JE: The belief that p is part of what justifies S in believing that q only if p is included in S’s evidence.
I think this principle is an assumption in C & K's attack on Williamson. Is it true? That is difficult to say. Here's an argument that it's not, inspired by Dodd's criticism of Williamson and some stuff Pryor has been dealing with because of his dogmatism. Suppose that p is the belief that I have hands and it is supported by experience. Let's say that the experience is the evidence for p. If you accept dogmatism, you'll say that the evidence of the senses could suffice for justified acceptance of p even though p is not certain given the evidence. But, then it seems that once p is itself part of the evidence, the evidential probability of p raises from some value less than 1 to 1. More plausible, I think, to say that if you accept that you can justifiably accept p on the basis of evidence that leaves p less than certain, that is precisely why justified acceptance of p does not necessitate p's inclusion in your evidence.
I haven't checked, but I think this deals with C & K's argument that E = K is incompatible with closure as well.
I haven't addressed Juan's comments yet, but I have a very rough draft.