Sunday, April 15, 2007

Logical options

There's an afternoon planned soon to review the Faculty's teaching, so it will be a good occasion to rethink some of our current arrangements for logic teaching. At the moment this looks to me to be about the right pattern, given the calibre of our students (good) and our resources (limited).

  • First year, propositional and predicate logic by trees (up to and including completeness for propositional trees: this is in fact what we do at the moment, using my Introduction to Formal Logic). We should also perhaps have a few lectures on set notation etc. (again, something we do at the moment). That's compulsory for all students.
  • Second year, we could have five units corresponding roughly to the five main chapters of Logical Options by Bell, DeVidi and Solomon. So that's a unit on other ways of doing logic, using propositional logic as the illustration -- in particular, natural deduction. A unit treating the semantics for predicate logic more carefully, and an explanation of the completeness proof. Something on axiomatic systems built using a first-order logic. A unit introducing modal logic. And a unit on non-classical logics, in particular intuitionistic logic. (Again nearly all those are already on the syllabus, but we don't teach them in a methodogical and integrated way. Using Logical Options as a course text could be a way of imposing order on the current slight mess. The book strikes me, having just got a copy for the first time, to be very good: it goes quite snappily and needs support from lectures, but it is the right kind of coverage and the right kind of level. This too is for a compulsory paper, though students can avoid answering too-technical questions by concentrating on some associated philosophical logic.)
  • Third year, mathematical logic. This could remain pretty much as we do it at the moment. Some basic model theory, comparisons of first and second order logic, etc. Then Michael Potter's course using his Set Theory and its Philosophy, and my course using An Introduction to Gödel's Theorems. We could also make the technical parts of the current paper available as a graduate course for those who haven't done enough logic when they come to us from elsewhere.

It is my impression is that even good and large departments elsewhere in the UK are dropping serious logic teaching (so that e.g. a Single Honours student may have access only to one optional honours module using Tomassi's very, very elementary book). But before getting too upset about this and bemoaning the Dumbing Down of Courses and the general Decline of the West, I am minded to try to organize some kind of survey to find out the state of logic teaching in UK philosophy departments. I've put a message out on Philos-L to check that no-one else is in the middle of doing this (and check too that a survey hasn't been done recently and I've just failed to notice!). Watch this space.


Richard Zach said...

I did a survey like this for US departments a while ago:

Peter Smith said...

Yes indeed, Richard! And one thing I'll try to do if I get the UK survey underway is to make comparisons between the provision at good UK departments and provision at good North American departments. My impression is that it won't show us in a good light: we are in danger of closing off whole areas of philosophical enquiry from the reach of too many UK students.

Ole Thomassen Hjortland said...

Some info from the University of St Andrews:

(1) The first-year course uses the first part of Jeffrey's 'Formal logic' 4th ed. Alternatively, the students can use Howson's 'Logic with Trees'. The course includes trees for propositional and first-order classical logic, but does not include completeness results. There is no set-theory.

(2) The second-year course is joint formal logic and phil. of logic. The formal part goes through most of Graham Priest's 'Introduction to Non-Classical Logic', but introduces natural deduction for the most central systems (the normal modal systems, intuitionistic propositional logic and first-order). Again, the course stops short of completeness results. The book has a short preliminary on set-theory.

(3) At Honours level there is usually a meta-logic course based on a selection of chapters from Boolos and Jeffrey's 'Computability and Logic'. I think the course goes through most standard meta-results for first-order classical logic, e.g., completeness, L-S theorems, compactness, etc. Other topics are sequent-calculus, recursivity, and Turing machines.

(4) Finally, there has sometimes been a M.Litt course (master level) on logic and algebra, based on compendium by Stephen Read. This year, however, the M.Litts get a course on Meta-logic, focusing on Hunter's 'Metalogic'.

Overall, I suspect that St Andrews is not among the worst UK universities, but my impression - although I haven't been here that long - is that the courses are getting easier across the line.