While teaching through Exercise 25, I was challenging my students on problem 3 to identify every possible syllogism making the fallacies of Two negative premises, and negative premise and affirmative conclusion, and no other fallacies.  I had original concluded that there were 32 such forms: EEA, EEI, EOA, EOI, OEA, OEI, OOA, OOI — all four figures of each.

Suddenly one of my students said, “But don’t some of those forms make others fallacies as well?” I realized he was right, and together we followed this rabbit trail, carefully working through the question to determine that, in fact, six of these forms do make additional fallacies: EOA-1, 2 and OOA-1, 2 have an Illicit Minor, and OOA-3, OOI-3 have an Undistributed Middle. Consequently, I have corrected my previous post on this topic.

I have some truly impressive logic students!