What is conditionalization, and why should we do it?
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What is conditionalization, and why should we do it? Richard Pettigrew1
The Author(s) 2019
Abstract Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend on it. As I show, whether this is possible depends on the formulation of the norm under consideration.
One of the central tenets of traditional Bayesian epistemology is Conditionalization. There are various formulations of this norm, but they all agree that it concerns the way your credences should change in response to evidence. I spell out the three formulations that I’ll consider below. On the first, Conditionalization concerns how you actually update your credences when you receive a piece of evidence; on the second, it concerns how you are disposed to update when you receive evidence; and on the third, it concerns how you plan to update. In this paper, I am concerned not so much with which formulation of the norm is correct—after all, they are not incompatible with each other, and some are independent of each other. Rather, I am concerned with which formulation is justified by the existing arguments. I consider three versions of Conditionalization, and four arguments in their favour. For each combination, I’ll ask whether the argument can support the norm when it is formulated in that way. In each case, I note that the standard version of the argument relies on a particular assumption, which I call Deterministic Updating and which I formulate precisely below. I’ll ask whether the argument really does & Richard Pettigrew [email protected] 1
Department of Philosophy, University of Bristol, Bristol, UK
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rely on this assumption, or whether it can be amended to support the norm without that assumption. This is important because Deterministic Updating says that your updating plan or disposition should specify, for any piece of evidence you might receive, a unique way to update on it. But this seems unmotivated, at least from the Bayesian point of view. After all, subjective Bayesianism is a very permissive theory when it comes to your initial credence function, that is, the one you have at the beginning of your epistemic life before you’ve gathered any evidence. But, once that initial credence function is chosen from the wide array that Bayesianism deems permissible, the theory is very restrictive about how you should update your credences upon receipt of new evidence. We tolerate this discrepancy because the same sorts of argument seem to give us both the permissiveness of Probabilism and the restrictiveness of Conditionalization. But if it turns out that these arguments only give t
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