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.
Try flipping the status quo. If AIs were already solving all the problems in your particular field, would you advocate for banning them from the field so that people would need you to solve those problems for them (presumably more expensively, presumably making some problems’ solutions too expensive to be solved at all) and so that you would feel like your work mattered? How does the idea of such advocacy strike you?