Topic neutrality is geek carte blanche

Tue 15 Mar 2011 10:22 AM

When writing problem sets for Intro Logic, I try to use interesting topics. Since the logical form of 'All capybaras are flammable' is the same as the logical form of 'All men are mortal', the structure of the problem is the same in either case.* Students have to get the structure right, so it doesn't matter if they know anything about the topic or not.

If students have to define their own key, then abstruse predicates can lead them to make overly complex translations. Where I provide a symbolization key, however, students have to do as well as they can with the predicates defined in the key. For example: We might argue about whether 'x is a liar' can be adequately represented as 'there exists some y, such that x lies to y'. Nevertheless, it is clearly the best representation possible if we have to express it using just the relation 'x lies to y'.

Today's exam illustrates how this can come together in odd ways. Students were given a series of sentences. The universe of discourse was specified to be commanding officers from Star Trek. The predicates included 'x was played by Avery Brooks' and 'x was commander of Deep Space 9'; there was a defined constant referring to Sisko.

On reflection, I may have cheated on the metaphysics by setting up the problem this way. It is true in the story that Sisko was commander of Deep Space 9, but it is true in the actual world that Avery Brooks played the role of Sisko. So perhaps 'Sisko' is equivocally used for both the character and the role. Are those different things? I'm honestly not sure.

On a tangentially related note: Although she recognized that it didn't matter for the exam itself, one student wondered about how some problem sentences were effected by the fact that the original series pilot (in which Pike rather than Kirk was captain) was aired after the series (in which Kirk was captain).**

* I used 'All capybaras are flammable' on a final several years ago. A few students raised their hand to ask what a capybara was. I answered that (a) it shouldn't matter, since there was a predicate defined to mean 'x is a capybara' but (b) it's a giant South American rodent.

** The exam did not mention Captain Pike by name! It's nice when somebody gets the references.