Questions: Their Raising and Their Begging
To raise a question is not to beg a question. 'Raise a question' and 'beg a question' ought not be used interchangeably on pain of occluding a distinction essential to clear thought. To raise a question is just to pose it, to bring it before one's mind or before one's audience for consideration. To beg a question, however, is not to pose a question but to reason in a way that presupposes what one needs to prove. Suppose A poses the question, Does Allah exist? B responds by saying that Allah does exist because his existence is attested in the Koran which Allah revealed to Muhammad. In this example, A raises a question, while B begs the question raised by A. The question is whether or not Allah exists; B's response begs the question by presupposing that Allah does exist. For Allah could not reveal anything to Muhammad unless Allah exists.
The phrase 'beg the question' is not as transparent as might be hoped. The Latin, petitio principii, is better: begging of the principle. Perhaps the simplest way to express the fallacy in English is by calling it circular reasoning. If I argue that The El Lay Times displays liberal bias because its reportage and editorializing show a left-of-center slant, then I reason in a circle, or beg the question. Fans of Greek may prefer hysteron proteron, literally, the later earlier. That is, what is logically posterior, namely, the conclusion, is taken to be logically prior, a premise.
Punchline: Never use 'beg the question' unless you are referring to an informal fallacy in reasoning. If you are raising, asking, posing a question, then say that. Do your bit to preserve our alma mater, the English language. Honor your mother!