In this post, I'll just try to wrap up the loose ends from my last one ... The question was: how do you teach logic using modern textbooks without indoctrinating your students with the relativistic notion of value that modern curricula encourage? How do you respect a diversity of views among your students without making them believe that values can be chosen arbitrarily?

Imagine sending your child to school and having him or her learn that it is okay to admire Hitler, that racism is a valid point of view, or that murder -- though criticized by many -- might be an acceptable way to resolve conflicts depending on your chosen system of values. You would be justifiably angry. Fortunately, our educational system doesn't have this problem -- any teacher in their right mind will stress that Hitler was a bad man, racism is unacceptable, and murder is wrong. In other words, objective value is already taught in our schools, and we unanimously agree that this is the right thing to do.

As I see it, the problem with teaching modern logic is of the same kind, if less obvious.

You might be thinking, wait now -- but isn't logic a value-free subject?

Hardly. For example, Confucius' teachings include the following analects:

"True virtue rarely goes with artful speech and insinuating looks."

"The higher type of person is catholic in his sympathy and free from party bias; the lower type is biased an unsympathetic."

"The wise man does not esteem a person more highly because of what he says, neither does he undervalue what is said because of the person who says it."

Confucius (551 BC – 479 BC) |

These are only a few examples of the sorts of values taught not only in logic but also in philosophy and religion. There are dozens of more relevant sayings in the Confucian Analects, all of which are relevant to the search for truth, unbiasedness, and objectivity.

So, even though logic teaches unbiasedness, this unbiasedness is itself a virtue, which means that logic does teach values, including Truth, Honesty, Sincerity, and Justice. There is no contradiction here -- logic does not teach unbiasedness in everything, but only in the process of determining the truth.

The question that remained for me was this: how do I teach my students these virtues in an explicit way without confusing them? If I start talking about Confucius and honesty and sincerity on the first day, they're going to have no idea how any of it is connected, for example, to the mathematical symbolism of logic.

Why not just play it safe and teach the usual curriculum, however flawed? Obviously, I'll be teaching these kids before they have a chance to form their character for good -- so not everything is at stake. On the other hand, it is common for former students at the Io Institute to say that II changed their lives forever, inspiring them to choose their future careers and so forth. It should also be kept in mind that I will have a single group of kids for 7 hours a day, 5 days a week for 3 weeks. This means it will be approximately an entire college semester's worth of material. So I do think I have a fairly large responsibility to my students.

As I contemplated this I ran across the following analect in Confucius:

"Let a pupil join with you in self-cultivation before you let him approach the general truths of philosophy, but let him approach these general truths before he is allowed to form his character for good. He should have formed his character for good before he is allowed to make exceptions to a general rule."

Here was the whole thing in a nutshell. I'll discuss this analect one phrase at a time.

"Let a pupil join with you in self-cultivation before you let him approach the general truths of philosophy ..."

Before I can teach my students any general principles of virtue, I must allow them to cultivate these virtues by practice. This is true in any discipline. Before you can learn the deepest laws of nature in physics, for example, you must learn how to problem-solve and develop your physical intuition. It will take years of practice in creative writing before a novelist can explain to you the secrets to writing great literature. So the plan I've come up with for my logic course is to focus on logical problem-solving to begin with. You would think that this would be common practice, but it is not anymore -- logic now generally follows the tendency of modern mathematics education to teach by means of "exercises" and to label real problems "story problems."

I was a math tutor for a time, and it was my job to fix the brains of poor students that had been led seriously astray by this way of teaching. For example, I had one college student who could solve problems like "If you have 65 dollars and you pay Ted 38 dollars, how much is left?" and could do the symbolic problem 65 - 38 = ? but had no idea that he was doing the same thing in both cases! Math education is a whole different subject that I could rant about -- but I'll leave that for another time. For now I just want to explain why I'm done teaching my II students primarily by means of symbolic "exercises." Intead, I'll start by giving them puzzles, riddles, and paradoxes (I'm actually using "What is the name of this book?: The riddle of Dracula and other logical puzzles" by Raymond M Smullyan as one of my texts this year). And to further distance myself from the notion of mechanical exercises and drills, I'm going to make sure that a few of the puzzles I offer them will be unsolvable. It will be their choice what to work on, and I'll be sure not to let them waste too much time on unsolvable problems, but I think it will do them a world of good to have a little practice the hardest lesson in logic: how to tell when you're stumped. Logic is just as much about moving on and accepting your ignorance as it is about applying the principles of reason.

"... but let him approach these general truths before he is allowed to form his character for good."

Then after we've had plenty of class discussion, debate, and paper-writing on these puzzles and paradoxes, I'm hoping the students will have had enough experience with logical controversy that we can move on to discuss more general principles, rules, and (yes) values that logicians hold to. This is also where I'll be discussing the limitations of logic, both theoretical and practical. (Smullyan has a nice discussion of Godel's Theorem for the layman in his book -- simple enough to be understandable but also rigorous enough to be meaningful.)

"He should have formed his character for good before he is allowed to make exceptions to a general rule."

Finally, I'll try to avoid the twin perils of either (a) teaching my students to avoid all controversial topics -- a strategy that destroys values be skirting around their existence or (b) plunging right into philosophical debates over the objectivity of values and the relativity of truth -- a strategy that asks the students to fly before they can walk. Instead, the focus will be on how logicians can maintain their objectivity even when tackling controversial subjects such as the existence of God or global warming. Rather than shy away from these topics, I'll encourage my students (around the third week) to tackle them in as honest and independent a way as possible.

Anyway -- this is solution I've come up with over the past few weeks. Of course, things never work out in practice as they do in theory -- I'm sure to learn as much or more than my students over the two three-week sessions I'll be teaching this summer ...

Meanwhile, it's farewell for the next few months. Thanks to everyone for following my blog so far, and hopefully I'll have time again next September to share some more thoughts!