The first and second man both believe P —> Q. I think the idea is that the first man started out believing P, and the second started out believing not-Q, and therefore the new piece of information “P —> Q” is accepted by both but used to make different (and opposing) deductions. The third man is a heretic who believes P does not imply Q, and has been cast out.
ETA: A common sort of example: First man believes that Bob is a good mathematician. Second man believes that statement X, in the realm of math, is false. Now Bob proclaims that X is true. Both men believe that if Bob were a good mathematician, then he would not make a mistake about whether X is true. Therefore, the first man takes “Bob says X is true” and deduces that X must be true, while the second man takes “Bob says X is true” and deduces that Bob is not a good mathematician.
The first and second man both believe P —> Q. I think the idea is that the first man started out believing P, and the second started out believing not-Q, and therefore the new piece of information “P —> Q” is accepted by both but used to make different (and opposing) deductions. The third man is a heretic who believes P does not imply Q, and has been cast out.
ETA: A common sort of example: First man believes that Bob is a good mathematician. Second man believes that statement X, in the realm of math, is false. Now Bob proclaims that X is true. Both men believe that if Bob were a good mathematician, then he would not make a mistake about whether X is true. Therefore, the first man takes “Bob says X is true” and deduces that X must be true, while the second man takes “Bob says X is true” and deduces that Bob is not a good mathematician.