I've just had an invitation to give a talk at the University of X, a distinguished place, with a philosophy graduate community of about fifty (according to their website). So I checked out how much logic/phil maths is going on, what I could reasonably take as given. Zilch. Apart from a first year course perhaps approaching the level of my intro logic book, nothing at all, as far as I can tell. Which leaves me a bit bereft of anything to go to talk about. But more to the point, it means that for students at X a central swathe of the work of lasting value from the last hundred years has disappeared over the horizon. Which is, shall we say, a pity.

My sense is that this is happening more and more in UK universities. I'd be delighted to learn that I'm wrong.

## Wednesday, July 29, 2009

### Logic disappearing over the horizon ....

Posted by Peter Smith at 11:26 AM

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## 23 comments:

What do you want to be on the course?

And why can't more of us mathematicians have more logic courses!

This is a bad thing for sure, though not dissimilar to cambridge's philosophy of mind offering in recent years?

Anon: There are various things one would like to see covered -- but at least make a start beyond baby logic! Good question as to why logic is often not taught to any extent in pure maths courses. Cambridge is a case in point.

Lee: At least the phil mind paper was kept as a suspended paper, indicating we knew we SHOULD be teaching it -- and indeed it is back this coming year. But there is a difference: if you've done related bits of phil and an intro mind course, it isn't too tough for a student to "catch up" on their own, without a lecture course (and indeed, people did write some excellent third year dissertations on the philosophy of mind). But it's a lot harder getting on top of logic under your own steam: if you don't do it as an undergrad/beginning grad, you probably never will do it.

Peter,

Agreed.

I'm glad to see Mind is making a reappearance at Cambridge.

I don't like to see any of the core areas being overlooked, although I guess departments have to make unpalatable decisions.

Hope to visit Cambridge again next January. Of course, that depends on me having an idea in phil logic.

best

Lee

Is it just that they aren't offering anything related this semester? Or does the entire course catalog not have the higher-level course you'd like to see?

I would be surprised if the situation were much different in the US. Logic curricula have been shrinking everywhere. It would be interesting to see how many ranked programs (in the US and the UK) require advanced logic of their graduate students.

Anon: The entire course catalog doesn't have even an intermediate level course (e.g. at the level of Bell, DeVidi and Solomon's

Logical Options, let alone a higher level course.Aldo: I don't think any grad programme in the UK

requiresadvanced logic. But at least one would like to see courses beingavailable. I have to say, depressingly, that as the number of students here in Cambridge, undergrad and grad, has grown, the number doing our Math Logic course -- which isn't very challenging -- keeps dropping.From what I hear, the reforms to the IB logic syllabus may reverse that trend. But perhaps that's merely wishful thinking.

The situation in Australia is just as dire, with logic teaching in Philosophy departments. At Melbourne we do better than most, but I'm struggling to keep our logic stream in Philosophy going. We teach

Level 1: team-taught with collaboration from Computer Science, Mathematics, Engineering, Linguistics and Philosophy: on propositional and predicate logic with little hints of applications to each discipline.

Level 2: Non-Classical Logics: Kripke semantics for modal, conditional, intuitionist and other logics. All propositional logic.

Level 3: Completeness + Incompleteness: on the metatheory of predicate logic, computability and Gödel's first and second incompleteness theorem.

I don't know of anywhere in Australia with a comparable program, but I do know that they do a good job of teaching logic in Auckland and in Wellington.

But regardless, we don't require

anylogic of our graduate students. It's just that we offer it to those who want it...Just for info, offerings (to philosophy undergrads) in Cambridge are not dissimilar to Melbourne.

First year, my intro Logic Book (minus completeness proofs). Logic by trees, in other words

Second year, bits and pieces of phil. relevant stuff. Idea of natural deduction (harmony, introducing prop. intuitionist logic). Modal logic (prop. again). Quantifiers (more on the semantics of first order languages). The idea of a formal theory: notion of categoricity, etc. So roughly in territory of Bell, DeVidi, Solomon.

Third year. Completeness, compactness, L-S theorems, etc. Some of my Gödel book. Some of Michael [Potter]'s set theory book.

At grad level there are some maths courses people can and occasionally do go to (though the culture shock of hard core Cambridge maths style can be harsh!). And we often have reading groups on techie stuff (we've recently dabbled in category theory, Wilfrid Hodges shorter Model Theory and next plan to do a term's serious modal logic).

Have you come across Ted Sider's Logic for Philosophy? It looks like a nice attempt to get grad students up to speed on the logic they need to follow most debates in metaphysics and language these days. It looks like it might be less technical than the Cambridge courses, but it would be nice if universities could offer grad students a course based on something like that.

