Many formal epistemologists think that Conditionalization is always the uniquely rational way to update one’s credences. But this cannot be correct. In certain troublesome cases, Conditionalization would take the thinker to rationally forbidden destinations. Conditionalization has to be restricted somehow, so that it does not apply in these troublesome cases.
There is actually quite a range of such troublesome cases. But the simplest example is that of certain Moore-paradoxical propositions – propositions that the thinker could express by uttering something of the form ‘P, and there is no time t at which I assign a high credence to the proposition that P’.
(In contemplating this proposition, the thinker has to refer to herself in a distinctively first-personal way. However, to bracket worries about how to accommodate indexical references to times in our formal framework, I have chosen a Moore-paradoxical proposition that quantifies over times in its second conjunct – rather than a proposition that contains a distinctively indexical reference to the present time.)
Now, nothing prevents the thinker from rationally having a prior system of credences that assigns arbitrarily high probability to this Moore-paradoxical proposition, conditional on a certain possible body of evidence E.
Indeed, E might just be P itself. It might be obvious from the nature of P that P is the kind of proposition that one is extraordinarily unlikely to have a high credence in even if P is true. For example, suppose that P is the proposition that the number of flies in the world right now is exactly 17,000,000,000,000,000. Even conditional on the truth of P, it is unbelievably unlikely that one will ever have a high credence in P. So, conditional on the supposition of P, one rationally assigns an extremely high conditional credence to the proposition that one could express by uttering ‘P, and I never have a high credence in the proposition that P’.
However, one’s prior credence in P is still non-zero. So, it could still happen that one day one learns that P is true. But then, if one updates one’s credences by Conditionalization, one will end up assigning an extremely high credence to the proposition that one could express by uttering the relevant instance of ‘P and I never have a high credence in the proposition that P’.
This, surely, is an irrational place to end up in. It is a priori obvious that if one has a high credence in this proposition, the proposition cannot be true (given that it is also a priori obvious that if one has a high credence in a conjunction, one also has high credence in each of its conjuncts).
So, in these cases, it seems to me, it is irrational to update by Conditionalization. Conditionalization must be restricted so that it does not apply to these cases.
Indeed, this point seems so obvious to me that I feel sure that someone must have thought of this point before. I would be very grateful if someone could let me know who (if anyone) has made this point before!