Here's another one of those exchanges you find over and over again in blog comments threads. Person A states something like, X has been accused of rape. Rapist! Person B says, What about the presumption of innocence? Person A: That's for courts. I'll make up my own mind.
Actually, there's a more sophisticated version of that last argument: Bayesian reasoning. For example, assuming that being accused of rape is actually correlated with being a rapist (which I'm pretty sure is true), a person's being accused of being a rapist should make you adjust your estimate of his being a rapist upwards. It's not clear by how much (because the quality of the available data is too low). It might at least seem defensible to say an accusation is good enough evidence to push you over the threshold beyond which you're comfortable saying that X is a rapist.
Presumption of innocence good. Bayesian reasoning also good. What now?
The paradox (if you forgive my lax use of the term) is resolved once you realize that the presumption of innocence is a prescription regarding the treatment of an accused person. The result of Bayesian reasoning is descriptive; a probability estimate. This took me a surprisingly long time to realize, probably because the terms presumption of innocence and it's German equivalent, the Unschuldsvermutung don't exactly go out of their way to let you know they're prescriptions. In fact, they sound a lot like probability estimates.
Does it follow that the presumption of innocence is for courts only? Not in my book. Before you call someone a rapist in public you should want to be really sure he actually is. In fact, the quality of discourse in blog comments sections and elsewhere would be much improved if people assumed less about what other people think or do and stuck more to what people actually said.