Prompted by a colleague and friend (thanks Ruth!), I’ve been asking students who took my upper level logic subjects last year what they learned about how to learn logic. This is helpful for me—I get a better understanding of how students are learning. It’s hopefully helpful for them, too, to reflect more explicitly on how they learn. But most of all, I hope that their reflections will help students who come after them. After all, advice from peers is fresh and direct in ways that advice from someone whose first encounter with the material was nearly 30 years isn’t.
I’ve been so impressed with the answers students sent me. They’re thoughtful and insightful and I’m sure the advice will useful for future students. I thought I’d share them, in case it helps you to learn logic, or to teach it to others.
Here is advice from two students from my subject phil20030: Meaning, Possibility and Paradox. This is a second year introduction to modal and non-classical logic, with a little bit of philosophy of language along the way. It’s taught using video lectures, a weekly two hour seminar, and students work in teams on weekly to prepare for each session, and as a support and study group outside classes.
Here are some things that worked well for me:
most importantly I engaged with my group heaps. We met up regularly and talked over everything, which was super helpful both in understanding the content and solving all those really tricky puzzles.
secondly I made an effort to really understand and take notes on all the lectures (well… most…), pretty much all the content it assessable, or at least potentially so, and the lectures were a great way to get it learned.
Things I could have done better:
engaged more in the tutes. I often found it hard to concentrate through 2 hours of pure logic, and I let myself slip up a bit in that regard, which was a pity, because that just meant I had to re-learn what I missed without Greg there to correct me.
Checked my work before submitting. That is to say, I checked it, but I should have double checked it and then checked it again for good measure, it’s easy to make silly mistakes.
I hope your new students have as much fun as I did!
Notes: One thing I recall clearly is spending far too much time at the end of the semester compiling notes so that I could have a worthwhile set for the exam. I strongly recommend students collate their notes throughout the semester, so that at the end, they can focus on applying their skills to practice questions
Team: My team was invaluable, especially in working through difficult questions. The approach should be twofold: learning from others’ approaches to difficult questions, and secondly, solidifying your knowledge through the process of explaining things to others. With that in mind, an effective strategy would be to allocate each member of the team some questions each week, and then meet before the class to discuss each person’s responses. In fact, I would argue that regularly utilising one’s team is essential in order to succeed in this subject.
What do I need to know? The content of the subject can appear to be broad, and it’s difficult to know what to do, in order to prepare for the exam. However, the information that is uploaded each week to the LMS contains a section that summarises clearly the intended learning outcomes for the week. I recommend using this as the first part of revision—ensure you know every dot point, for every week, and have notes which you understand for each dot point. Once this has been achieved, you can be confident that you have all of the core skills required in order to answer exam-style application-based questions.
Assignments… can be difficult. Start them as early as possible. Answer what you can, even if the final answer eludes you. And remember to use a high degree of clarity, neatness, precise definitions and wording (try to imitate the wording of the text-book). Precision and ensuring that each step of working has been explained, is a great way to gain marks (especially when you have understood the answer conceptually, but have merely failed to elaborate upon each step on paper).
Practice: Is the key to succeeding in the exam. I strongly recommend that students prepare themselves so that practice can be their priority (i.e. have their notes completed, understand the basic concepts, so that at the end of the semester, they have the opportunity to do every practice question from the past exams). Furthermore, upon completing each question, I would recommend turning the answer into a set of notes, by placing an explanation of the working, next to the answer. This way, the next time a similar question comes up, you can refer to your notes, to refresh the concepts that are needed in order to answer the question.
And here is advice from three third year students, from phil30043: The Power and Limits of Logic. This is a third year introduction to the metatheory of classical first order predicate logic, taking students from soundness and completeness to Gödel’s incompleteness theorems and Löb’s Theorem. It’s taught using video lectures a weekly two hour seminar, and students work in teams on weekly to prepare for each session, and as a support and study group outside classes.
Definitely make sure you understand and be comfortable with the initial foundation part of the course before even attempting to understand the more difficult components.
If you are having trouble with a concept, use Google and YouTube. There are plenty of resources out there that try to explain logic concept in layman’s terms with pictures and diagrams.
My advice would be to not get too bogged down by symbol pushing and notation. At least until we got to the last bit (Löb’s theorem, Godel’s First and Second Incompleteness Theorems) I found that making simple pictures really helped to distill complex concepts into nice digestible chunks. This also saves a lot of writing time when it comes to making those exam notes…
Watch the videos before class and don’t ‘spray and pray’ the LMS questions. Also work hard to participate during seminars (this is something I didn’t do enough of) and give everyone a chance to do the same.
At the beginning of the subject, start compiling one big document with all your notes for each topic. This will greatly help come exam time, when you already have your pages of notes to take in.
The notes should be updated each week…and it’s really important that you keep up your understanding as you go, and make sure things make sense as you go. This is for two reasons:
It’s really not possible to ‘cram’ in way it is for many other subjects, seeing as a large part of the material is just understanding very difficult concepts. It’s very hard to get your head around concepts like these in a short period of time. Gradual learning with plenty of breaks helps.
It is likely that having learnt a topic you will have a few burning questions or uncertainties about it. The best case scenario is that you can just ask these at the next seminar. If it’s the night before the exam, you may have less luck. Particularly the last third or so of the course is conceptually quite difficult. It will help to be on top of everything at this point! That said, make sure you nail the more concrete and straightforward aspects, for example Hilbert Proofs, or DNF. These just require practice.
Lastly, the two ways I found to maintain passion and interest in the subject are
I’m Greg Restall, and this is my personal website. ¶ I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology ¶ I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.