 However, GJ generates paradoxes (Kyburg 1961). To see why, notice that if the chances of winning a lottery are sufficiently remote, I am justified in believing that my ticket, ticket 1, will lose. I am also justified in believing that ticket 2 will lose, and that 3 will lose, and so on. However, I am not justified in believing the conjunction of these propositions. If I were, I would justifiably believe that no ticket will win. If a proposition is justified when probable enough, lottery examples undermine GJ. No matter how great the probability that suffices for justification, unless that probability is 1, in some lotteries we will be justified in believing, of an arbitrary ticket, that it will lose, and thus, by GJ, we will be justified in believing that all of the tickets will lose.