Suppose that there is both an objective ‘ought’ and a subjective ‘ought’. Which of these two kinds of ‘ought’ figures in the anti-*akrasia* principle that it is irrational to do something at the same time as believing that one ought not to do it?

There is a simple of way of understanding the relation between the objective and the subjective ‘ought’ on which the answer to this question is: Both! It is irrational to do something at the same time as believing that one *objectively* ought not to do it; and it is also irrational to do something at the same time as believing that one *subjectively* ought not to do it.

Our concern is with agents who intentionally do *A* at the same time as holding a belief of the form ‘I ought not to do *A*’. In fact, for complicated reasons, it may matter exactly how this option *A* (and the available alternatives) are individuated. But let us set those issues aside for the time being. Suppose that we have somehow focused on an option *A* of the right sort.

Suppose that there is some kind of *value* such that for it to be the case that you objectively ought not to do *A* is just for there to be some alternative to doing *A*,* B*, such that *B* is better in terms of this value than *A*. (For our purposes, this value can be anything: it could be subjective utility, modelled by a utility function that measures your subjective preferences; it could be your lifetime level of happiness, or the total amount of happiness in the world as a whole; or it could be some more objective value, such as some kind of objective goodness. For our purposes, this does not matter.)

Now, suppose that there is a *probability function* that models the degrees of belief that it is ideally rational for you to have. And suppose that for it to be the case that you *subjectively* ought not to do *A* is for there to be some alternative to doing *A*, *B*, such that *B* is better than *A* in terms of the the *expectation* of this value according to this probability function.

Suppose moreover that it is rational for you to do something if and only if doing it maximizes the expectation of this value according to this probability function.

Finally, suppose that when the anti-*akrasia* principle speaks of your “believing” the proposition that you ought not to do *A*, they mean having credence 1 in some proposition of the form '*B* is better than *A* in terms of [the relevant expectation of] this value'.

I shall now show how we can derive both versions of the anti-*akrasia* principle from these suppositions.

First, take the case of an agent who believes that she *objectively* ought not to do *A*. Given these suppositions, if this belief is rational, then the relevant proposition that *B* is better than *A* in terms of this value will have probability 1. It follows that doing *A* cannot maximize the expectation of this value according to this probability function, and so doing *A *cannot be rational. So, the objective version of the anti-*akrasia* principle comes out true on these suppositions.

Secondly, take the case of an agent who believes that she *subjectively* ought not to do *A*. Given our suppositions, if this belief is rational, then the relevant proposition that *B* is better than *A* in terms of the expectation (according to this probability function) of the value will have probability 1 (according to this probability function).

Now suppose that this probability function must meet the following condition: it *never misinterprets itself*, by assigning probability 1 to false propositions about this very probability function (including false propositions about expectations that are defined in terms of this probability function). If the probability function meets this condition, then the proposition that *B* is better than *A* in terms of the expectation (according to this probability function) of the relevant value will be true. Again it follows that doing *A* cannot be rational. So, again, the subjective version of the anti-*akrasia* principle comes out true on these suppositions as well.

In short: assume that rationality consists in maximizing expected value – where the expectation in question is defined in terms of a probability that *never misinterprets itself* in this way; define the objective ‘ought’ as what maximizes this value; and define the subjective ‘ought’ as what maximizes this sort of expectation of this value. Then both versions of the anti-*akrasia* principle will be true.

## Comments