Suppose we think that knowledge is the norm of assertion (hereafter the K/A thesis), and suppose that a given speaker S asserts p. Further, suppose that the assertion satisfies the norm of assertion. Suppose S is then asked why S asserts p, and S says, “Because I know that p is true.” Question: could the first assertion be acceptable and the second one not?
One way to argue for the “yes” answer is to appeal to a denial of the KK thesis: the KK thesis is false, so it is possible to fail to know that you know, and since knowledge is the norm of assertion, it follows that the second assertion could be improper while the first isn’t.
I hereby prohibit such an argument. OK, more weakly, please don’t give this argument. It cheats in the context of finding out what the norm of assertion is. We should look at the practice of assertion and try to describe features of a situation that would make the second improper and the first proper. If we can’t find such features, then adopting the idea that knowledge is the norm of assertion will conflict with our denial of the KK thesis. So, bracketing any argument that directly employs the falsity of the KK thesis, can we imagine faulting S for the second assertion but not for the first?
So, suppose we grant that it is true that S knows that p, but questions whether this knowledge claim is assertible for S. There is a “trickle-down” problem here. Think of a usual account of knowledge: some kind of undefeated justified true belief. The trickle-down problem is most obvious in the case of the truth clause: if the truth clause for the meta-claim is false (i.e., if it is false that S knows that p), then the K/A theorist is forced to classify the first assertion as improper. How about the other conditions for knowledge. Could we assault S’s sincerity: “you don’t believe that, do you?” Suppose S blushes or cringes, admitting that s/he doesn’t really think s/he knows. Then S should take back the original assertion, since it is perfectly legitimate ask for a better explanation of why S said that p. Since the only story available to S to explain/justify asserting p depended on knowing p, S’s admission amounts, in his/her eyes, to an admission that nothing justifies asserting p. So S will (or should) say, “Sorry, I should have said either of the things I said; the second I don’t believe and without it, I’ve got no good reason for the first. So I take back both of them.” So assaulting sincerity has the same trickle-down effect as assaulting truth.
What of the other conditions? “Does S really have sufficient evidence that the evidence for p is adequate?” Suppose the answer is “No,” leading the K/A theorist to disallow the second assertion. One feature of evidence sufficient for knowing, however, is that it is also evidence that justifies concluding that one’s inquiry need proceed no further. It is evidence, that is, for the experience of closure to further investigation that is appropriate when one has knowledge. It is evidence that one’s evidence for p is more than adequate to conclude p; it is evidence that no further inquiry is needed. (Now you have 3 different claims to consider, which isn’t quite fair on my part, but I’ll refine later if that’s the issue.)
But maybe S is just wrong about this; maybe S has sufficient evidence of the sort in question but thinks otherwise. No argument can be mounted from this quarter. On some views, such thoughts are not relevant except at the next level up, the level where we ask whether you know that you know that you know (on these views, you can think you don’t have adequate evidence and just be wrong). To make such thoughts relevant, we have to adopt the view that there can be merely subjective defeaters for justification, that thinking your evidence is weak is itself a defeater of the confirming power of that evidence. But then the trickle-down effect can’t be stopped. If the subjective defeater undermines knowing that you know, it will undermine your evidence that further inquiry is not needed, and hence will undermine your justification for thinking that p.
Finally, is there a way for a gettier condition failure to undermine the second assertion without undermining the first? I don’t have an argument for ruling out this possibility entirely. The best I can come up with for finding such an example is this: suppose S’s meta-claim is gettiered because a trusted professor asserts (out of hearing range), “no one can know whether or not they know.” (Stop laughing: some professors really are trusted!… Oh, you were thinking of epistemologists… never mind…) So suppose S were to come to know that the professor said this. For a gettier situation to occur, we have to assume that S would no longer be justified in thinking that s/he knows. But then it is hard to see why the trickle down phenomenon doesn’t occur, especially since the first assertion’s legitimacy depends on S’s total evidence establishing both that p is true and that further inquiry could undermine present opinion only by revealing misleading information. It is the latter part here that threatens to trigger the trickle-down effect. The argument for trickle-down goes like this. Imagine S to be perfectly rational, so that S concludes, “I don’t know whether I know that p.” Then imagine S considering the question of whether his/her belief about the point of further inquiry is itself justified. S should reason as follows, shouldn’t s/he? “Well, I’ve no good reason to conclude that I know p, so further inquiry might have a point. Since I might not know, my evidence can’t be sufficient to justify an closure experience I’m having with respect to further inquiry about p.” And in fact, since we’ve imagined S to be perfectly rational, any closure experience S might have had with regard to further inquiry will have disappeared as a result of becoming uncertain whether s/he knows. Since these claims are claims about what the total body of evidence supports, the reasoning S would go through yields further facts about the total body of evidence, facts that remain even when we drop the idea that S actually goes through this line of reasoning.
OK, there’s lots here that is suspicious. The arguments themselves might have problems, and the most obvious suspicious point is that I need to be able to generalize from the one gettier case I’ve used. The arguments suggest, though, that the K/A theory might be in conflict with facts about how the KK thesis is false.
(One last word: If you’re a J/A theorist about the norm of assertion (that epistemically justified belief is the norm of assertion), you can grant all of the above arguments and still embrace the ways in which the KK thesis is false. Since epistemic justification is no guarantee of truth, you might know that p is true and not know that you know this, even though you are epistemically justified in believing both claims. That is, the J/A theorist might have to admit that both assertions stand or fall together on the basis of the above arguments, but that only commits the J/A theory to some kind of JJ thesis, not to any denials regarding how the KK thesis can be false.)