This may be the second in a series of fairly silly posts inspired by the APA Central meeting, tho' I may try to slip some philosophy into this one.
As I mentioned, the Central was during a no-beer period, so I was drinking wine the whole time. (When I was drinking, I mean. Couldn't find any Woodchuck.) At one point I found myself drinking wine in the bar of the Hard Rock Hotel, which I hasten to add was not my idea. I said to my companions, "This is not really a good wine. And if I can tell this is not a good wine, it means something."
MC said, "It means it's really awful."
This, I think can give us some insight into the KK thesis.
[But before I begin: I did not really use any of the wisdom of Winesmanship (scroll down). My current gambit is to say, in any context where no one will be actually insulted by this, "Quaffable but not transcendent"--in an inverted-quotes tone meant to demonstrate my ironic awareness of my lack of wine knowledge, appearing to deprecate myself while actually attempting the damn-good chap "Blindfolded experts can't tell red from white" gambit (see Pop-skull--scroll down again). This is especially Lifemanlike because I haven't even seen the movie I'm quoting.]
I think I could appropriately reason something like this. I'm going to stipulatively change "really awful" to "fairly bad," for reasons that will become apparent.
1. This is not a good wine. [judged immediately on tasting]
2. I have judged, with complete confidence, that this is not a good wine. [by introspection]
3. I know that this is not a good wine. [from 2--I have no reason to doubt my judgment.]
4. If I know by tasting it that wine is not good, it must be pretty far from good--fairly bad. [I am familiar with my limited capacities as a judge of wine]
5. This wine is fairly bad. [3, 5--and 2!]
Now, I think I know 1-5. In fact, I'd be happy to assert that I know 1-5. (Though I don't think that that means I know I know 1-5, since knowledge isn't the norm of assertion.)
There are two points where I think you might object to my claim that I know 1-5. You might think I don't know 3, and you might think that I don't know 4.
It may look like 3 comes from 2 by the application of the KK thesis--if I know p, I must be in a position to know that I know p. Well, it could come from such an application. But this time it doesn't. It comes from my ability to know what my judgements are and to reflect on them.
And it may look like, though 4 is true, I don't know it. But I do know it. I know my palate well enough to know that it's not very sensitive (and I don't know much about wine), so that whenever I can judge with complete confidence that a wine is not good by taste alone the wine is really fairly bad.
In fact, I can judge with complete confidence that the wine is fairly bad. Because I am confident in my reasoning abilities, and my knowledge of my palate, even if I'm not always confident in the palate itself. So not only do I know 5, I think I know that I know it.
Now compare this possible reasoning--if my immediate reaction had been "this wine is fairly bad":
1'. This is a fairly bad wine. [judged immediately on tasting]
2'. I have judged, with complete confidence, that this is a fairly bad wine. [by introspection]
3'. I know that this is a fairly bad wine. [from 2'--I have no reason to doubt my judgment.]
4'. If I know by tasting it that wine is fairly bad, it must be very bad indeed. [I am familiar with my limited capacities as a judge of wine]
5'. This wine is very bad indeed. [3', 5', and 2']
Same goes throughout. I think I know every step, and I think at the end I know that this wine is very bad--and indeed I know that I know it.
But in the initial case, can I continue to reason as follows?
5. This wine is fairly bad. [as before]
6. I have judged, with complete confidence, that this wine is fairly bad. [introspecting on 5]
7. I know that this wine is fairly bad. [from 6--no reason to doubt my judgment]
8. If I know that this wine is fairly bad, it must be very bad. [familiarity with my limited capacity]
9. This wine is very bad. [7, 8]
I cannot. 6 and 7 are OK, but 8 is wrong. The reason 8 is wrong though 4' is right is that in this case I do not know that the wine is fairly bad by tasting it; I know by tasting it and by reasoning about my limited capacities. That doesn't support the further inference to 9.
This is all by way of picking on Timothy Williamson. His models of knowledge in Knowledge and Its Limits lay heavy emphasis on the margins for error required for knowledge; so that S typically is in no position to know that some quantity x is no less than 5 unless x is at least 7 or so. Williamson considers that possibility that the margin for error varies with the value of x (in the previous example, the margin for error at 5 is 2; maybe the margin for error at 8 is 0.5, so that S is no position to know that x is no less than 8 unless x is at least 8.5).
He never, IIRC, models the possibility that the margin for error depends on how knowledge is acquired. That is, he never models the possibility that S is not in a position to know by perception that x is no less than 5 unless x is at least 7, but S may be in a position to know by inference that x is no less than 5 if x is greater than 6. That's what's going on here. I'm in no position to know by taste that the wine is fairly bad unless it's very bad; but I may be in a position to know by taste and inference that the wine is fairly bad even if it is only fairly bad.
And this suggests, perhaps, that the examples that threaten the KK principle--if you know that p, you're in a position to know that you know that p--don't threaten the KKK principle--if you know that you know that p, you're in a position to know that you know that you know that p. Frequently KKp will be true because you reflected on your judgment that p, and saw that it amounted to knowledge. It's not obvious that in these cases you won't be able to reflect on your reflection, and see that it amounts to knowledge to--so KKKp will also be true.
This may be laid down to Delia Graff's observation that knowing that you know that you know that you know that you know that you know something is not very clear at all. But I think Williamson runs into problems with respect to this, that show up even if we stick to two levels of knowledge. I'll post something about that sometime in the next couple of weeks. (But if you check the blog once a day, you won't know that I've posted about this that day until you actually check the blog.)Posted by Matt Weiner at May 3, 2005 04:13 PM