There are four related issues here. First, how did "begging the question" come to be a technical term for (a certain kind of) circular reasoning? Second, do people really need a way to talk about circular reasoning, anyway? Third, why did "begging the question" get re-purposed in common usage to mean "dodging the question" or "raising the question", rather than simply subsiding, along with the rest of the terminology of medieval logic, into the midden heap of obsolete idioms? And fourth, should you go with the flow and use "beg the question" to mean "raise the question", or should you fight for the traditional usage, or what? I'll take up these issues one at a time.

1–1 (1)