The Probable Liar

In 1984, philosopher William Lycan published a paper with this statement:

The probability of the title of this paper, given itself (and the fact of its being a generalization), is less than 1/2. Yet the probability of any contingent statement given itself is 1. So 1 is less than 1/2.

The title of the paper was “Most Generalizations Are False.”

In other words, the chance that any statement is true, given itself, is 1. But the chance that Lycan’s title is true, given itself, is less than 1/2. Thus 1 is less than 1/2.