We've discussed 'begging the question' several times here on AWAD. I came across a site on logic and found this definition of 'arguing in a circle,' which I think is pretty good. The example is clear. Please read the definition and let me know whether this application of 'begging the question' works for you:

ARGUING IN A CIRCLE - one assumes the truth of a premise, draws a conclusion from the premise, and then uses the conclusion to prove the initial premise:

"Boxing is a dangerous sport because it is unsafe."

"Unsafe" conveys the same idea as "dangerous" thus the speaker has not proven that danger exists.

ALSO CALLED: Begging the question, circular argument, petitio principi