Problems with An Objective Counterfactual Theory of Information

Jonathan Cohen and Aaron Meskin (C&M) published a paper several years ago titled `An Objective Counterfactual Theory of Information’. Here is its abstract

Philosophers have appealed to information (as understood by [Shannon, 1948] and introduced to philosophers largely by [Dretske, 1981]) in a wide variety of contexts; information has been proffered in the service of understanding knowledge, justification, and mental content, inter alia. While information has been put to diverse philosophical uses, there has been much less diversity in the understanding of information itself. In this paper we’ll offer a novel theory of information that differs from traditional accounts in two main (and orthogonal) respects: (i) it explains information in terms of counterfactuals rather than conditional probabilities, and (ii) it does not make essential reference to doxastic states of subjects, and consequently allows for the sort of objective, reductive explanations of notions in epistemology and philosophy of mind that many have wanted from an account of information.

We’ll first present our counterfactual account of information (1), and show how it sidesteps a problem that has been raised for its traditional, probabilistic competitors (2). Next we’ll compare the counterfactual account against that proposed by Dretske (3), highlighting the differences between the two. After that, we’ll turn to questions about objectivity: we’ll bring out a conflict between the essentially doxastic character of traditional theories of information and the reductive purposes philosophers have had in mind in appealing to information (4), and we’ll show how the account of 1 can be formulated in non-doxastic terms. Finally, we’ll consider objections against the proposed account (5). Ultimately, we’ll suggest, the objective counterfactual account of information should be taken as a serious contender to more traditional rivals.

The central definition of information that they provide is:

(S*) … x‘s being F carries information about y‘s being G if and only if the counterfactual conditional “if y were not G, then x would not have been F” is non-vacuously true.

Also, in a footnote C&M mention that x‘s being F and y‘s being G are construed as actual events, so one event carries information about a second only if they are actual.

As outlined in this document, some exploration reveals that using the standard logic of counterfactuals, C&M’s definition gives some results that disagree with what it seems are fairly straightforward properties of information flow.