Reverse Lottery Stories
Reverse lottery stories, which focus on the fortunate holder of the winning ticket, raise different issues.1 Here is an example. Imagine again a fair lottery with one thousand tickets. The winning ticket has been selected, but there will be no announcement of the winner until tomorrow. S herself did not witness the drawing and has not heard a report from any of those who were present, nor has she seen the script for tomorrow’s announcement. She nonetheless believes that she has been lucky and her ticket T345 has won. Moreover, she is right. She has in fact won. Despite having a true belief, she does not have knowledge, but what are the important gaps in her information?
There is no shortage of candidates. Had she witnessed the drawing or heard the report of those present or read the script of tomorrow’s announcement, she would have been in a position to know, but she hasn’t, and hence these gaps are available to explain why she doesn’t know.
On the other hand, suppose that no information of this sort is available. No one was allowed to witness the drawing; a secure device was used to select the winning ticket in utter secrecy; and this device was programmed, again with complete security, to generate the announcement tomorrow.
Even so, there are other kinds of information she might have had. If she had somehow been aware of the exact position of her ticket in the drum, the rate of the drum’s revolutions, the detailed workings of the device that was used to draw the winning ticket from the drum, and the precise time at which the ticket was drawn, she might have been in a position to know, and not just correctly believe, that her ticket has won. But then, once again, her lacking such information is available to explain why she doesn’t know. She lacks knowledge because given the security surrounding the drawing, she has no direct information about which ticket has won, nor does she have detailed enough information about the workings of the drawing to infer that her ticket has won.
Suppose, however, that a random number generator was used to pick the number of the winning ticket. S correctly believes that this is how the winner has been chosen, and she also correctly believes that her ticket has been picked. What then?
If “random” here means what it means in everyday contexts, it does not imply that the outcome could not have been predicted with enough information about initial conditions and the mechanisms used by the number generator but rather that we don’t have enough of this information. So, we cannot infer which ticket has been chosen, but in principle someone with sufficiently precise and detailed information could have done so. If the number generator is random in this sense, there again is no shortage of truths S lacks that are available to explain why she doesn’t know.
On the other hand, suppose we push the story to its limits by imagining that the processes by which the winning ticket is picked are governed by indeterministic laws, and even relative to full information about these processes and the initial conditions, it is highly improbable that her ticket has won. S correctly believes that the lottery is in this way indeterministic but nonetheless thinks that the improbable has occurred and she has won, and she is right. Even so, she does not have knowledge. Moreover, she would not seem to know regardless how complete a grasp we imagine her having of the initial conditions and relevant mechanisms.
In particular, suppose it is Sally, whose beliefs are maximally accurate and comprehensive, who holds ticket T345. She believes that her ticket has been chosen the winner, and this belief is true. Given the complete security surrounding the drawing, there is no available information about the current situation that would indicate to her that her ticket T345 has won. She does have maximally accurate and comprehensive information about prior conditions and the processes used to pick the winning ticket, but this information doesn’t put her in a position to infer that she has won. On the contrary, she is aware that relative to this information, it is highly unlikely that she has won. Hence, under these conditions, it would seem that not even Sally knows.
Why is this? Whenever there is a knowledge story far removed from the ordinary, it pays to take a step back in order to assure ourselves, first, that the situation as imagined really is possible and, second, if we judge that it is indeed possible, whether our intuitions about it are the same once we more appreciate in some detail what the situation would look like.
In reexamining the story here, one question that arises is whether its details are inconsistent with the assumption that Sally believes her ticket has won. After all, as the story has been told, she has maximally accurate and complete information about prior conditions and processes, and she correctly believes that relative to this information, it is highly improbable that hers is the winning ticket. But if one believes that a proposition is highly unlikely, it is not obvious that one can simultaneously also be confident enough of its truth to be said to believe it. At the very least, there is enough ambiguity about this to help explain why we are reluctant to grant that Sally has knowledge. It is less than clear that she can know that her ticket has won because it is less than clear that she can even believe this, given that by hypothesis she believes it highly unlikely to be true.
Suppose, however, we were willing to grant for the sake of argument that Sally does in fact believe that her ticket has won. What then? Then there would be another problem, a problem that can make it appropriate to invoke blocking conditions. For under the circumstances now being imagined, Sally’s having fully accurate and comprehensive beliefs would involve her having irrational beliefs, since she simultaneously would have to believe both that T345 is the winning ticket and also that it is highly improbable that this is so.2
Earlier I noted that there may be arguments to the effect that Sally’s beliefs couldn’t possibly be maximally accurate and comprehensive without also meeting minimum standards of rationality.3 Here the situation being imagined is reversed; she cannot have maximally accurate and comprehensive beliefs about certain matters without also having highly irrational beliefs about these same matters. But if circumstances are indeed structured in this way, we may want to conclude it is impossible for anyone to know, that knowledge is blocked.
Recall the previous discussion of blocking conditions, which were introduced as a way of dealing with extreme cases. Since intuitions about such cases are apt to be diverse, the suggestion was that blocking conditions be introduced as a way of explaining why a subject might seem to lack knowledge even if she has a true belief and seems not to lack important information. The further suggestion was that blocking conditions be construed in terms of some kind of minimal standard that is not being met. In the beetle in the box story, it was minimal standards of information that were absent. Here in this revised Sally story, it seems to be minimal standards of reasonability.