In symbolic modal logic, it would be along the lines of... if an action is done to you, then accept the belief of the imperative of doing that action to another. So, it would be a command for you to intend to do that action to another.
Axu -> _u_: A_u_y
(those are supposed to be underlines indicating imperatives.) This is the same sort of convention that Harry Gensler uses to prove the Golden Rule using his Formal Ethics system. (I should note I am not a logician and this is probably only a rough approximation - not sure whether it's appropriate to use A instead of a, etc.)
Is it clear to everybody from the context whether he meant "pass it on" in the sense of "pay it forward" or "pass it on" in the sense of "repeat this message"?
I was thinking first of the game of Telephone. "James Simons is a mathematician, pass it on!"
Well, I'm not going to have a compact answer for you, but to do so you need to develop some kind of self-reference. (Like Godel!) If you like thinking about this sort of thing, Raymond Smullyan has a lot of great writing - I'd recommend eg Forever Undecided or To Mock a Mockingbird for a more informal treatment, or First-Order Logic for a formal one.
