A Problem for the Simple Theory of Counterfactuals

In a recent blog post called 'The Simple Theory of Counterfactuals', Terrance Tomkow argues extensively for a theory of counterfactual conditionals along broadly Lewisian lines, explicitly restricted to counterfactuals with nomologically possible antecedents. The theory, Tomkow says, was first proposed by Jonathan Bennett in 1984, but later abandoned. Lewis held a more complicated theory.

Tomkow argues successfully, in my opinion, against Bennett's reasons (given in his Philosophical Guide to Conditionals) for rejecting his own theory. (Tomkow tells me, in a private communication, that Bennett has agreed with these arguments of Tomkow's, also in a private communication.) There is much else of value in the post as well. However, I cannot agree with Tomkow that the theory as he states it, even with its restriction, is correct.

The Simple Theory, or the Bennett-Tomkow Theory, is this:

THE SIMPLE THEORY
A > C iff  C is true at the legal A-worlds that most resemble @ at TA.

('A > C' is a shematization of 'counterfactual statements of the form: If ANTECEDENT had been the case then CONSEQUENT would have been the case.'

'@' denotes the actual world. 'Tp' denotes the time that the proposition 'p' is about. 'Legal' worlds are nomologically possible worlds.

The restriction of the this theory is then given as follows: 'To keep things simple, we will only deal with cases where A is false at @ but nomologically possible.')

Now, before giving the objection which is the main point of the present post, I want to note a simpler but less powerful objection. Some counterfactuals with nomologically possible antecedents are categorical - that is, require that all A-worlds are C-worlds. For example 'If I had met a bachelor this morning, I would have met an unmarried man this morning', in the context of a language-lesson. I argue for this here. The Simple Theory seems to assign the wrong meaning here, since it says that such a counterfactual is true iff C is true at the legal A-worlds that most resemble @ at TA, and these won't be all A-worlds, as intuitively required by the counterfactual. This objection is less powerful than the one I am about to give, because it can be easily avoided by simply restricting the theory to non-categorical counterfactuals.

Now the more powerful objection. This is inspired by my cartoon understanding of the confirmation of relativity, but let's just treat it as a fiction. Einstein asserted a law in paper N which actually holds, and which, together with the facts of some experimental setup E, predicts that some light will bend.

Now, it seems to me we can evaluate counterfactuals where the relevant closest A-worlds are worlds where the law doesn't hold, for example ones with the antecedent '~L' (where L is the law in question). Tomkow seems to agree, saying in a comment that 'we do need an account of counterfactuals with contra-legal anteced[e]nts'. So far, no problem for the Simple Theory.

My idea is that there are counterfactuals whose antecedents are legal, but where the similarity relation is contextually understood in such a way that the closest relevant A-worlds are counter-legal. So, with the following counterfactual:

(H) If Einstein had been wrong in paper N, this light would not have bent.

both what Einstein wrote and the experimental setup may be held fixed during evaluation (i.e. match in these respects required for close similarity), while the actual laws of nature are not held fixed. The antecedent itself is legal, however, since there are legal worlds where Einstein is wrong in paper N, but where he writes something else.

I will now try to make this more precise, and spell the objection out.

For a given counterfactual and contextual understanding of it, call the 'focus set' the set of A-worlds at which C is required, by the counterfactual, to be true. (This of course assumes that a theory with broadly Lewisian/strict-implication outlines is basically right.)

The special property (H) was designed to have is thus: having a legal antecedent, yet being legitimately and naturally understandable such that its focus set contains counter-legal worlds.

If there are counterfactuals with that property, that's a problem for the Simple Theory as stated, since it says that 'A > C iff C is true at the legal [my emphasis] A-worlds that most resemble @ at TA'.

Their having legal antecedents puts them in the scope of the Simple Theory as stated, but the presence of counter-legal worlds in their focus sets (on the relevant understandings of them) conflicts with it.

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'.)

Reference

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