The Indifference Principle

It's obvious that you can care about matters which are vague: for example, you can rationally care about being rich, being happy, having lots of friends, and so on and so forth.

Let us assume that the algebra of propositions is a complete atomic Boolean algebra. Every proposition can thus be thought of as a set of indices. As usual, we can also partition these indices into maximally strong consistent precise propos­itions: consistent propositions that are precise and which entail any other precise propositions consistent with them. (Here, as in earlier chapters, we assume that the precise propositions themselves form a complete atomic Boolean subalgebra of the algebra of propositions, as discussed in section 3.2.) For the supervaluationist, for example, the indices could be represented by ordered pairs consisting of a world and a precisification, and the maximally strong consistent precise propositions by a partition of pairs such that the members of any element of the partition all have the same world coordinate. But our characterization here is completely general, and our discussion applies to any theory that accepts the Booleanist assumptions outlined above.

With these notions in place, we can state the principle that correctly encodes the thought that one should not care intrinsically about the vague:^[CXLV]

Indifference. If, for every precise proposition, either both A and B entail it, or entail its negation, then one should be indifferent between A and B.

Note that this principle does not entail that you couldn't rationally care about being rich. For simplicity, let's assume you only care about your financial situation and let's also assume that whether you're rich supervenes on how much money you have. Given these assumptions, Indifference does entail that you should be indifferent between states that agree on how much money you have. If you furthermore know how much money you have, you should be indifferent between all the different maximally specific

10.3