Last week we used object-level contraposition to derive four new syllogisms, starting from Barbara. This week we will use meta-level contraposition to derive two more new syllogisms from each of the five we now have, to give a total of 15 sound syllogisms.
Meta-level contraposition takes a sound syllogism and produces two new syllogisms — each assuming the denial the original conclusion, assuming one of its assumptions, and inferring the denial of the other.