Live from the Logic Colloquium

While everyone else is blogging from the NDC, I'm in Turin at the European Summer Meeting of the Association of Symbolic Logic, aka LC'04.  Highlights so far: Grisha Mints' opening talk on Monday, in which he presented a result showing that all intuitionistic Frege systems polynomially simulate each other.  It uses some interesting recent work by Rosalie Iemhoff (Vienna), who showed that all intuitionistically admissible inference rules can be generated from a finite set of rules; Grisha's result means that superexponential lower bounds on proof lengths for one intuitionistic Frege system extend to all others.  Michael Möllerfeld presented his recent work on systems equivalent to Π¹₂-CA. Π¹₂-CA is the cutting edge of ordinal analysis (work of Rathjen and Arai). One of the systems Michael showed is equivalent to Π¹₂-CA is the μ-calculus, which is a formalism  with a fixpoint operator which is really important in theoretical computer science. Also interesting were the talks by Anton Setzer on extensions of Martin-Löf type theory, and by Andrea Cantini on constructive set theories with operators. Not much on the more philosophical side, but I should mention the talks by Phil Ehrlich on the pre-Robinson history of infinitesimals in mathematics (a long paper forthcoming in the Archive for the History of the Exact Sciences), by Luca Belotti on consistency of large cardinals, and the panel discussion on "Kant's legacy for the philosophy of logic."  It was mostly on Kant, and not on the legacy.  I wished there was more on Frege vis-a-vis Kant or something like that; in particular I thought it was a shame that no-one discussed John MacFarlane's recent work on Kant and logic.  Today is sight-seeing day, more proof theory tomorrow (as well as a talk by yours truly on Gödel logics).  Oh, and thanks to Greg Restall for pointing to the beamer class a few weeks ago.  They don't have projectors here for the contributed talks, but as it turns out, beamer also makes very nice overhead transparencies.  I recommend the "lined" template.

Two Interesting Conferences Next Year

Two exciting conferences coming up next academic year: In November, the 5th Midwest Philosophy of Mathematics Workshop will be held at Notre Dame. I went last year, and it was a fabulous experience. There will be a special presentation by Dana Scott. And at the end of March 2005, the 1st World Congress and School on Universal Logic will take place in Montreux, Switzerland. Nice place, exciting topics, interesting speakers (inter alia, Arnon Avron, John Corcoran, J. Michael Dunn, Dov Gabbay, and Krister Segerberg). Unfortunately, March is an impossible time for me to get away from teaching for more than a few days.

The Status of Logic in Philosophy II

As a follow-up to my previous post, I took it upon myself to survey graduate program logic requirements. Of the top 50 US PhD programs (according to the Gourmet Report), every one has a logic requirement of some form or another. 15 require only an introductory course in formal logic (propositional and predicate logic, formalization, and proofs). I was surprised that Harvard and MIT are among them. The others require at least some metatheory: 17 programs want their students to do completeness, Löwenheim-Skolem and compactness proofs. At some schools (Rutgers, Pitt, Texas, Wisconsin, Washington), the advanced logic requirement is satisfied by a one-semester course covering completeness, undecidability and incompleteness. (I suppose it's possible to do that, but I have a hard time getting all that covered in an entire year.) Only at Arizona you can get away without taking logic.

Very few programs seem to make their students learn logic that's specifically interesting for philosophy. At CUNY, Rohit Parikh teaches the Logic Core course that covers propositional and predicate logic, Kripke semantics, Lewis's and Stalnaker's theory of conditionals, and incompleteness. That is the only program, as far as I can tell, that requires a specifically philosophical logic course. Several others have a requirement that stipulates that students take "an approved logic course," and I assume a course in modal logic or formal semantics would count there (Irvine, Davis, UMass, Syracuse, UConn, UVa, and Miami).

At the undergraduate level, logic requirements are also still common in the US. Only Arizona, Cornell, Duke, Johns Hopkins, UConn, and USC don't seem to have a required logic course in their BA programs. Almost all the top 30 require formal logic; however, almost none of the programs between 30 and 50 require more than informal logic.

Of the five ranked Canadian programs, Toronto and Western require formal logic; McGill requires a course in metalogic; UBC doesn't have a logic requirement; and I couldn't tell from their website if Alberta does or not. Outside North America, I had a hard time figuring out program requirements. It seems that UK and Australasian departments don't have formal breadth/depth/etc. requirements. I found reference to a logic requirement only on LSE's website.

So: The consensus still seems to be that it's important to a philosophy graduate education to learn logical metatheory (at least model theory). That's good, I think. It gives students an appreciation for what logic is about. I don't know what to think of the one-semester course on everything (completeness, incompleteness, undecidability, etc.). That seems to me to be way too much to cover in one term; at least, too much to cover well and in depth in one term. But maybe someone can tell me how to do it? Is that a more useful course to have than just a basic metalogic course? And is it better to have a course like that, or like Parikh's?

Blog Rules

Brian Weatherson has started a discussion about rules as to what it is ok to write about in philosophy blogs. This was taken up by Lindsay Beyerstein and Gustavo Llarull. In the comments at TAR, I suggested that it's doubtful that new rules are needed. Blogging is a relatively new phenomenon, but academic discussion (in print, at conferences and seminars, and also on the internet) is not. Jeremy Aarons replied that I may have underestimated the fact that blogging is a form of publishing. But so is posting to Usenet, publishing a paper, giving a talk or filing a dissertation.

