OK, everybody, to beg the question is a term in debate or argument--and really only there--for taking a position that covertly assumes the answer to the issue in question. Suppose, for instance, two people were debating whether computers could ever have intelligence and one of the debaters said, "let's presume that for whatever reason, nature was constructed so that only carbon based life forms could have intelligence," he would be begging the question. What Jeff did was supply an answer to his own riddle. Pete's explanation of his meaning comes close enough to the real meaning to entail that probably Rahsaan and I were slightly out of line in giving him grie, but it still is technically a misuse, and worse, doesn't attend to the flavor of the cliché.
As a mnemonic, go back to the original version "to beggar the question," which means, metaphorically, to impoverish the argument, which is what one does by begging the question. Only if you are claiming that someone is ruining a perfectly good argument by assuming what is in question, thus impoverishing the argument or begarring the question, is he begging the question.
And now I officially give up on this bit of pedantry.