logicandlanguage.net

One. Even students who never really understand the explanations might learn the useful practical skill of Boolean searching. I don't think we should scoff at this. One of the nice things about undergraduate teaching is that even when we fail to get a student to do good philosophy, we can still help them to improve their writing skills, close-reading skills, and maybe research skills like Boolean searching. This is very cool and likely to be of use to them in later life. Similarly, A basic logic course which gives half the class a grounding in logic, and half the class C+s and the ability to do Boolean searches, is surely better than a basic logic course which gives half the class a grounding in logic, and leaves the other half in tears with C-s, and no new skills.

Two. Students can see the point of learning to search, and everyone learns better with a motivation.

But here are some worries you might have about teaching logic this way, the first two are just developments of things that Adam touched on himself:

One. Maybe the success of teaching logic through searching is a product of the extra excitement and interest involved in teaching such an experimental class. If that were true we might expect results to tail off as the method became standardised. (Well, that might be the explanation, but we should not assume that. We could say the same thing about any new, successful teaching method, and presumably some of those would be better than the methods we use now.)

Two. Searching isn't so helpful when it comes to thinking about conditionals. Students are puzzled when asked to search for "if it is English then it is non-fiction". This matters because the collection of arguments known as "the paradoxes of material implication", for example, these guys:

are traditional sticking points with students, just like disjunction introduction. (You might think this is fine though, since teaching conditionals is a bit tricky anyway. I might have more to say about this in a latter post, since I thought Goldfarb's explanation of the truth-table for the conditional in his recent Deductive Logic was one of the best I have seen.)

Three. New logic students already have difficulty separating syntax and semantics and often find it difficult to understand the point of a completeness proof. I worry that this method risks confusing them further by mixing up the semantic notions with the more syntactic looking database records. Maybe this worry is unfounded; after all, when we give Tarski-models for first order logic, we represent them using linguistic items - numerals, brackets etc. Maybe the database entries are just like that. But in that case shouldn't we be saying that what we're searching for is not itself a database entry, but whatever that entry represents? (like a book?)

Four. I'm a bit worried that searching encourages sloppiness with respect to the objects of certain properties. In taking about searching it's natural to end up talking about searching for "things that are in English" and then end up saying "being in English entails either being in English or being non-fiction since everything that is either in English or non-fiction is English." Though I am sure this makes perfect informal sense, it isn't the way we normally talk about entailment: entailment is a relation between interpreted sentences (or rather a set of interpreted sentences and a sentence. Or multisets of interpreted sentences, or...(sigh)), not between properties, (or even predicates.) Learning to be sensitive to such things is one of the tasks that is difficult for some students, and encouraging insensitivity to it early on might not be a kindness. (Though, thinking about it, one standard exercise is to ask students to demonstrate that "intransitivity entails irreflexivity", i.e. to show ∀x ∀y ∀z ((Rxy &Ryz) → ¬Rxz) entails ∀x¬Rxx. Perhaps by the time we start talking like this their understanding of validity is already safely entrenched.)

Finally, I have worries about introducing all this complicated build-up to the stuff we actually want to teach. There is potential for introducing all kinds of confusion. We'll be multiplying the definitions of validity, the kinds of objects students have to think about when thinking about logic, and with that the potential for confusing those objects and definitions. So a database record is kind of, but not entirely, like a model, but more familiar to non-logicians. This makes it helpful, but treacherous.

Lots of these worries are things that might be allayed by the details. Surely we can be as strict in the way that we talk about searching as we are when we talk about satisfaction. Perhaps this class is best aimed at high school students? Perhaps the class might only be aimed at students who are never going to need to follow a completeness proof. Perhaps there is a way of teaching the conditional through searching. If someday a version of this idea could help to overturn those teacups, then I'm all for it.

Adam also had some interesting things to say about the relation between searching and human reasoning, so I might talk about that in the near future.

Sounds like a good way to introduce logic for those who are having difficulty 'picking it up'.

I suspect it's a bad way to teach an entire course, but would make a good first couple of lectures.

As someone who spent 2 decades in industry before returning to academia, I have been very surprised by the emphasis I have found in academic research on "searching", on "question and answer", on "information retrieval", on "requests and responses", etc. This seems to be the trope underlying most of theoretical computer science, at the moment, for example, and now I see even philosophers are fascinated too by the metaphor.

It all strikes me as beside the point: the real world is about doing, not about finding.

I've found that the two things that stick in students' craws are material implication and the use of the exclusive 'or'. And, when they get to quantifiers, the idea that "All unicorns have horns" doesn't presuppose that there are any unicorns.

I guess one problem with explaining explosion in terms of searching might be that it presupposes that they have bought into the idea that "Every search that returns A & ~A returns B" will be true when no search returns A & ~A.

The practical ability to library searching does seem appealing, though.

If you haven't seen this already, David Velleman has some very nice interactive tools for teaching logic via library searches (among other things) as part of his blogic: A Web Logic Textbook.

I hadn't seen that, and, when I spoke to him today, neither had Adam Morton. Thanks for the link; I think I'll be adding it to the sideblog.

I love the English language and the logic (words) to use it. It also seems to me you can embed word numbers into it and make greater reason of it as well.I will continue to study the math part of logic as word logic. pljames@brmemc.net