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PHIL3110 – Modal and Non-Classical Logic 84.2

This review covers two parts. Firstly, what the course is about, and what the course can provide you with. Secondly, what prerequisites you need, and what the course assessment is like.

The course is mostly about the formal properties (the symbols, syntax, semantics, and proof theory) of various logical systems beyond classical logic.

The course doesn't cover much in the way of translation familiar to those who have done the formal logic course PHIL2110 (or PHIL1020, if you had done it years ago), i.e. there is no translating from natural language arguments to formal arguments, or vice-versa.

There is some discussion about philosophical issues. The majority of the time philosophical issues are raised, it is about whether a logic in question is able to capture the nature of the if-then conditional, or whether certain common inferences (like modus ponens) hold under different systems of logic.

For philosophy majors, you'll come out of the course with several useful logics for philosophical analysis. For instance, you'll be able to formally model arguments that have modalities in them, e.g. temporal claims or epistemic claims.

For mathematics or computer science majors, there are several useful logics in the course. The most obvious one for mathematics majors is intuitionist logic, which formally models claims about proof. Mathematics majors would probably also like the alternate proof technique (natural deduction) that Dominic gave at the end of the course during SWOTVAC. For CS majors the many-valued logics and modal logics would come in handy, and make a good partner-course to CSSE4603 (Models of Software Systems).

If you don't care about tools and applications, and think that it is intrinsically rewarding to study logic unto itself, then I probably don't need to convince you to take the course (the course is pretty much an intrinsic, rather than instrumental, exploration of various logics).

Even though PHIL2110 is a prerequisite you only need propositional logic to do the course. The course covers the first half of Graham Priest's textbook. As such, PHIL3110 covers propositional extensions or rivals, and doesn't cover predicate logic extensions. If you are a philosophy major, the only re-reading for the course you would need is propositional logic. Make sure in your re-reading to do as many truth trees (semantic tableaux) as possible, as the majority of assessment in the course is doing proofs in the form of truth trees.

There are also natural language proofs that are familiar to students of mathematics. If you have done MATH1061 you'll be ok with the proof techniques in this course (nearly all the non-tree proofs are direct proofs, proof by contraposition, or proof by contradiction. I could count on one hand the number of times I had to do mathematical induction).

Anyone that has done MATH1061 (and not done the logic courses under philosophy) would be able to do this course with the added condition that they read up on semantic tableaux (truth trees), which aren't hard (you could learn propositional truth trees in a day, check out Roderic Girle's textbook in the library under Call Number BC108 .G57 2008).

This is one of those courses where you should be studying from day-one, as later chapters build on earlier chapters. Many of the later chapters build on the possible world semantics in chapters 2 to 4. If you can do those chapters ok, you should be set for the rest of the course.

The course has two major assignments and a final exam. Every week there are homework problems in tutorials, but these are not assessed (do them anyway, as they are very close to the assessment). In the 2014 course, the first assignment covers chapters 1-3. It wasn't hard, as it mostly semantic tableaux with a couple of proofs. The second assignment covers chapters 4-7. I found the second assignment much harder than the first assignment. The final exam covers chapters 7-9. It was similar both in layout and difficulty to the first assignment (lots of trees with a handful of proof questions), and similar to the homework questions given at the end of chapters 8 and 9.

In the 2014 course we ran out of time and didn't get to cover relevant logics or fuzzy logics. This wasn't too bad, as the course covers the background needed for reading up on these logics anyway.

Semester taken

Semester 1 - 2014

Your program/major

BSc / BA

  • Dominic Hyde is an engaging and informative lecturer
  • Covers a wide variety of logics that are both instrumentally and intrinsically rewarding
  • Didn't get time to cover all the logics in text.
  • Text only has one or two worked examples per section.
Posted on July 5, 2014 9:23 pm

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