The indefiniteness of indefinite articles

The trickiness of the English definite article is legendary. Bertrand Russell apparently wrote a whole book on the subject, and anyone who has tried to teach it to foreign students will appreciate this. But the indefinite article is almost as bad. For ages I just thought it was a non-specific veridical thingummybob, such that "a foo" meant "some member of the set of foos that I am not interested in specifying at this moment" (as opposed to "the foo", which means "one specific thing that I choose to attach the label 'foo' to and which is probably but not necessarily a member of the set of foos"). But then today, while thinking about the saying "Nature abhors a vacuum," I thought "Which vacuum?" Now this is obviously wrong; "a vacuum" here means "all vacuums", which is a very different use of the indefinite article from that in "I'd like a cup of tea," which certainly doesn't mean that I would like every cup of tea. I want at least one, and probably only one, cup of tea. This in turn contrasts with "I do like a nice cup of tea," which seems to be the indefinite equivalent of "The sleek Brazilian jaguar Does not in its arboreal gloom Distil so rank a feline smell As Grishkin in a drawing-room." Ho hum, I should go and brush up on my reading.