Any thoughts / rumours / speculation on

whylogic is disappearing?And is it going in maths and CS as well, or only in philosophy?

It's especially strange since, it seems to me, there are so many applications these days in CS and even linguistics.

Anon: I saw an early draft of Ted Sider's book, which I frankly didn't think was that great; but the finished version could well be better. Though there's a sample of the finished product on his website. And I notice e.g. that the Löwenheim-Skolem theorem doesn't even get a mention; so it's not going to help someone who wants to understand e.g. Putnam's model-theoretic arguments against metaphysical reaslism. So Sider's range is limited.

RM: my impression is that logic is flourishing in some theoretical CS depts., and indeed in some maths depts. -- I think there is a history to why it doesn't feature much in maths here in Cambridge.

There seem to be plenty of logic texts, For model theory, for example, there's long Hodges, shorter Hodges, Marker, Dover's reprint of Models and Ultraproducts, a forthcoming 2nd ed of Saturated Model Theory, plus various others. Lots of set theory texts too, and books about modal logic.

So presumably someone is (or was?) buying them. I hope the market isn't collapsing.

a.c. Yes: and I have no complaints about the sales of my Gödel book (not astronomic of course, but respectable enough). So there must be enough logic going on in enough places round the world! My worry is a local one, that it is being squeezed out of too many UK departments.

Logic is seen as part of mathematics now and not philosophy, I suppose.

And of course computer science, which has a complicated relationship with mathematics due to pressures of spewing out code monkeys versus researchers.

Actually maybe you should be seeking some comp sci invites. Maybe print out some flyers.

Andy: Sure, technical research in logic belongs to mathematics and computer science. Most of it, anyway (philosophers have still made notable contributions recently in some new areas -- e.g. in the development of plural logic). But

knowledgeof some basic logic is still a prerequisite for serious work in various areas of philosophy. And what I was bemoaning was not the absence of courses which could lead to a philosophy student becoming a techie logician at a research level, but the lack of courses which would tell her even what she needs to know to work on various central areas of philosophy.A question which doesn't settle how important knowing logic is, but is interesting nonetheless: how often have you read recent work in philosophy of language, science, or metaphysics and thought that the work was weak because of a lack of knowledge of relevant logic? (I'm not thinking of botched presentations of logical stuff, such as the Bueckner you recently mentioned, but work where knowledge of the logic helps.)

As someone with not much beyond the typical intro course, I'm not in a position to answer that, but it would be interesting to know what you thought.

Matthew: I think my worry is that good work that IS logically informed becomes opaque to students without enough logical background (rather than that much published work is vitiated by logical ignorance). Take, for example, Hartry Field's recent

Saving Truth from Paradox. A must read for those interested in truth, which is hardly an esoteric topic! But -- although Field is careful to make the book accessible and keep technicalities to a minimum -- it would surely not be readable by someone who hasn't even done a second-level logic course.The lack of good logic courses for philosophy students seems a general problem in most West-European universities. I come from Poland, I've studied philosophy in Warsaw, and though perhaps I wasn't the best in my group in advanced logic, my knowledge of logic is much better than any Belgian or American student I've met during my stay abroad as an Erasmus student. Philosophy faculty at Warsaw University offers a number of seminars and elective courses for students interested in logic.

I also agree, that the development of logic shifts towards more "technical" issues and therefore is more common in computer science/mathematics faculties. This might also be a cause, that it's nearly impossible to have a strictly logic-based research project accepted at a philosophy faculty, whereas at a computer science faculty it is still possible (even for someone with only philosophical background).

This comment is heavily colored by my situation in mathematics in the US (where many have also proclaimed the impending death of logic). Still, it may have broader applicability.

The original post reckons that the lack of logic in the local curriculum "leaves me a bit bereft of anything to go to talk about."

Quite to the contrary, it leaves you the whole world to talk about! We who believe that logic is important have our reasons, and many of them are accessible to non-logicians. The audience will not have heard everything before. They will be attentive (at least for the first few minutes) to see if you have anything worth hearing.

The correct response to the impending death of logic is to dial up the explanation of why the world would be worse without it.

I just came across this thread... I can report happier news from the University of Sydney, where logic is flourishing. Our first year logic course has roughly doubled in enrolment each year for the past four years (it's now around 400), and we also have three upper-level courses:

First Year: Introductory Logic. Propositional logic; predicate logic with identity; first-order model theory; tree proofs.

Second and Third Year:

1) Intermediate Logic. Some proof theory and some metatheory, e.g. compactness, completeness.

2) Exploring Nonclassical Logic. A selection of extra- and non-classical logics, e.g. many-valued, tense, modal, relevance, intuitionist.

3) Logic and Computation. Some set theory, theory of computability, and then some more metatheory, e.g. decidability, incompleteness.

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