In 1965, still a graduate student in Pittsburgh, I got a part-time teaching job at Point Park Junior College. I was to teach two sections of a critical thinking course. There were two textbooks, a baby logic for syllogisms and some sentential logic, the other was Language in Action. That was by S. I. Hayakawa, who would find sudden fame a couple of years later as hero of the right, by suppressing a student revolt in San Francisco.
Hayakawa had studied in the Institute for General Semantics, in Chicago. This had been founded by a Polish aristocrat emigre, Alfed Korzybski, an erstwhile intelligence officer in the Russian army — one of the few, I think, who wasn’t murdered in the 1917 Russian revolution. The principles of General Semantics were both simple and profound:
- The map is not the territory.
- Words are not things.
- Words never say all about anything.
- The meaning of words are not in the words; they are in us.
- No word ever has exactly the same meaning twice.
- Cow1 is not Cow2.
I tried to tell the Dean that among logicians, Korzybski and General Semantics were never mentioned in polite company. But the books had been ordered by the other logic teacher, so that was that. (Or maybe not: one of Korzybski’s slogans was “This is not that”.)
The evening section of the course was for mature students, who typically came in after work. Coming into the room I could feel the interest and goodwill all around. Right in front, in the first row, was a stocky, short man with well-combed black hair and a look and smile on his face that said “I am going to be a fan!” This was a two-hour session with a break and I used the first half getting them to introduce themselves and talk about what we would do. The look was clearly changing to “I am a fan!”
After the break I wrote a syllogism on the board, saying “Let’s discuss what is a valid argument.” I turned around, and looked at my fan. A look of utter and total incomprehension had now come over his face. Undaunted, I told myself that this man was ready to be taught. Little did I realize that this look would never leave his face, not in any single session, not even for a single moment …
The other course section was during the day for the full-time students. Most of these, I soon came to know, did not want to be there. I entered the room, and there they were, all 124 of them, row upon row. I stepped up the platform to the microphone. Introducing myself I was painfully aware of my still very Dutch accent, and worried that I might be sounding too academic. I put up my first slide — optical slide projector, does any one remember them, changing one page at a time? It didn’t focus, so I started moving the projector stand. After a bit of struggle, a more shoving, and adjusting, a student called out “Try turning the knob!”
I suppose I lost their respect that very first day. I certainly did not gain it back a couple of weeks later when we had an example of a politician’s stump speech. “You know very well”, I said, “that it is no qualification for an office to score a home run in some football game”. The whole class was laughing, it took me a hesitant few seconds to realize why … wrong game? oh well …
Looking out over the class I could see that the rows were ordered by size: the back was full of huge lumpy guys with attitude. They were noisy, laughing too loud, passing remarks … I tried to joke a bit with them, no use … One day I stepped down from the platform. Everyone became quiet, I walked down the long center isle to the back rows. There I stopped, I faced one of those louts, pointed at his chest: “Out!” He could probably have smashed me with his thumb, like Sean Connery in Presidio. But he walked out. The respite did not last, though.
After I graduated I got to teach much better logic classes, and it became more of a pleasure, though I stayed quite apprehensive for some years. The logic I knew. But teaching skills weren’t taught, you had to learn those by trial and error. The logic texts were clear, but they needed to be livened up with examples, by drawing out the students’ comments, by putting on a bit of an act.
I remember, with some misgiving still, how I kept asking myself once, when preparing a class, would I be up to it? I wanted to bring them a long example to keep the course cool and funky. Trouble was, I was still subject to awkward moments of self-consciousness, even embarrassment, blushing, faltering at the wrong times — and this example would skirt some of teaching’s unstated limits … But I went ahead.
The principle of Reductio ad Absurdum is controversial, I told them. Intuitionists think its strongest version is just a fallacy. But even they agree that if something absurd follows from a premise, then the premise is false. I want to tell you the story of a famous Reductio argument in the Middle Ages.
(As I said this, I noticed that my hand still holding the chalk was trembling.)
Especially around the year 1000 AD there was great anxiety about the possible advent of the AntiChrist, as prophesied in the Johannine Epistles. Much speculation about how this could come about focused on witches: witches were in league with the devil, consorted with demons in the black Sabbath rituals, lay with demons, had carnal knowledge of demons … so, a baby could be born of such a union!
These were the days of scholastic disputation, and the first argument was that this was not possible: there could not be offspring of two distinct kinds of being, not even of horse and ox, let alone of human and demon.
But counterargument: demons have no specific sex. Hence the same demon can appear as succubus to a warlock and as incubus to a witch. Thus the demon could collect the man’s seed from the warlock and deposit it when consorting with a witch as incubus.
(Now my knees had a slight quiver … my mouth was becoming dry …)
The counter-counter argument followed swiftly. By the witches’ own testimony the demon’s organ was far colder than ice, the seed could not survive!
And was refuted: demons are not limited by space and time. A demon could disappear in one place and materialize in another at the very same instant — no time for the seed to freeze.
( I realized that I was licking my dry lips. I was suddenly afraid that it might signal a sensuous, prurient interest in the subject …)
But in the 12th century, a monk came up with the final refutation:
Suppose per absurdum that a child were born of such a union. The demon would not be the father since it would not be his seed. The warlock would not be the father since he did not have carnal knowledge of the witch. So this would be a child without a father, which is absurd, and therefore cannot exist.
(These last few words I almost did not manage to utter, my dry mouth could hardly form the words, my face felt too hot, I did not know where to look …)
Some students were laughing a bit self-consciously. One was frowning hard. Some, I think, had not been able to follow the argument.
But they had certainly heard the words ….
Bas van Fraassen's Commonplace Book 