“Might”-Counterfactuals and Reversed Sobel Sequences

19 05 2008

To which extent are counterfactuals context-dependent? Lewis suggested that we can do without a systematic dependence on context by combining an invariant similarity relation with a variably strict analysis of counterfactuals. Recently, this approach has been challenged partly by drawing attention to the phenomenon of reversed Sobel sequences: sometimes it seems as if the order in which two counterfactuals are uttered makes for a difference in truth-value. Philosophers who take this phenomenon to be semantic in nature have reacted to it by allowing the similarity relation to vary from context to context (for instance, have a look at von Fintel’s semantics for counterfactuals, which you can find here). In this note, I’d like to challenge the semantic analysis of reversed Sobel sequences by arguing that it does not square well with a plausible link between “would”-counterfactuals and “might”-counterfactuals.

Here is the phenomenon. In an initial context, the counterfactual

(1) If she had been at the concert, she would have seen Mick Jagger

may be truly asserted, or so it is assumed. Subsequently, the counterfactual

(2) If she had been at the concert and got stuck behind a group of tall people, she would not have seen Mick Jagger

may be accepted, too. All this is to be expected on Lewis’s account: strengthening the antecedent is not a valid rule of inference. But now suppose that (1) and (2) are uttered in reversed order: it seems that asserting (1) after (2) is not o.k. There is something odd about saying

(3) If she had been at the concert and got stuck behind a group of tall people, she would not have seen Mick Jagger, but if she had been at the concert, she would have seen Mick Jagger.

So, can the order in which these counterfactuals are uttered affect their truth-values?

 Posted by Moritz.

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A Counterexample to the Principal Principle

25 01 2008

In his paper ‘A Subjectivist’s Guide to Objective Chance’, Lewis proposes an intimate connection between subjective probabilities and objective chances: the Principal Principle. In Lewis’s eyes, this principle captures almost all there is to know about our conception of objective chances.

In a forthcoming paper entitled ‘Knowledge and Objective Chance’, Hawthorne and Lasonen mention in passing a counterexample to the Principal Principle (a draft of which you can find here). Essentially, they think that instances of the contingent a priori provide a source of potential counterexamples. This idea stands in an interesting relation to a recent paper of Williamson (‘Indicative versus Subjunctive, Congruential versus Non-Hyperintensional Contexts’), in which the modal status of statements involving objective and subjective probabilities is discussed (a draft of which you can find there). It seems to me that Williamson’s considerations may provide a deeper reason to explain why we should not expect something like the Principal Principle to hold. In the following note, I will present a structurally similar counterexample by way of relating it to Williamson’s claims about the modal nature of the two kinds of probability.

Posted by Moritz.

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