Suppose that every man has two donkeys, one running and one not running. Then every man's donkey is running, for the donkey of this man runs, the donkey of that man runs, and so on for each individual man. But on the other hand, a donkey of this man does not run, (namely the other one of his which is not running), a donkey of that man does not run, and so on for each individual man. Therefore every man's donkey is not running. Therefore it is not the case that every man's donkey is running.
This is one of those puzzles which caused medieval logicians all sorts of mental strain, but which is completely resolved by translation to modern predicate logic. It can easily be shown that the scenario of each man having two donkeys, one running and one not running, implies the following two propositions of predicate logic
(1) (x) Ey x owns y and y runs
(2) (x) Ey x owns y and not (y runs)
where x ranges over men and y over donkeys. Obviously the two propositions are not contraries: they can both be true at the same time. Yet the English sentences which they translate ('every man's donkey runs'and 'every man's donkey does not run') do appear contraries. This is clearly a problem for English, not for logic.
The program of modern analytic philosophy was to resolve all philosophical puzzles by means of the same kind of translation into modern predicate logic. I think this has failed, but that does not imply there can't be some way of formalising paradoxical or aporetic sets of English sentences in a way that dissolves the aporia.