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.
David Lewis famously observed that one man’s modus ponens is another man’s modus tollens. The first man argues:
While the second man argues:
But Lewis forgot about the third man:
I called this “modus delens” here.
Damn, you beat me to it by seven years.
you both forgot about the fourth man [1] :
well, if, having forsaken reason, he still deserves to be considered human
All three of you forgot about the fifth man:
A nice definition of “paradox”.
I’m impressed that you managed to put a hyperlink inside your LaTeX.
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.