implicit hypotheticals). Letimplicit-hyp ⊆ ℘(X)be a

nonempty set containing sets of imaginative contents. Then atomic change semantics with implicit hypotheticals is given by rewriting Definition47with the following clause.

wRϕv iff v=wc

∪h_{for somec∈ci(}

ϕ)andh∈implicit-hyp

We recover the original of definition of our accessibility relation under the atomic change semantics (Definition49) by defaulting to implicit-hyp={∅}.

Turning back our coin flip example, Figure5.2depicts the resulting model in which(50)is true with respect to the implicit hypotheticals of dialogue 1 (viz. none), but false with respect to those of dialogue 2. In the diagram, the dotted arrow representsR1_{bet T}, the accessibility relation of imagining at the dialogue with ending 1 if Bob had bet tails, and the dashed arrow representsR2_{bet T}, the accessibility relation of imagining at ending 2 if Bob had bet tails. The straight line represents lawful temporal succession, and the actual worldwis filled in.

Bet Coin T H T H H T win lose 2 1 2

Figure 5.2: The coin flip, an example with implicit hypotheticals

The calculations behind Figure5.2are worked out in full in the appendix (sectionA9). As the diagram shows,{bet T, coin H} |=lose but{bet T, coin T} 6|=

lose. Then inM1where implicit-hyp1={∅}, we haveM1,w|= [bet T]lose but inM2where implicit-hyp2={{↑},{↓}}, we haveM2,w6|= [bet T]lose.

The next section shows how implicit hypotheticals can invalidate a contested rule of counterfactual inference.