John Hawthorne gives the following example:
I ask S whether she agrees that P. She asserts that she does: “Yes,” she says. I then ask S whether she realizes that Q follows from P. “Yes, ” she says. I then ask her whether she agrees that Q. “Im not agreeing to that,” she says. I ask her whether she now wishes to retract her earlier claims. “Oh no,” she says. “I’m sticking by my claim that P and my claim that P entails Q. I’m just not willing to claim that Q.” Our interlocutor now resembles perfectly Lewis Carroll’s Tortoise, that familiar object of ridicule who was perfectly willing to accept the premises of a modus ponens argument but was unwilling to accept the conclusion…
This example is supposed to provide an argument for a closure principle about knowledge, in some way depending on the idea that you aren’t supposed to assert what you don’t know to be true. I don’t see how to reconstruct the argument using this knowledge norm, but that’s not the point I want to pursue here.
Instead, I want to consider whether we can expand the above case so that S turns out not to be a ridiculous assertor, but a sensible one. If we can, we won’t have shown that closure is false, but we will have undermined any simple argument from S’s ridiculous stance here to a closure principle.
So suppose S thinks about epistemology on occasion, and thinks there is an order of knowledge among types of knowledge claims. She thinks, that is, that some things can’t be known on the basis of other things. She isn’t sure whether there is a way of ordering claims, even a partial ordering, so that we can always say what has to be known before what. So she sticks with the negative characterization of epistemic priority just given.
She’s talking with Dretske. He says to her, “Is that a zebra?”, and she says, “Yes”. Dretske says, “Do you realize that it can’t then be a disguised mule?”, and she says, “Yes,” again. Dretske smiles, but Hawthorne is perturbed. He taps her on the shoulder, with the verve of expression characteristic of his nature: “so it’s not a disguised mule, right?” She says, “I’m not comfortable saying that yet. I can see it’s a zebra, and that this implies that it’s not a disguised mule. But I can’t learn that it’s not a disguised mule like that. And now that Fred points out the implication to me, I’m unsure of how or whether I know that it’s not a disguised mule.” Hawthorne then says, “So, I take it, you’ll want to retract one of your earlier claims.” “No,” she says, “I’m not questioning whether it’s a zebra–it is, I saw it–but I’m not sure I should be claiming that it’s not a disguised mule, since I can’t know that claim by inferring it from the zebra claim, and without knowing it in that way, I’m really not sure how I know it at all. So I think for now I should just remain silent on the point until I get this figured out a bit better, or until I go check to make sure it’s not a disguised mule.” John presses a bit: “You do agree that it has to be a non-mule, right?” “Yes, but I hesitate, not because the claim might be false, but because I’m not sure I’m entitled to be saying anything about it at this point.”
The point of expanding the story in this way is this. S is not a ridiculous assertor in this story. She is confused and there are various possibilities to explain how she can sensibly find herself in this predicament. One is Dretske’s explanation that closure is false; another is that closure is true, and she’s presupposing the idea that you shouldn’t assert a claim when you’re not sure that, or how, you know it to be true. Whatever the explanation, however, one can’t accuse her of being like Lewis Carroll’s tortoise, and so one can’t infer from the expanded story that denials of closure are somehow incompatible with the practice of non-ridiculous assertion.
There’s a quicker way to put this point, if you’ve read Stew Cohen’s piece on easy knowledge. In the expanded story, S is bothered by the problem of easy knowledge and so ends up talking in a way that may look like a denial of closure. Since there are other plausible ways of making sense of her responses that don’t require a denial of closure, there’s no reason from the sensibility of her responses here to deny closure. But neither is there a good reason to say that she is a ridiculous assertor, and take that as evidence for closure.