Traditional Logic II , by Martin Cothran, is a continuation of Memoria Press' Traditional Logic I . It covers the four figures of the traditional syllogism, the three forms of rhetorical arguments (called enthymemes), the three kinds of hypothetical syllogisms, the four kinds of complex syllogisms, as well as relational arguments. The book also includes a wealth of examples of arguments from the Bible, Lewis Carroll, Isaac Watts, St. Augustine and Tertullian, as well as extended case studies of famous arguments throughout history, such as Rene Descartes' famous 'I think, therefore, I am'; C.S. Lewis' disjunctive syllogism proving the deity of Christ; Plato's hypothetical argument concerning the power of love; Christ's conjunctive 'You cannot serve both God and mammon'; David Hume's famous dilemma stating the problem of evil; the stoic Seneca's justification of the virtuous life; and St. Thomas Aquinas' cosmological argument for the existence of God.
Like the other one, this book did not provide complete explanation. For example, it was missing five valid forms. I researched it and it seemed to be because of the existential fallacy, which was never even mentioned, and which Aristotelian logic supposedly does not support. They also affirm subimplication, which contradicts their elimination of these otherwise valid forms. I am not certain that this is the reason for the missing forms, but I do know that it is not explained. This is one example of this book’s shortcomings, but there are others as well, like the utter pointlessness of reduction of particular negative conclusion syllogisms. I again recommend Canon Press Introductory and Intermediate logic!
Wow, this got very advanced at the end, and I feel they didn't give very many examples for the last few chapters. But I think with the DVD lectures and workbook, this is the absolutely best formal logic course out there. Excellent straightforward and clear presentation.