Believing and knowing that if A then B
Sue believes that rain will stop the match, but is unsure whether it will rain. Does she believe that if it rains, the match will stop? Yes, says intuition. No, say those who think that conditionals are not propositions, since what is believed has to be either true or false. Question: how might such a view - call it `NPC’ - account for intuition?
Jill knows that rain will stop the match, but is unsure whether it will rain. Does she know that if it rains, the match will stop? Yes, says intuition. No, says NPC, since what is known has to be true. Question: how might NPC account for intuition?
One might respond to the first question as Edgington (1995) does: Sue’s purported belief that the match will stop if it rains is not really a belief that something is true, but a conditional belief that the match will stop, given that it rains. To grasp the difference between beliefs and conditional beliefs, compare bets with conditional bets. A bet on `The match will stop’ is settled by either a win or a loss, but this is not so for a conditional bet that the match will stop, given that it rains. One wins the conditional bet given that it rains and the match stops, and loses it given that it rains and the match does not stop. But supposing it does not rain, the bet is called off. In short, the conditional bet is not something that is either won or loss; rather, it is something that is either won or loss, given that it rains. Analogously, Sue’s conditional belief that the match will stop if it rains is not something that is either true or false; rather, it is something that is either true or false, given that it rains. The conditional belief is true given that it rains and the match stops, and false given that it rains and the match does not stop. But it is not a belief that something is true, because given that it does not rain, it is neither true nor false. (See Edgington, 1995, p. 290).
Granting that the above response is satisfactory, how will a parallel response to the second question fare? I think it depends on whether the notion of conditional knowledge, if it’s not just knowledge that certain conditionals are true, makes sense. One may conditionally believe something, but can one conditionally know something? In many (but not all) cases, if one has a conditional belief that B given A, then one is disposed to believe B upon believing A. Does it make sense to claim that in such cases, if one has conditional knowledge that B given A, then one is disposed to know that B upon learning A? I’m inclined to say `No’, but I’m not sure.
Perhaps one might claim that when we say `Jill knows that the match will stop if it rains’, we really mean `Jill knows that C’, where `C’ (which may be something like `Rain will stop the match’) grounds the conditional. The obvious reply to this is that in uttering the former, we most definitely do not mean the latter. Also, arguably, there are things we know even if we have forgotten the grounds for them.
Is there any other way that a proponent of NPC may explain (or explain away) the intuition that Jill knows that the match will stop if it rains?
References
1. Edgington, Dorothy (1995). Mind, Vol. 104: 414, pp. 235-329.
May 5th, 2007 at 12:59 pm
Great question. I think it is certainly intuitive that there is conditional knowledge. But it does lead to problems. E.g. take a version of the Sly Pete case where A knows that Pete has a 3 or a 5, and B knows that Pete has a 5 or a 7. Then intuitively, A knows that if Pete doesn’t have a 5, he has a 3, while B knows that if Pete doesn’t have a 5, he has a 7. We can even allow that B has seen the 3 elsewhere, so that B knows that it’s not the case that if Pete doesn’t have a 5, he has a 3. But it’s not really clear how all of these things can be knowledge! It’s certainly hard to see how they can all be true. I suppose that one could go contextualist/relativist about truth here. But I suppose a fallback position would be to allow that there’s justified conditional belief in these cases, without bringing in an analog of the truth requirement.
May 6th, 2007 at 11:41 am
The same problem seems to arise for other factive embeddings: Sue proved that if A then B; Sue learned that if A then B; Sue realized that if A then B; Sue forgot that if A then B; Sue remembers that if A then B; Sue regrets that if A then B.
Reinterpreting all these constructions for the special case in which they embed conditionals doesn’t look very attractive. Also, the inference from “Sue knows that if A then B” to “if A then B” seems okay, which it wouldn’t be if knowledge here were merely justified belief. And all is fine in the Sly Pete case if the embedded conditionals are material, right?
Perhaps the NPCer could accept that conditionals are true in a disquotational sense, without corresponding to any facts. That is, among the things I commit myself to by saying “Sue knows that if A then B” would be whatever I commit myself to by saying “if A then B”. This would be a kind of quasi-realism a la Blackburn and Gibbard wrt morality (if I recall correctly).
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