Lottery paradox a paradox involving two plausible assumptions about justification which yield the conclusion that a fully rational thinker may justifiably believe a pair of contradictory propositions. The unattractiveness of this conclusion has led philosophers to deny one or the other of the assumptions in question. The paradox, which is due to Henry Kyburg, is generated as follows. Suppose I am contemplating a fair lottery involving n tickets (for some suitably large n), and I justifiably believe that exactly one ticket will win. Assume that if the probability of p, relative to one’s evidence, meets some given high threshold less than 1, then one has justification for believing that p (and not merely justification for believing that p is highly probable). This is sometimes called a rule of detachment for inductive hypotheses. Then supposing that the number n of tickets is large enough, the rule implies that I have justification for believing (T1) that the first ticket will lose (since the probability of T1 (% (n † 1)/n) will exceed the given high threshold if n is large enough). By similar reasoning, I will also have justification for believing (T2) that the second ticket will lose, and similarly for each remaining ticket. Assume that if one has justification for believing that p and justification for believing that q, then one has justification for believing that p and q. This is a consequence of what is sometimes called ‘deductive closure for justification,’ according to which one has justification for believing the deductive consequences of what one justifiably believes. Closure, then, implies that I have justification for believing that T1 and T2 an. . . Tn. But this conjunctive proposition is equivalent to the proposition that no ticket will win, and we began with the assumption that I have justification for believing that exactly one ticket will win. See also CLOSURE , JUSTIFICATIO. A.B.