James Chastek on the teaching of logic -- part 1 and part 2.

I must have reed St Thomas a thousand times before it hit me that he defined logic in relation to the rational faculty. Logic, by his definition, is the art that directs reason in its own act. This act is governed by the proper object of reason, the what-sensible-things-are. On this account, logic is subordinate to things by definition. The goal is not to give a universal system of all possible arguments, but to give a general account of how we figure out what things are. On St. Thomas’s account logic is the answer to the question: “generally speaking, how does one use an intellect?” or “how does an intellect work?” On this account, you first give its object, then the order we follow to attain the object (general to particular) then the most general things known that can do logical work (the categories) and then how we can refine these general things into definitions (Topics) then the laws that govern how we combine them to form a proposition (de interpretatione) and an argument (the books of Analytics)

The part on the Topics would be the easiest one to leave out, and the one we contemporary thinkers are most in need of.

Logic. Something all aspiring academics should be studying; it would also be useful for those who are engaged in ecumenical dialogue, particularly the "Latins" and the "Greeks". Most philosophy departments that take a historical approach to teaching philosophy do not have a basic logic course for both majors and non-majors. How much would majors benefit from having just one good logic course. It would help them deal with the sort of 'relativism' that one finds in such departments.