Course: Introduction to Logic
School: Stanford via Coursera (free)
Instructors: Michael Genesereth, Eric Kao
Logic is one of the oldest intellectual disciplines in human history. It dates back to the times of Aristotle; it has been studied through the centuries; and it is still a subject of active investigation today.
This course is a basic introduction to Logic. It shows how to formalize information in form of logical sentences. It shows how to reason systematically with this information to produce all logical conclusions and only logical conclusions. And it examines logic technology and its applications – in mathematics, science, engineering, business, law, and so forth.
The course differs from other introductory courses in Logic in two important ways. First of all, it teaches a novel theory of logic that improves accessibility while preserving rigor. Second, the material is laced with interactive demonstrations and exercises that suggest the many practical applications of the field.
[Addendum: This course has been converted to the new Coursera platform; content may have changed, and the experience is likely to be different]
I keep looking for some area of math that isn’t such a nightmare for me. Logic seemed a, mmmm-hm, logical choice: no numbers, and I greatly enjoyed the logic portion of Intro to Mathematical Thinking – so this should work out well, I should be able to do this!
Not so much, no.
The first three weeks went fine. Lecture videos introduced material, quizzes were very manageable, and the supplementary logic puzzles were fun. I was feeling pretty cocky: I got this.
Then week 4 hit.
Caution: steep drop-off. Mendelson. Fitch. Perfectly innocent-sounding common-sense sentences like “If by assuming φ we can infer ψ, then we can infer the sentence φ implies ψ” turned into vicious monsters laughing at me in the dark in nightmares. That’s what happens when you take a course given to Stanford computer science majors.
The exercises were designed to provide instant feedback. This is the first time I’ve seen a MOOC instructor up-front admit that there’s no way to prevent “cheating,” so why not take pedagogic advantage of what’s possible:
Finally, a few words about the online problems. First of all, you can submit your answers to any problem as often as you like, and the system will take your highest grade. Second, all problems provide immediate feedback. When you check a checkbox or make a selection from a menu or compete a proof, the system will tell you immediately whether the answer is correct, even BEFORE you submit your answers for grading. The upshot is that, for some problems, there is no reason not to get a perfect score.
Yes, we realize that it is possible to “game” the system by dumbly trying all answers until you get the right one and then submitting that answer. However, this is already possible. There is nothing stopping you from signing up twice, getting the right answers from one account and using them in your other account. Besides, for many problems, mostly proofs, finding a correct answer is a challenge, and you will have to work hard to get that coveted green checkmark. And we do not reveal proofs until after the hard deadline.
This wasn’t as much of a giveaway as it seems. In fact, I flunked the course (correction: To my surprise, I didn’t flunk, at least not in terms of obtaining a Certificate of Achievement with a score of 78%) because so many of the proofs eluded me. And, to be frank, the discussion boards were so loaded with “hints” that most of those, I might’ve been able to eke out as well. But call me crazy; I have a conscience, so I used the hints, sure, but if I couldn’t come up with something on my own, I didn’t submit the solution for points. I don’t see any particular advantage to “passing” these courses (other than ego, and I have little ego when it comes to math), so I’d rather have an accurate record of what I was able to do, should I try again some time. The instant feedback on the checkbox and multiple choice questions, on the other hand, was a great idea. Yes, I probably got a higher “score” than I would have otherwise, but it helped to clarify some points. I’m a little surprised they didn’t have ungraded homework questions with instant feedback, and then more traditional quiz questions, but I don’t teach MOOCs, I just take them.
Staff was very active on the boards – the TA was even available on Sunday evenings, time I tend to use a lot, and he was very helpful. Mike (funny, how some professors are so clearly Professors, and others are so clearly Mike) also did a lot of board-prowling, and while that has tremendous value in and of itself, I’m afraid I wasn’t able to understand his explanations any better than the original material being questioned.
However, there was Rachel.
If the proofs were monsters lurking in the dark, Rachel was the angel from heaven sent to show the way through the forest. A fellow student with some background in math and logic, she had a knack for explanation, and the patience to deal with troubled souls lined up for miles. I personally would have never gone past week 4 had it not been for Rachel. Many others felt the same way.
Plenty of supplementary material was available in the course. We had access to proof editors for each system, so we could work out simple examples or the samples in the lectures, to get the hang of how they worked. The entire syllabus was available in a single document, complete with formatted examples and diagrams, which are so important in a course like this. A set of extra resources was available for each week – tips on proofs, background and advanced materials. Several “logic puzzles” were provided for group discussion, each demonstrating some topic from the lectures; I’m afraid I was too mired in proofs to work on most of them, but I enjoyed the few I did.
Staff seemed quite restrained, somehow, but that may be because the humor was dry and ironic. The tip sheet on handling the Fitch proof editor was titled “Be-Fitched.” Michael picked up on my Stevie Smith reference when I signed a post, “Not Waving, But Drowning.” And, best of all: Box logic. I was probably the only student stupid enough to think this was an actual thing, like the Fitch editor or Relational Logic, so feverishly took notes and made diagrams. Then I “got” it. Coming right after Week 4, I needed a smile.
I was impressed with the instructor involvement, with their responsiveness to questions and problems, and with the resources provided; it’s not their fault I can’t think. And I will admit I’m not as well-prepared in mathematics as the typical Stanford student (how’s that for dry, ironic humor; I’m probably not as well-prepared in mathematics as the lawn at Stanford). I hope they follow through with the “boot camp” idea. There has to be some middle ground between week 3 and 4, between “I got this” and “Huh?” I’ll be taking the upcoming logic courses from University of Melbourne shortly, maybe that will help fill in the gaps, or maybe I just need to try again.
Some day. When I can handle the nightmares again.