Sunday, March 28, 2010

Disagreement and Defeat

Just some whataboutery. Here's a diagram:

Diagram:
_______________________
A eating with B


C eating with D spying on A.
_______________________

Let's suppose that C and D are spying on A. Initially, C doesn't see B. A is calculating the tip and C and D are watching her. C and D know that A is really good at math. They see that A has calculated 20% of the check correctly (they use a calculator to check her math (and theirs)) and know she believes that the tip is $12. I think it's safe for C to say to D:

(1) A knows that the tip is $12.

Now, D knows something A doesn't (yet). D knows that A is dining with B, one of A's epistemic peers. D knows that B has calculated tip and come up with an answer that differs from A's ($11). D tells C that B has an answer that differs from A's and so asks whether C would like to retract (1).

(i) I think, at this stage, C doesn't have to retract (1) or say (1) isn't true any longer.

D then informs C that B is about to reveal that B's answer differs from A's.

(ii) I think, at this stage, C doesn't have to retract (1) or say (1) isn't true any longer.

D then informs C that B has revealed that B's answer differs from A's but that this has no impact upon A's attitudes at all.

(iii) I think, at this stage, C doesn't have to retract (1) or say (1) isn't true any longer.

If (i)-(iii) are right, is this trouble for the equal-weighter? Maybe my intuitions are off, but I think (i)-(iii) are right and it's weird to think that this is right but then to add that A's justification is defeated by virtue of the revelation of a disagreeing peer. (Knowledge does, after all, entail justified belief and it's hard to see how the equal weighter could say that A's belief in this case could be justified post revelation.)

If equal weighters are supposed to deny (i), (ii), or (iii), which should they deny? I think you don't want to deny (i). I don't think it's a necessary condition on having knowledge based on calculation that you cannot have a peer that shares evidence that could come to a different answer. But, if you accept (i), why can't someone like A know that there could be peers out there and just react to the observation that there's an actual disagreeing peer rather than a merely possible one by shrugging her shoulders and saying that the tip is $12.

3 comments:

Sean Landis said...

I thought the disagreeing tip cases are usually about what to do BEFORE you recheck your work. It seems your use of a calculator to check A's math brings about a relevant asymmetry in favor of A's position, so I don't see how this is a counterexample to the EW view.

Now, if C & D didn't do this rechecking, I'm not inclined to accept (i).

Clayton said...

"I thought the disagreeing tip cases are usually about what to do BEFORE you recheck your work."

That's right. But, I also think that since the calculator isn't used by A to check A's work but is used by an outside observer, our intuitions about the correctness of this outsider's knowledge ascriptions might show something interesting about the disagreement cases which (I think) typically focus on the subject's perspective and might distort things because of that. What C and D do is not something A is aware of and while my K-ascription intuitions might be off, I'm tempted to accept (i)-(iii).

Sean Landis said...

Ah, I understand the case better now. It seems to me that (iii) is the claim to deny. A's awareness of an actual disagreement is relevant.

In his 2005 paper, Tom Kelly puts forward the same line of reasoning as you seem to toward the end of your post: actual disagreement doesn't seem to be more significant than merely possible disagreement. However, Kelly retracts this argument in his later paper (on page 23) because the fact that one has responded correctly to the evidence is not transparent. We may always in some sense recognize our fallibility (and so recognize that peers possibly disagree with us), but when presented with an actual peer who disagrees, this is much stronger evidence that we are, in fact, wrong in this case (even in cases when we're actually right!).