Thursday, June 4, 2009

How Much Logic?

In keeping with the recent posts about graduate programs and their requirements, here are a few further questions:

How much logic should graduate students in Philosophy have to learn? Why? Is there more than the (I'm guessing typical) prudential reason about needing to be able to teach basic logic? Is the logic requirement like the language requirement (arguably not necessary for all)? Or is the logic requirement more like an area requirement in, say, Metaphysics? And so on.


Robert said...

Clearly training in logic is not *necessary* to being a first rate philosopher; there are too many counterexamples (e.g., Jeff McMahan). One might think there is something like the 'well-rounded philosopher' who is educated in all major areas of philosophy up to the point that she or he can appreciate the philosophical problems at the heart of that area. (I myself like this model of grad education, but I have doubts about its viability, given the need to master one's area of research.) Getting to that point in logic takes more than the usual 'logic 101' grad course. But if I were king, I would require some sort of survey course in formal semantics instead of something in logic. That contains much of the lingua franca of contemporary philosophy, and one really should be acquainted with it, if for no other reason, than to be able to read much of what is in the journals.

PA said...

Insofar as our concern is with research competence (and not prudential concerns or disciplinary nostalgia), I would say that grad students need to learn (1) propositional/ predicate logic and (2) modal logic (understood broadly to include deontic, doxastic, and alethic modalities) but not (3) meta-theory. Familiarity with (1) is simply a basic skill all philosophers need. Familiarity with (2) is required because, among other reasons, it is presupposed by a lot of the professional literature. Familiarity with (3) is, however, only required for those specializing in logic.

Anonymous said...

I say toss 'em all into a set theory course first semester and be done with it.

Anonymous said...

I'm with PA. I'm a grad student specializing in ethics, some of which is kind of technical, but I see no need (from a research standpoint) for me to know anything about meta-theory.

Anonymous said...

Interesting, PA. The two schools I am familiar with require 1 and 3, but their course on 2 is sometimes not taught for years at a time.

Is 2 really presupposed by that much of the literature? It seems as though that would only apply to some specific sub-fields.

MK said...

One advantage of a basic course on metatheory is that it's often the first chance people get to see and (especially) to write mathematical proofs, and this can be useful even if the particular content (soundness and completeness of classical 1st-order logic or whatever) isn't relevant to someone's reseach. This may be one consideration in favor of requiring a course on metatheory, rather than (say) a course on modal logic that doesn't touch on metatheoretic issues in detail.

PA said...

@ MK and Anon 5:42:

Two things:

1. Don't get me wrong. I really liked meta-theory in grad school (and was even pretty good at it). If I get I excited I might even describe it as nifty. But even though I tend to work on relatively technical stuff, it really hasn't come up in my research.

2. Don't misconstrue my point about modal logic. A lot of philosophy revolves around "ought"s and "must"s (as opposed to "is"s): some might say it's our stock and trade. As a result, a working familiarity with both the inferential roles and interpretations of "ought" and "must" claims is something most grad students will need to have in their philosophical toolboxes. Whether or not that requires they take a self-standing course in modal logic is another matter.

Jon Cogburn said...

Georg Kriesel used to say that he never saw the point to completeness proofs until he took it to be the case that their main point was to show that one can generate an effective procedure for enumerating logical truths. So he didn't see the point of the stuff we teach in the general meta-theory until you see how that is related to things involving limitation results typically taught in another course.

I didn't really see the point of the beginning meta-logic until I'd done modal logic. It's when you get to Kripke's completeness proofs that you see the importance of semantics over just proof theory. The semantics actually do give you a hang on the different meanings to be able to make sense of what is really different about necessity in S4 and S5. At that point soundness and completeness of classical first order logic didn't seem like a weird exercise any more.

So this is another reason to have modal logic mandatory. If you've have a user friendly introduction to modal logic (with a little meta-theory) you can get a lot, lot more out of a standard meta-logic of first order logic class.