Is there anything that makes blogging different from other occasions where you might be faced with a judgment call as to whether it would be acceptable to use someone else's ideas, and in what form? Permanence only distinguishes it from oral communication; the actual audience for any particular blog is probably not greater than the audience for any particular newsgroup; the potential audience for anything published in written form is more or less the same; and the original authors of the ideas have an opportunity to respond on blogs just as they do in other media (publicly or privately).

Is there anything that makes academic blogging about philosophy different from academic exchange in other media? Again, I don't think so, but I'd be interested to hear what others think.

That is not to say that bloggers shouldn't be reminded of the issues that Brian raised. In particular, they should be reminded of the dangers of doing anything right after leaving the bar. It is generally a bad idea to blog about a drunken discussion about philosophy where you write about someone else's views. Not only might it be rude, if not unethical, to publicize what someone else said while drunk, the chances that what you yourself say about it will be wrong increase significantly as well.

Free-variable Tableaux

Wolfgang Schwartz asks here if there is a "canonical" way to build free-variable tableaux which are guaranteed to close if the original formula is valid. It seems to me that this must be the case, since free-variable tableaux are a complete proof method. But maybe I don't understand the question.

The point of free-variable tableaux is to postpone substitutions of strong quantifiers until such a substitution results in a closed branch. So instead of expanding a branch containing ∀x A(x) by A(t) for all possible t, you keep the free x around until you get a formula ¬ B on the branch where A(x) and B unify. Closure, i.e., the actual substitution of x by a term only happens when this is the case. So at each stage, you should check if you can apply Closure (i.e., if you can close the branch) but you don't actually apply it until you can.

The Status of Logic in Philosophy

It is a commonly accepted view (among logicians working in philosophy [departments]) that while logic was considered central to philosophy in the mid-20th century, it has since moved closer and closer to the margins. It is said, e.g., that while in the 1950s and 60s it was common to find "pure" logicians working in philosophy departments (and consequently, that as a pure logician you could find a job in a philosophy department), this is no longer the case to a similar extent. It is also believed that while a few decades ago logicians enjoyed a reputation (among philosophers) as people who were doing important (and hard) work, now much of logic is just not considered philosophy anymore. I wonder how accurate this cluster of suspicions (henceforth "the belief") actually is .

Anecdotal evidence certainly suggests that it's difficult to find a job as a logician. But is it more difficult than finding a job, period? And is it more difficult now than it was 30 or 40 years ago?

Anecdotal evidence also suggests that logic is not held in particularly high regard among some (many?) philosophers. But is this more true now than it was 30 or 40 years ago?

These are difficult questions to answer; difficult to answer, that is, other than by adducing more anecdotal evidence. One would think that if the belief is correct, then the number of logic jobs advertised should have declined over the last 30 years (as a percentage of all philosophy jobs). One would also think that the philosophy curriculum would have changed reflecting the changing status of logic in philosophy as a whole. Thirdly, it would likely be the case that as fewer logicians were trained and hired by philosophy departments, there should be fewer logic papers published by logicians in philosophy departments.

I have no idea of how to come up with hard data on the first two cases, but I'd be interested to hear anecdotal evidence, especially on the second point. Does your department offer fewer advanced logic courses now than it did 20 or 30 years ago? Did your department use to require a graduate logic course of its grad students but no longer does?

There is some hard data on the third issue, thanks to the Web of Science. I've done some searches on logic papers in the past three decades. The data is a little skewed, I'm sure, since they don't have extensive coverage of the period 1975-1984, but the results are nevertheless interesting. I tried to compare output by people working in philosophy departments (in the US, Canada, the UK, Ireland, Australia, and New Zealand) in logic journals (The Journal and Bulletin of Symbolic Logic, and the Journal of Philosophical Logic). The results are interesting:

	1975-1984	1985-1994	1995-2004
Journal of Symbolic Logic + Bulletin of Symbolc Logic	10/1473 0.6%	50/1579 3%	53/1040 5%
Journal of Philosophical Logic	32/252 12%	89/196 45%	79/243 40%
Total logic papers	52/3,406 1.5%	202/8,963 2%	385/10,156 3%

In the first two lines, I gave the ratio of papers by authors in US/ Canadian/ British/ Irish/ Australian/ New Zealand philosophy departments to the total number of papers in the respective journals. In the last line, you have the ratio of logic papers to all papers in the index (by authors in US/Canadian etc. departments). It looks like the output of logicians in English-speaking philosophy departments has increased since the 1970s.

I conjecture that what happened in philosophy vis-à-vis logic is not that logic has become (seen as) less central, but that as philosophical logic has matured over the last 50 years, it has been integrated into the appropriate areas of philosophy. So perhaps it isn't logic per se that's seen as less central to philosophy, but the kind of logic you could still commonly find being done in philosophy departments in the 50s and 60s, which wasn't that much different from the logic done in math departments.

UPDATE: Updated the table to include New Zealand, as well as Ireland, Scotland, and Wales.

UPDATE: Followup posted here.

Promoted!

I got the official letter today: I'll be Associate Professor as of July 1. Yay!