Tuesday, 5 February 2013

A Modification to Lewis's Theory of Counterfactuals

I propose a modification to Lewis's (1973) theory of counterfactuals, which has come to be treated by many as the standard semantics for counterfactuals. Lewis's theory is that a counterfactual conditional with antecedent A and consequent C is true iff all the most similar A-worlds (worlds at which A is true) are C-worlds. Lewis admits that what matters for similarity varies a lot from sentence to sentence, and from context to context.

What I propose is that similarity sometimes plays no part at all, and that whether it does also varies with sentence and context. When it plays no part, the truth of the counterfactual in question requires that all A-worlds are C-worlds. (To state the modified theory elegantly, we could speak of 'all relevant A-worlds', defining 'relevant' using 'most similar' but adding that sometimes all A-worlds will be relevant.)

The argument for this modification involves what could be called categorical counterfactuals. Consider the following sentence, uttered in the context of teaching someone how to use the word 'bachelor':

(A) If I had spoken to a bachelor this morning, I would have spoken to an unmarried man this morning.

Intuitively, the truth of this hinges on the fact that bachelors are necessarily unmarried men. Lewis's analysis, without my proposed modification, although it gives the right truth-value, gives the wrong truth-condition and thus distorts the meaning of (A); it is false to say that the truth-condition for this sentence is that all the most similar A-worlds are C-worlds - on any understanding of similarity.

The modified theory handles (A) much better: this is one of those cases where similarity plays no part, and so (A) is true iff all worlds where I spoke to a bachelor this morning are worlds where I spoke to an unmarried man this morning. This seems right.

(A note on the structure of Lewis's theory as formally developed with systems of spheres: this can remain as is, but in the case of categorical counterfactual conditionals the “innermost” sphere will contain all worlds, and so it would be misleading to call the worlds in this sphere 'the most similar A-worlds'.)

Rachael Briggs has made me aware that the resulting theory bears a resemblance to Angelika Kratzer's “strict conditional” theory of counterfactuals, which has been taken up by others. (I haven't compared them.) Indeed, Lewis refers to his theory as a 'variable strict conditional' analysis.

Worries and replies

Worry 1 (thanks to Rachael Briggs):

It's not clear to me that Lewis does give the wrong truth condition for (A). Your account seems to yield the result that (A) is necessarily true, since at all worlds, all worlds where I speak to a bachelor are also worlds where I speak to an unmarried man. Lewis's account also yields the result that (A) is necessarily true, since at all worlds, there is either no world where I speak to a bachelor, or some world where I speak to an unmarried bachelor closer than any world where I speak to a married bachelor. So both readings of (A) appear to agree about its truth condition---i.e., the set of worlds where it is true. Perhaps your complaint is that Lewis's analysis somehow fails to pinpoint the facts that ground (A)'s truth?

Reply to Worry 1:

Admittedly, if a truth-condition is considered as a set of worlds, then I cannot say Lewis gives the wrong truth-condition. But it seems pretty clear to me that:

(i) Lewis is trying to give the meaning of counterfactuals with his "truth-conditions" - with the RHSs of instances of his analysis. (Recall his remark at the beginning of
Counterfactuals about what the kangaroo conditional seems to him to mean.)

(ii) A set of worlds by itself does not fully characterise the semantics of a sentence in use; necessary truths don't all mean the same thing. Perhaps a set of worlds
specified in a particular way can do this in a sense, but then the way is doing important work that the set alone doesn't do.

In light of this, I guess I should either say more about what I mean by 'truth-conditions', or drop the term and talk about 'meaning-giving clauses' or something instead, as well as making it clear that I am assuming (ii) (plausibly, I hope). What do you reckon?

Reply to reply to Worry 1 (thanks to Rachael Briggs):

You're right that that there's a lot to meaning that isn't captured by functions from worlds to truth values, and that Lewis seems to be after it. I think what I said was really more of a quibble than a substantive criticism. People usually use "truth conditions" for intensions - functions from possible worlds to truth values, and "hyperintensions" for anything finer-grained than intensions. Saying you're trying to capture their meanings makes good sense, and saying that there's something hyperintensional about their meanings also makes good sense.

Worry 2 (thanks to Michael McDermott):

Are you saying that the ‘if’ construction means different things in (A) and (B)?

(B) If I had spoken to a bachelor this morning, I would have learnt something interesting.

That does not seem plausible. It would be like saying that ‘=’ means different things in (C) and (D) because (C) is a necessary truth.

(C) The number of boys = the number of boys.
(D) The number of boys = the number of girls.

Reply to Worry 2:

I don't want to claim that here, no. My own background view about meaning is that we can carve up meanings at different levels of granularity, so that while a meaning distinction could be made here, we can also be less fine-grained and say that the 'if' construction means the same thing in (A) and (B), which we can gloss as 'All relevant A-worlds are C-worlds'.

Analogously, a quantifier like 'all' can be used in an unrestricted sense, or with implicit restrictions. We can say that 'all' means different things depending on this, but we don't have to.


Lewis, D. 1973. Counterfactuals. Basil Blackwell: Oxford.

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