First, I want to clarify my views on the previous post. I take it to consist of two parts: (1) a thought experiment; (2) a diagnosis of my own intuition regarding that thought experiment. My intuition regarding the thought experiment is just that Kurt doesn't know that p, the conclusion of his proof, at time t1 (or t3). Part of my diagnosis was that knowledge must be stable in the sense that we can't gain and loose knowledge over relatively short intervals of time.
Unfortunately, the way the the post is written, I am arguing that Kurt doesn't know on the basis of the claim that knowledge can't be unstable. I think it is clear from the discussion that this latter claim is generally false. Nevertheless, I am left with the intuition that Kurt doesn't know that p at t1 (whatever the diagnosis). If that intuition were to hold up, the case would be a nonGettier-style counterexample to JTB. Alas, others fail to share my intuition.
Still, I do think that the instability claim isn't that far from the truth. My reasons may be related to Schaffer's view that knowing is fundamentally knowing the answer (knowing-wh). Specifically, the veracity of our claims to knowledge may depend on our purposes in making them. If I claim to know that p for some purpose R, the nature of R may well affect how stable my knowledge has to be. Here's an example:
The other day I was going out of town and was supposed to call some friends when I got into the airport. My wife wrote their number down and I glanced over it. As I was leaving, she reminded me to take the number. I said, "I know it" and proceeded to recite it from memory. Knowing that the number was still fresh in my mind her response was, "Do you really know it?"I think her question was exactly right. It was not necessary for her to ask, "Will you know it (at the relevant future time)?" Specifically, in order to correctly claim to know that our friends' number was such-and-such, my belief that their number is such-and-such had to be sufficiently stable that I would still believe it when I got to my destination.
There is another aspect of the example I find interesting. It seems to me that my wife's use of "really" here is designed to contrast my knowing the number with merely feigning knowledge. In this case, reciting the number from memory counted as merely feigning knowledge (since she rightly surmised that I hadn't sufficiently internalized it). But at that point in time, I clearly had a justified, true belief that our friends' number was such-and-such!