Wednesday, August 6, 2008

Reductio ad frustratum

I'd be interested to know if anyone out there has some techniques for teaching students reductio ad absurdum. In my experience, what's true of reductio arguments is similar to what I believe Strawson once said about the Euthyphro dilemma: If you get it, you'll likely be pretty good at philosophy, and if you don't, well ...

I'm interested in student understanding of reductio outside of teaching logic per se; on the few occasions I've taught logic I've noticed that it seems to be the one inference rule that large numbers of students have trouble appreciating. This doesn't preclude them from doing proofs using reductio, but they do so mechanically and don't seem to grasp why using that strategy proves a conclusion in the way that they appear to grasp why modus ponens, disjunction, etc., prove a conclusion. But I'm more interested in how to instill an appreciation for reductio in order to help students with their writing. I've encountered many arguments in student papers that would probably be expressed more clearly and forcefully as reductio arguments, but have struggled to help students craft such argumenta in part because the students sometimes don't fully understand reductio anyway.

Thoughts or counsel welcome!


  1. I like the title :)

    I've had problems getting students to understand reductio ad absurdum as well. I thought Weston's explanation of it in his Rulebook for Arguments would help students to get it, but not so!

    One analogy I tried out is this. When there are bugs in Windows and it crashes, the programmers check the program to locate the source of the problem, and then they correct it. (The bugs are like the absurdities, the source of the bugs is like the initial assumption that needs to be refuted, and fixing the problem is like giving up the initial assumption.)

    Seems intuitive enough, but students still bombed the reductio question on the exam (that may just be because I'm bad at teaching though).

  2. Baggini and Fosl have a great example in The Philosopher's Toolkit. They compare high concept comedy with the reductio to show how beginning, or granting, a simple concept can lead to absurdity (or comedy) upon examination. Then they offer an example from Plato's Republic to demonstrate.

  3. I've also found that students have a hard time grasping reductio. Pointing out the similarities between reductio and modus tollens seems to help a bit. (Technically, you can think of reductio as a conditional proof plus modus tollens.)

    I've also been more successful when I introduce reductio as a technique for proving someone wrong than when I introduce it as a general technique for proving that p. (Someone says that q. You want to prove him wrong. "Suppose, for the sake of argument, that you're right about q," you say....) After students see why it works to prove someone wrong, point out that you can prove other things with it, too.

    When I taught it this summer, I also tried (with moderate success) adapting a metaphor of Thomas Reid's. Reid says, "A traveller...may be unawares led into the wrong track...but when [the road] ends in a coal-pit, it takes no great judgment to know that he hath gone wrong." When someone points you down one road, and that road leads you somewhere that you don't want to go, you know that the problem is with the initial directions.

  4. I remember way back when I was first learning formal logic, that I came to understand reductio better after being shown that with a disjunction-introduction and a disjunction-elimination, one could prove anything from a contradiction.

  5. Like David says above, I've often thought that any reductio argument can be more staightforwardly presented as a modus tollens type argument. Is that not true?

  6. This year when I taught logic, one of my students compared RAA to the "Chewbacca Defense" from South Park.

    Showing this clip seemed an effective way of getting them to see what's going on with RAA.

    I also found an example or two from Stephen Colbert where his humor relies on RAA, and it helped them to see real life instances of the argument form.

  7. I don't get how reductio is like the Chewbacca defense. What do you tell your students after showing them the clip to get them to understand reductio?

    I'm a big fan of using clips from Colbert in class, BTW. (Actually, I think it was someone's comment on here about the clip of Colbert interviewing Peter Singer that got me started doing that.)

  8. Our student newspaper has sudoku. Ask them what they do on really hard ones when they're stuck. Usually they understand the strategy of trying a number out and working backwards to see if it's wrong.

  9. The Chewbacca defense works by suggesting that anything follows from an absurdity. It helped my students understand that anything follows from a contradiction, which they need to understand to get RAA.

  10. Logic as it is taught in philosophy is poorly understood, see:


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