Monday, February 11, 2008

Teaching Necessary and Sufficient Conditions and Others with Examples

I came across this post at Show-Me the Argument, the blog of Mizzou philosophy grad students. I often find that it can take a while for some of these things to click in the minds of my students. Offering a variety of examples is one good way to get the desired result. Apart from the ones at the Mizzou blog, does anyone have some especially effective examples in this area that you'd like to share?


  1. Well, this isn't an example per se, but rather a situation I use to explain it. I say: imagine you were on the Price is Right (Bob Barker graduated from my school, so they like that, lol).

    Anyway, imagine that ol' Bob has "curtain #1" up there and said "there's an object back there, if you can guess what it is, I'll giver you 1 million" (get it wrong and you get a life supply of turtle wax or something).

    Next, Bob says: I'll give you one description of the object. You choose. It can be:

    1. Neither NC or SC
    2. A NC
    3. A SC

    I then tell them to remember that if Bob gives a SC, they are guaranteed the 1M. If he gives a NC, they have a decent shot, and if he gives the neither NC or SC, then it's like winning Lotto (1 in a million). I then use some object to explain how it works.

    For some reason, the larger story seems to work -- they remember how it works, and it also allows them to think of what it all means too.

  2. Since people seem to handle this much better in terms of socially salient rules rather than abstract concepts (cf. differing performances on structurally identical Wason selection tasks), I give this example to teach necessary conditions:

    "If you are going to graduate, then you need to satisfy your General Education Requirement (GER), right? You are required to fulfill the GER. It's a necessary condition for you to graduate. If you haven't done it, then you can't graduate. So we can say that if you've graduated, then you've fulfilled the GER.

    But is satisfying the GER enough for you to graduate, all by itself? No. It's not enough—it's not sufficient. There are other things you need to do, like take 120 credits and complete a major.

    So, satisfying the GER is a necessary, but not sufficient, condition for graduating."

    This seems to work quite well. I get a lot of "aha" looks in the class when I do this. Unfortuantely, I don't have anything that gets the same result for sufficient conditions. Maybe getting kicked out of school would work? "There are many ways to get kicked out of school, but turning a bunch of llamas loose in the dean's office might be sufficient. If you do that, then you'll get kicked out of school."

  3. Maybe I have babies on the brain, but I often use pregnancy examples.

    Being a female is necessary for being pregnant.

    Being a female is not sufficient for being pregnant (thank goodness).

    Also, to illustrate how the material conditional is neither temporal nor causal, I often use: If the test strip turns blue, then I am pregnant. (You have to assume no false positives).

  4. Sort of similar to David's suggestion: I've used my department's curriculum as a way to illustrate these concepts. If you take Moral Philosophy, that's sufficient for area A but not necessary, etc. The students seem to learn the concepts well enough, and it functions as a kind of collective student advising session!

  5. I like that, Becko. Maybe we could add that giving birth is sufficient for being a mother?

  6. I was originally taught with the example of being a UK citizen. Some of the following are strictly false, but I imagine that they're close enough for students to get the point.

    Being human is necessary but not sufficient for being (legally) British.

    Being born in the UK is sufficient but not necessary for being British.

    Owning a UK passport is necessary and sufficient for being British.

    Being female is neither necessary nor sufficient for being British.

    And an inclusive disjunct: You can be British either by being born in the UK or by having parents who were (or..).



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