Who's asking: Tom and Hayley Ehrenfeld, Cambridge, MA
Tom writes, "It certainly seems like begging when you say 'I beg of you,' but when you're politely disagreeing (i.e. to differ-ing) then the word 'beg' seems a bit much, yes?"
Maybe -- but "beg" here is used as an excess of courtesy. I don't know about you, but I only use the phrase, "I beg to differ," when what I really want to say is, "You are wrong, wrong, wrong, you total moron." I remember a story many years ago about the administration at Duke reprimanding basketball fans for chanting "Bull----!" at referees; for a game or two, the chant changed to "We beg to differ."
One of the definitions for the word "beg" is "to make an earnest or urgent request," and synonyms include appeal, beseech, crave, implore, entreat, plead, pray, sue and supplicate. We beg to differ the same way we crave someone's pardon or pray silence for the speaker -- as an archaic usage that acknowledges the vast and charming history of our language.
On the subject of vast and charming history, I spent a wonderful morning yesterday at the Archives Center of the National Museum of American History. Thanks to Reuben, Wendy and Susan for being so helpful; the Smithsonian is a treasure house, and made me feel lucky and proud (a nice change) to be American.