ABSTRACT
In what follows, I’ll assume that the ordering source yields the same set of propositions at every world (i.e. that there’s a single uniform ideal), and that all of the propositions in the ordering source can be jointly satisfi ed (i.e. that the ideal is consistent). 42 Given this framework, we can accept the formulations of Conditionalization provided in the text, as long as we understand them as implicitly requiring the modal base to be broad enough to admit at least one ideal world – a world at which all of the propositions in the ordering source are true. The formulations given in the text then assert that, given such a modal base, the highest ranked worlds (and thus the worlds a subject should aim for) will be worlds at which subjects satisfy that formulation of Conditionalization. 43 This is equivalent to thinking of these formulations of Conditionalization as providing partial descriptions of the ordering source. In particular, we can think of these formulations as requiring the propositions in the ordering source to entail that subjects conditionalize (in the manner specifi ed by that formulation). 44 I didn’t say that the ordering source consists of the proposition that subjects conditionalize for two reasons. First, if one thinks that there are other epistemic norms that bind subjects (e.g. the Principal Principle) then propositions concerning these norms will appear in the ordering source as well; so the ordering source won’t just consist of propositions regarding Conditionalization. Second, if one wants a detailed ranking which takes into account things like partially satisfying the requirement to conditionalize, or approximately conditonalizing to a greater or lesser degree, then one won’t want the claim that subjects conditionalize to appear as a single proposition in the ordering source. Instead, one will want to use a batch of weaker propositions that together entail that subjects conditionalize – this allows one to assess the magnitude of deviations from this ideal, by seeing how many of these weaker propositions are violated. 45 This framework allows us to give the claim that Conditionalization is ‘an ideal at which to aim’ a precise meaning. At the ideal worlds, in which all of the propositions in the ordering source are satisfi ed, subjects will conditionalize. And given an appropriate decomposition of the claim that subjects conditionalize into weaker propositions, the ordering source will tell us how to move closer or farther from this ideal – i.e. it will tell us in what direction to aim. Likewise, this framework provides a way to spell out the relationship between a subject’s cognitive limitations and the rule’s ability to provide guidance and satisfy ought-impliescan. A norm can only provide a subject with guidance and satisfy ought-implies-can if that subject is cognitively capable of ‘getting to’ the highest ranked worlds picked out by the modal base. And since Conditionalization, as I’m understanding it, implicitly requires us to work with a modal base that admits at least one ideal world, this norm will only provide guidance and satisfy ought-implies-can for subjects whose cognitive capabilities are powerful enough to allow them to get to ideal worlds. So the norm won’t provide guidance or satisfy ought-implies-can for more cognitively limited subjects like ourselves. (If we can complete the diffi cult task of working out what exactly to put in the ordering base, we can construct a norm that provides guidance to any subject: we simply require the modal base to admit all and only worlds that the subject is cognitively capable of getting to, and then direct her towards the subset of those worlds that are highest ranked. This norm would have the same ‘normative heart’ as Conditionalization, since it makes prescriptions based on the same ordering source. But, unlike Conditionalization, it would not always tell subjects to conditionalize, since many subjects aren’t capable of doing so. (If we distinguish between ‘evaluative’ and ‘guidance’ norms, then we can think of Conditionalization as the evaluative norm suggested by this ordering source, and this other norm as Conditionalization’s ‘guidance counterpart’ – the guidance norm suggested by the same ordering source.)) Appendix 3
Suppose that Ought Implies Can, that the Past is Immutable, and that the posterior answer to the Time of Evidence Question is correct. Then the narrow and wide scope formulations of Conditionalization will be equivalent. Let’s see why this is so. To begin, recall that since the time of evaluation is t
worlds, and a fortiriori (given that Ought Implies Can) at all O - accessible
worlds. Given the posterior answer to the Time of Evidence question, A only describes events at t
