Here's what Zagzebski says. She understands Gettier as having refuted the JTB theory thus: imagine a case in which JB but not T. Now change the case so that T, but just by luck -- not in a way connected to JB. Now you have a Gettier case -- an intuitive counterexample to K = JTB. That's what she said Gettier did. Then she says we can generalize the argument. Her target is any view that tries to analyze knowledge as T + X, where X doesn't entail T. Do just the same thing, she says, as Gettier: take a case in which X and not T (guaranteed possible), then tweak the case so as to make T true in a way unrelated to X.
(One might worry here as to whether this latter step is always possible. Juan Comasaña told me via Twitter that he wants to resist the argument here. I have a hard time seeing how it couldn't be done, for any X that's plausibly natural enough to figure into an analysis. We'd need X to be consistent with not-T, but for X & T together to entail that X and T are closely connected. That seems, at least, really weird. Maybe there's an argument lurking that this is impossible? Or maybe it's possible after all? I'm not sure. Thoughts? Anyway, this isn't the point I wanted to press.)
Ok, so, modulo the parenthetical, we've generated a case according to Zagzebski's recipe. Now, she tells us, we have a counterexample to the K = T + X theory. She offers:
...a general rule for the generation of Gettier cases. ... Make the element of justification (warrant) strong enough for knowledge, but make the belief false. ... Now emend the case by adding another element of luck, only this time an element which makes the belief true after all. The second element must be independent of the element of warrant so that the degree of warrant is unchanged. ... We now have a case in which the belief is justified (warranted) in a sense strong enough for knowledge, the belief is true, but it is not knowledge.
What's interesting about this passage is that she's making a general claim about the ultimate outcome of all instances of her argument schema. But the original Gettier argument, it is traditionally thought, depends on a particular sort of judgment about a particular case; we think about the story about Smith and Jones and Brown in Barcelona, and see that this is a case of JTB without K. If that's right, then it's totally mysterious how Zagzebski or anyone could be confident that the same pattern will hold of other attempts to analyze. But the argument isn't a non sequitor; it's (at least) prima facie compelling. Why?
At a workshop on thought experiments I attended in Brazil this summer, Anna-Sara Malmgren suggested that thought experiment judgments carry with them a kind of implicit generality that is best explained by their being products of nonconscious inferential reasoning. This, it seems, might be just the sort of case to support her suggestion. Our initial Gettier judgment constituted a kind of commitment to a general principle that rules out the kind of luck that Zagzebski is focusing on. If that's right, then metaphilosophical emphasis on cases may be misplaced; lots more of our thought experiment judgments may be more based on theory than is always realized. Without a move like that, it's hard for me to see how Zagzebski's argument could make any sense.