Problems for Pritchard's def of Luck

If luck is to be the conceptual anchor for an analysis of the 4th condition on Knowledge, then non-lucky justified true belief should entail knowledge. That is, the following entailment should hold

(P) JTB~L --> K

Rich Feldman and I (and others for all I know, since I think the case suggests itself) independently came the same sort of counterexample to that entailment if luck is interpreted as Pritchard suggests:

(L1) If, an event is lucky, then it is an event that occurs in the actual world but which does not occur in a wide class of the nearest possible worlds where the relevant initial conditions for that event are the same as in the actual world. (p. 128)

He latter adds that the event must matter to a subject, but I think we can gloss over that and over what the relevant initial conditions are, for I don't think either make a difference to the counter-example. He also considers strengthening the definition so that there are very few nearby worlds in which the event in question does not hold. The c-e skirts that as well.

What I did was to take some counter examples which he considers and add "and it's a natural law that ___" to them. Since natural laws are crucial to ordering worlds (L1) will allow cases of the following form:

(~P) JTB~L & ~K.

Rich's approach, as is not surprising, is more direct. He simply takes a justified true belief about a natural law *itself*. So consider the following belief

(B) Law L holds in W at t.

as held by S in W at t. Suppose (B) true and suppose it justified for S at t. Finally, suppose that S is gettiered w.r.t (B). Since we have assumed that (B) is JTB, if it is ~L but ~K then we've got a case of the form of (~P) and thus a c-e to (P).

So now consider the ordering of worlds around W. Since L's holding is the most important (at least one of the most important) features of W there will not be a large class of worlds near W in which (B) is false. Thus (L1) fails to count the case as one of inappropriate epistemic luck.

Not all epistemic luck is vicious. There are several kinds of benign epistemic luck (EL).

Content EL: It is lucky that the proposition is true.
Capacity EL: It is lucky that the agent is capable of knowledge
Evidential EL: It is lucky that the agent acquires the evidence that she has in favour of her belief.
Doxastic EL: It is lucky that the agent believes the proposition.

For each of these Pritchard is willing to grant that they do not *necessarily* bar knowledge. I'm not sure if he thinks that they *can* destroy knowledge. The last seems to me to be able to bar knowledge in some circumstances.

There is one kind of luck which is said to be incompatible with knowledge

Veritic EL: It is a matter of luck that the agent's belief is true.

I assume this is more than the conjunction of Content EL and Doxastic EL, but I'm not sure.

At any rate. The way the c-e is set up it will be a matter of luck that the agent's belief is true. Because of the cruciality of natural laws in ordering worlds, there will not be a significant number of nearby worlds in which it is not the case that the agent's belief is true.

So I think it's back to the drawing board on the definition of luck, but, as I said, I'm still hopeful that a suitably defined notion of luck can do the work which Duncan assigns to luck in the analysis of the 4th condition on knowledge. That's a separate debate though.