Counterfactuals, Probabilities, and Information: Response to Critics

Abstract

In earlier work we proposed an account of information grounded in counterfactual conditionals rather than probabilities, and argued that it might serve philosophical needs that more familiar probabilistic alternatives do not. Demir [2008] and Scarantino [2008] criticize the counterfactual approach by contending that its alleged advantages are illusory and that it fails to secure attractive desiderata. In this paper we defend the counterfactual account from these criticisms, and suggest that it remains a useful account of information.

Notes

¹The work is fully collaborative; the authors are listed in anti-alphabetical order.

²Demir's footnote 1, added after discussion with us, notes this possible misrepresentation. We hope the present comments clarify our intentions.

³Moreover, the usual problems about the authority of intuitions (e.g., as pressed by Swain et al.[2008]) apply here in spades.

⁴Don't we argue against probabilistic theories on intuitive grounds—viz., that they don't limit application of the Xerox Principle and, consequently, require (counterintuitively) that the probabilities underwriting information relations are unity? In principle we're flexible here, too. If you accept the requirement of probability one, then the drawback mentioned is no longer a reason to disfavour probabilistic approaches. Our claim is conditional: if the requirement of probability one is unreasonable in relevant theoretical contexts (as many philosophers have held) then probabilistic theories won't suffice. What such considerations amount to is not a debate about what could count as a theory of information, but an open-eyed assessment of the advantages and costs of theoretical alternatives.

⁵The world Demir considers (the closest not-B and not-C world) is relevant to the evaluation of his counterfactual, but not to (3).

⁶Here s₁ … s_n are discrete alternative states of s with probabilities P(s₁ ), … , P(s_n ) respectively, and r₁ … r_k are discrete alternative states of r with probabilities P(r₁ ), … , P(r_k ) respectively.

⁷Indeed, arguably we want a notion of information that is neither symmetric in all cases (see above) nor fails to be symmetric in all cases (for two distinct states might, in certain restricted circumstances, be thought to carry information about one another).

⁸We are officially agnostic about the semantics for counterfactuals, so (as Demir anticipates) we might respond by rejecting the standard (possible worlds involving) semantics for counterfactuals. Demir responds that this would (i) make the counterfactual account incomplete, and (ii) make the account equivalent to that proposed by Loewer [1983].

 We remain undaunted. As for (i), we never aspired to explain every piece of technical apparatus used by the theory we proposed (a good thing, too, since filling in the semantics for counterfactuals wouldn't do that either). Regarding (ii), (S*) would become equivalent to Loewer's theory only given the adoption of something like Loewer's (controversial) Humean understandings of counterfactuals and laws. Even granting all this, we see no reason for alarm; as we said in C&M, ‘[W]e are happy to think of our proposal as a notational variant of that suggested by Loewer (we are delighted to have philosophical company)' [338].

⁹As we point out in C&M, this won't result in a non-doxastic theory of information unless the distributions in question are themselves independent of the doxastic [346].

¹⁰We ignore solutions that depend on a non-standard semantics for counterfactuals.

¹¹Thanks to an anonymous referee for this journal for helpful comments.