Thursday, September 22, 2011
How to Teach Formal Logic in Texas
It's probably because there's an exam next week, but quite a few students come in for my office hours for the logic class that I TA. For those of you who aren't familiar with doing formal logic proofs they are mechanical, at least at the basic level. Think of it as math. You have rules, and as long as you apply the right rules to the correct instances of "sentences" you will eventually solve the proof.
The most common issue that students have when they first encounter formal logic is they want to ask "why" a rule works the way it does. But in doing proofs there is no real "why". It's kind of like asking "why do I write the number "4" after I see the sentence "2+2". That's just what the rules of the "+" symbol dictate, you combine the two values. You don't question the rule, you just follow it. Of course we've sort of internalized the abstract notions of numbers and arithmetic symbols, so it's not quite as strange for most people as manipulating letters with logic symbols. Dealing with purely abstract meaningless symbols and operators is bewildering to just about everyone when they start learning formal logic.
In logic we have a rule called "modus ponens". It goes like this: if you have an instance of a formula that looks like this "p ---> q", and you have an instance of "p" you get to write down "q" in your proof. Often students struggle with this because they get hung up on the "why". And no matter how many times you tell them "that's just the rule", they are still somewhat bewildered. You write "q" because that's what the "-->" symbol tells you to do.
So why am I telling you all this? Well, I had a moment of pedagogic insight while I was teaching. As with most good ideas, it happened by accident. Since I am hardwired for sarcasm (for better or for worse) as we were doing the proofs, whenever a student asked a "why" question about how the rules work I'd say, "because yesterday I had a dream that sweet baby jesus flew down from heaven and told me that if I ever see 'p --> q' and I have 'p' then I should also write 'q'". "He told me it was a law from god himself, and that I should not question it, but have faith in his perfection and goodness." After about the 3rd time an amazing thing happened...they started applying the rule without asking "why" and were able to do the proofs! Of course after the 3rd time I said "Mohamed came to me in my dream" to deflect any possible mobs with torches and pitch forks (and I'm an equal opportunity ridiculer).
Anyway, if you're ever teaching formal logic in Texas, that's how you dooz it!