Each week The Old Editor will attempt to address your entreaties for information and advice on grammar and usage, writing, writer-editor etiquette, and related subjects.
The Old Editor does not address marital and relationship matters, dietary questions, or automobile mechanics.
An old friend inquires: "Would you tell me what 'begs the question' means? Has its meaning changed in recent years?
The Old Editor answers: Ninety percent of the people you will ever write or edit for think that beg the question means "prompt the question," "invite the question." Or in some instances, "dodge the question.")
To the other ten percent of readers, beg the question is going to be understood as labeling the logical fallacy called in Latin petitio principii—assuming the very point that your argument is supposed to prove. "Circular argument" is another term for it.
The Old Editor's advice is that if you are writing or editing for a publication aimed at that ten percent, say The American Scholar or The New York Review of Books, you can confidently describe some addlepated argument as begging the question.
Otherwise, much as you're free to grumble about the public's ignorance of logic and the corruption of everything that was once fine and noble, you're better advised to submit to the commonly understood sense with such good grace as you can muster.