One of those paradoxes, called "The Dichotomy" claimed that you could never traverse a finite stretch of space, for in order to get to the destination one would have to first get to the half-way point, but before that one would have to reach the quarter-way point, and so on. So since traversing a finite stretch of space entailed performing an infinite number of tasks, reaching the destination, Zeno argued was impossible.
We could rephrase this paradox in a way to claim that finishing a goblet of wine is impossible. For before one drinks the whole lot, one need's to drink half first etc.
Now, either Zeno was also a very unusual Greek insofar as he abstained from wine - which is very doubtful, and would surely be insulting to even assume - or when it came to wine drinking he could perform the impossible!
I'd take that as a valid defense, if Zeno chose to use it.