Wednesday, 31 July 2013

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.

6 comments:

  1. Tristan,

    I take a "contra-legal" to be a counterfactual proposition whose antecedent is inconsistent with the laws of the actual world. The Simple Theory does not give us an account of how to deal with these, but then neither does any other theory of counterfactuals. It cannot therefore be an objection to the Simple Theory that it doesn't deal with the contra-legal case.

    The Simple Theory is not a theory about how to determine which counter-factual proposition a speaker might have in mind when he asserts a vague or an ambiguous or an elliptical, subjunctive sentence. In particular, when such an assertion is ambiguous between legal and countra-legal interpretations the theory does not require the legal interpretation. Problems about how to accomplish such a disambiguation cannot, therefore, be problems for the Simple Theory.

    I do agree we need an account of contra-legals. More urgently, we need a good account of laws.

    best
    tomkow

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    1. I don't think this avoids the objection. The whole point of (H) is that its antecedent is consistent with the actual laws, and yet (contra what the Simple Theory predicts) its focus set contains worlds which depart from the actual laws.

      I am not objecting that the Simple Theory fails to cover or deal with such counterfactuals. It deals with them wrongly; I am objecting that, since they fall within the scope of the theory as stated, counterfactuals like (H) show the theory (as stated) to be false.

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    2. To be absolutely clear:

      'It cannot therefore be an objection to the Simple Theory that it doesn't deal with the contra-legal case.'

      That isn't the objection; (H) is not a contra-legal case.

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  2. Tristan,

    I am clearly not understanding your objection. Can you help me out by clarifying?

    With respect to:

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

    I take it that you do not want us to read the antecedent of H as entailing that light doesn’t bend; that reading would make (H) counter-legal.

    That means, as you say, that there are nomologically possible A-worlds: the ones where Einstein writes something else. Fine.

    Now Bennett’s SIMPLE THEORY requires us to say that
    i) the state of the closest worlds at TA be nomologically possible and
    ii) the worlds obey the laws of the actual world after TA.

    That would make make (H) false.

    But note that Lewis’s theory (either CD&TA or Analysis1) has exactly the same requirements (as, indeed, do FIXED PAST and FIXED LAWS) and gives exactly the same result.

    The only difference between Simple and the standard reading on this score is whether or not the closest worlds will have had the same laws prior to TA.

    Reading it your way, Lewis would say that the closest A-worlds are ones in which some small miracle causes Einstein to write something different than he actually did. The Simple Theory will say the closest A-worlds are the legal counterparts of those miraculous worlds.

    Since Bennett’s Simple Theory gives the right results for (H)— in any case, the same as every other available theory –-how is it a counterexample?

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    1. OK, I think we're getting somewhere now!

      'Now Bennett’s SIMPLE THEORY requires us to say that
      i) the state of the closest worlds at TA be nomologically possible and
      ii) the worlds obey the laws of the actual world after TA.

      That would make make (H) false.'

      Yes. But I argue that there's a natural way of reading (H) such that (a) its antecedent is legal but (b) its focus set contains counter-legal worlds (violating your (i)). The Simple Theory isn't able to get that right.

      'But note that Lewis’s theory (either CD&TA or Analysis1) has exactly the same requirements (as, indeed, do FIXED PAST and FIXED LAWS) and gives exactly the same result.'

      I'm totally fine with that, and never meant to indicate otherwise. I was just concerned to argue that the Simple Theory is false. I'm perfectly happy if my arguments carry over easily to the theories you mention.

      'Since Bennett’s Simple Theory gives the right results for (H)— in any case, the same as every other available theory –-how is it a counterexample?'

      There's a big difference, conceptually, between 'the right results', and 'the results of every other available theory'! It is a counterexample, because, while perhaps it does agree with other prominent theories, it doesn't seem to agree with the truth.

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  3. I am late to the party, as usual. But in my view, this requires only a minor revision to the Simple Theory. Rather than always requiring the same laws in the nearest worlds, require them *unless the context makes clear that some other modality is relevant instead*. In your example, the modality would be evidential: if Einstein is wrong at the relevant passage, our next best theory implies that light doesn't bend.

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