First put forth by

Henry Kyburg in 1961. It tries to demonstrate that three principles of

rational acceptance are

logically inconsistent. These principles are:

- If it is very likely that a certain conclusion is true, then it is rational to accept that conclusion.
- If it is rational to accept that
*p* is the case, and it is rational to accept that *q* is the case, than it is rational to accept that both *p* and *q* are the case.
- It is never rational to accept propositions which you realize to be inconsistent.

And now, the paradox:

Suppose that there is a lottery in which 100,000 tickets are sold (and only one will win). The probability that any one given ticket will win is very low -- 0.00001. Therefore, by principle 1, it is rational to believe that my ticket, #1, will lose. And it is also rational to believe that ticket #2 will lose. And #3, and #4, and #5, .... and #99998, and #99,999, and #100,000. According to principle 2 above, it is rational to assume that all 100,000 tickets will lose. But as already stated, one ticket *will* win.

The solution? Deny principle 1, 2, or 3. (Or engage in some tricky philosophical judo. That's good too.)

Have fun!