My brain is currently being anesthetized as I grade logic take-home quizzes for my Intro Phil course. One of the things this extraordinarily dull and slow exercise (and it is very slow, because in philosophical logic, unlike mathematical logic, there can be different acceptable answers depending on exactly what interpretive moves that are made, so you have to look at each attempt on its own) -- I say, if you have lost the thread of my sentence, as I almost have, that one of the things this extraordinarily dull and slow exercise does is confront you with the perpetual question of what you could have done differently in teaching it. For instance, despite my best attempts to make clear to students that a string of letters and symbols is not an argument until it is clear what the letters and symbols are supposed to mean, a number of students (some bright ones, too) simply wrote down letters without giving me the slightest clue how they are interpreting them. So, for instance, when I ask them put the following in a literal diagram,
All philosophy is a footnote to Plato,
They will give me the diagram marked with the letters Ph and Pl and never tell me whether they take Pl to mean "Plato" or "footnote to Plato" or, for that matter, "the twenty-third pavement stone in front of the City Hall of Timbuktu". I did insist on the importance of making clear how things are to be interpreted, but the regularity of the problem suggests that in future classes I'll need to be even more insistent. (And, I suspect, make sure actually to write every little thing on the board, since I suspect some of them are here and there looking at a few problems we did in class where I had identified the letters verbally but they didn't write them down in their notes because, oddly, they seem to think that their notes should copy exactly what's written on the board and nothing else. So when they go back to look at their notes, they don't pick up the interpretations.)
In any case, it occurred to me that one of the problems I'm constantly struggling with -- and constantly adapting the little logic sections I teach in Intro classes in order to overcome -- is providing simple, very clear and clean ways of teaching logic. So I use Carroll's literal diagrams -- the students hate it, but it forces them to look at all the right things in order to analyze arguments -- and some basic Sommers notation -- which has the advantage of getting across the basic idea of a syllogism without sending us on the hopeless of quest of getting the students to understand figure, mood, and distribution of terms in a few weeks. And I also teach a few basic inference rules (modus ponens, modus tollens, disjunctive syllogism, etc.). But there are bound to be other means that people use to get across the basic ideas of logic to people who simply cannot, for the life of them, figure out what subcontrariety is, no matter how much you explain it, and whose minds boggle at sorites. Have any of you come across such things -- particular ways of teaching some point of logic that are simple, clean, and effective (or as much so as could reasonably be hoped)?
