“A is sufficient for a condition that is necessary for B” implies “B is sufficient for a condition that is necessary for A”.
Does this seem transparent to you? I mean by that, is the truth of the statement obvious? Does it seem true?
A long time ago, someone called Achilles Grytpype-Thynne (a riff on a Goonshow character?) responded to this statement after I posted it on a message board as an example of an implication that isn't immediately obvious. But to Achilles it was, and he explained why. It remains one of the few examples of a fast, non-googleable and marvellously modest yet intelligent responses I've had in all of my dialogues.
Let me know what you think.