A lot of departments use the standard meta-theory in first order classical logic class as a hoop, and most students don't really see the point while doing it and don't remember any of it afterwards.

In our department (an MA program) we're now using Priest's second edition of Non-Classical Logics for both of our upper level logic classes. We've found that this works much, much better for just these reasons. Plus, the students who just take the first one can actually use it in their research (again, philosophical ubiquity of "must" "ought" and related notions).

Anonymous said...

Part of what Spiros seemed to have in mind with his post was the following parallel argument:
If competence in a foreign language should not be a general requirement for a PhD in philosophy since it is necessary only for whose who specialize in the history of philosophy and not in contemporary M&E/core, competence in meta- and modal logic (or anything beyond propositional and predicate logic) should not be a requirement since it is necessary only for those who specialize in certain areas of contemporary M&E/core and not in the history of philosophy.
Other than Anon 1:00, who seems to concede the conclusion, (and perhaps elements of Robert's post), I haven't seen much in response to this line of thought. So, does Spiros concede the point (i.e., that any meta- or modal logic requirement stands or falls with a foreign language requirement)?
My own view is that *if* one accepts as a counter-argument to any requirement that there might be some students for whom satisfying that requirement would not be particularly useful for their ultimate area of specialization, it's actually quite difficult to articulate a good justification for these kinds of requirements.
I reject the antecedent, but rather doubt that there is any consensus on what it would take for something to be a good justification of a requirement. That is, I am skeptical that there's widespread agreement about what would justify requirements beyond that they contribute to one's area of specialization. And with increasing specialization, the idea that any requirement might be necessary for the wide range of specialties becomes increasingly remote, or so it seems...

Jon Cogburn said...

The self image of analytical philosophy right now is for the most part this story. The logical positivists put forward a neo-Kantian linguistic account of necessity. Quineans showed that to be a dead end. Kripkeans (with the help of Lewis and Stalnaker) saved the day and made the world safe for metaphysics again.

I personally think that's a bad story (there were lots of reasons to be a transcendental idealist besides the problems of necessity), but I can't really understand what's going on unless I understand that story. And I can't understand that story without modal logic.

Besides the hope of making any progress whatsoever on the other three problems Kant wrestled with requires knowing logic as well. Well two of the three (the paradoxes of self reference and totality, and the problems of normativity- must, ought, etc.), maybe you don't need so much for addressing the problem of the external world.

So three of the four things that gave rise to Kant concern modern logic. And we do understand these issues better than people did in Kant's time just because of the development of modal logic.

So yes, anyone getting a PhD in philosophy should learn modal logic. Unless you think of history of philosophy as just history and not really a part of philosophy, you should learn modal logic (and arguably limitation results relevant to the history of paradoxes and thoughts about limitation) too.

Here I assume: (1) that contemporary logic actually is progress, and (2) it makes sense to read historical philosophers as worried about the same things we are. I don't think these should be controversial.

Anonymous said...

Jon Cogburn: Isn't this only the case when one takes "analytical philosophy" to be LEM (and possibly just M), rather than as "the style of philosophy predominant in the majority of US and British philosophy departments"? The case for a philosopher working primarily in metaphysics seems easier to make than the general one.

But perhaps the motivation for the logic requirement is different from what seems to be presumed here. What if instead of being a type of knowledge that people need to pursue philosophy, the ability to do formal logic is being used as a weeder, or more particularly, as a proxy for certain styles of thinking. It might be as simple as "if you can't do this, maybe you should work in a different field, even if you won't do much of this in practice."

K. M. Berry said...

There is only one professor at my university who teaches the more advanced logic courses. I agree strongly that some advanced logic courses (or demonstrated competence) ought to be required of all philosophy graduate students. Sadly, said professor is bloody incompetent and did little more than read directly from the text and give crazy looks when anyone expressed confusion.

Tenure: both a glorious benefit and a serious bane.