Jeffrey on kinematics and dynamics. Jeffrey Conditioning is intended to be kinematic rather than dynamic, and indeed is called "probability kinematics." But Jeffrey himself clearly thought that it had dynamic relevance, specifically, that its legitimacy counted as an argument against strong foundationalism a la C. I. Lewis.

I. Problem: How do you know when the posteriors--P (H|E), P (H|-E)--are rigid as required for JC?

A. The problem as stated by Judea Pearl.

B. The problem as pressed by I. Levi--Here it has a normative twist: How do you justify the required rigidity, together with the change in the probability of E, as rational rather than merely caused?

C. The problem in its practical form as put forward by Mary Hesse: Conditioning of any sort is only scientifically useful if we can get a grip ahead of time on what will happen to our probability distribution under some new evidential conditions, but radical personalism seems to make this impossible.

D. Elaboration of normative version of the problem and relation to foundationalism. The normative problem and, indirectly, the practical problem, arise from the attempt to use JC as a way of doing away with strong foundations.

II. Solution to the problem found in foundationalist model.

A. Pearl's version of solution based on screening off and the introduction of certain evidence.

B. My version, similar to Pearl's but with different emphases. (Handout below) Under the conditions as stated, screening off is both a necessary and a sufficient condition for rigidity of posteriors.

III. Epistemic relevance of the solution--The strong foundationalist has a complete, non-arbitrary condition for the applicability of JC. A moderate foundationalist or a personalist does not have this. A strong foundationalist holds that all differences in rational credibilities arise ultimately from differences in the foundations. A change from one rational probability distribution to a different one thus must be occasioned by a change in the foundations, though this change may manifest itself by way of its impact upon various intermediate premises.

IV. Two objections and replies.

A. Accessibility

1. Why should the screening-off condition be any more accessible than the rigidity condition itself?

2. Psychologically, it may well be easier to access rigidity if we can get at a reason underlying it. But epistemologically, it is rationally preferable to have a reason for rigidity in any event, whether the SO condition is more easily accessible or not.

B. The fate of Jeffrey Conditioning in a foundationalist epistemology

1. Doesn't the reintroduction of strong foundations make JC irrelevant, as Jeffrey seemed to assume? And isn't that an argument against their reintroduction, since JC does seem so useful?

2. No, it does not, because epistemic routing is real.

a. Brief description of epistemic routing and of Jeffrey's early misquotation of C.I. Lewis. Jeffrey's early use of Lewis implied that foundationalists take all non-foundational propositions to be based directly on the foundations. Jeffrey even implied that the search for foundations arises from an inability to "see how uncertain evidence can be used." (Later, he seemed to realize that this was not a correct representation of foundationalism, though he never appeared to notice the actual misquotation, but he still considered JC to be necessary since certain foundations are unavailable.)

b. Relation of epistemic routing to the continued relevance of JC in analyzing epistemic structure. Since uncertain beliefs are often not based directly on the foundations, JC is important in showing us the fine structure of a rational cognitive corpus; it allows us to see how shifts in the foundations make a difference to the probabilities of intermediate premises and thereby to other inferred beliefs.

Handout

Take the definition of screening off according to which E SO p from H on some background k iff P(H|E & k) = P(H|E & p & k).

Suppose that k- is some body of given background evidence that does not include p. Now assume that, in the old evidence situation, p is not present. k- consists of S's given background information but does not include p. Then,

prob (H|E) =def. prob (H|E & k-)

(Note that this does not mean that E SO k- from E, as the k- is merely suppressed on the left side and expressed on the right.)

Assume that the only difference between prob and PROB is the addition of p at probability 1. Hence

PROB (H|E) = prob (H|E & p & k-)

Suppose that the addition of p does make a difference to the probability of E, so that

prob (E) … PROB (E),

although neither value is 1 or 0. Suppose that E and H are intermediate-valued propositions in both probability distributions and that we are wondering whether we can use JC to model the change in probability of H as a result of the shift in probability of E.

Now, on the one hand, suppose that E SO p from H on k-. Then,

prob (H|E & k-) = prob (H|E & p & k-)

Therefore, by definition of SO, rigidity holds under these circumstances, that is, prob (H|E) = PROB (H|E), since the two terms in the above statement equal, respectively, prob (H|E) and PROB (H|E). So, under the circumstances as described E SO p from H is a sufficient condition for the rigidity of the posterior. Under these circumstances, it is also a necessary condition. For suppose, on the other hand, that E does not SO p from H on k-. Then,

prob (H|E & k-) … prob (H|E & p & k-).

Hence, in the circumstances as described,

prob (H|E) … PROB (H|E).

So, when the only change is the addition of some piece of certain evidence p, E SO p from H on k- is both a necessary and a sufficient condition for the rigidity of P(H|E).

For JC, we would also have to see that a similar screening-off condition held for P(H|-E), and the argument would proceed as above, mutatis mutandis.