Our common ways of thinking about the lottery pose problems for our conceptions of knowledge.
Plato is considered responsible for a definition of knowledge, which dominated thinking in epistemology for thousands of years: knowledge is justified true belief. What else could it be? The idea that knowledge is justified true belief remains appealing – even to those who are convinced it isn’t strictly true.
Rene Descartes looked for certainty in knowledge by first challenging himself to skepticism and then trying to answer to it: consider that, for all you know, there could be an evil demon tricking you so that everything you “know” is wrong.
Maybe we can avoid skeptical worries by accepting that probability based on evidence is enough to justify our beliefs. It’s possible that an evil demon is tricking us but there’s no evidence of it.
A contemporary challenge was offered by Edmund Gettier in a very brief 1963 paper, which could be used to similar purposes as Descartes’ evil demon. He offered a number of counterexamples to this definition of knowledge. Since that time even more problems have been suggested. One of them has been called “the lottery paradox”.
Considering these problems can reveal why it seems so appealing to think of knowledge as justified true belief and exactly how it fails. Following Descartes, it might even point a way to saving the definition from skeptical doubt.
The Lottery Paradox
The lottery paradox considers how lotteries, and lottery-like events, affect knowledge of the future. We often act as though we have knowledge of the future, thinking things like “I know I’ll be at the supermarket tomorrow night, so I’ll buy the milk then”. You have the belief that you’ll be at the supermarket tomorrow night. Perhaps you have good evidence of it (you never forget to do such things). Making it true seems to be up to you. We also tend to make such knowledge ascriptions in hindsight: “I knew you would say that”.
Now, if your friend buys a lottery ticket you might say she will not win. When it turns out she doesn’t win might say you knew it. First, you did indeed have the belief that she wouldn’t. Second, that belief is probabilistically justified. Finally, it turned out to be true.
But if your friend says that she knows she will not be able to to buy a yacht this year, you might tell her she could not know such a thing. Perhaps she has a very strong desire to buy one. If she had the money to do so, she would immediately. Alas, her job pays far too poorly for her to think this is possible. “But you might get an inheritance,” you say. At the end of the year she doesn’t have the money. She tells you she knew it: she had the belief, good evidence to justify it, and it turned out true.
You could reply that knowledge requires certainty. She isn’t certain she doesn’t have a long lost uncle. Likewise, you aren’t certain she will lose the lottery; you only have probabilistic evidence. But are you certain after the numbers are announced? She might very well have thrown away a winning ticket after misreading the numbers in the newspaper. She might have checked the numbers against an old ticket kept in the same place. The newspaper could be wrong. The lottery could have been fixed and the corruption later exposed. Neither of you have time to check these possibilities.
If you think that the probabilities of such events can be added together, they might even make it probable that her belief that she lost is wrong. The possibility that you will bit hit by falling space debris means you can’t be certain you will finish this sentence. After all, we do have evidence that there is a lot of space debris up there and that it sometimes falls to the earth.
If you agree that the overwhelming odds against winning the lottery are enough justify the belief that her ticket will lose, then you should accept that she knows she won’t be sailing this time next year. If you think that even the slight possibility of a long lost rich uncle proves her negative thinking wrong, then you don’t know she will lose the lottery. In our every day life, we often use the verb “to know,” in inconsistent ways. Knowledge can’t be sometimes probabilistically justified and sometimes not.