Course: The Semantics of First-Order Logic
Length: 4 weeks, 5-10 hrs/wk
Instructor: John Etchemendy, Dave Barker-Plummer
Quote:First-order logic is a restricted, formalized language which is particularly suited to the precise expression of ideas. The language has uses in many disciplines including computer science, mathematics, linguistics and artificial intelligence.
We will describe how to write sentences in the language, how to determine when a sentence is true in a particular situation, how to recognize important relationships between sentences, and describe some limitations of the language.
It’s been a while since I took a logic mooc. I still miss the one from the University of Melbourne, which had logic trees and subunits on linguistics, philosophy, math, and a few other things. But that disappeared when Coursera brought up their new platform in 2017. The last time I took a logic mooc from Stanford, I got so depressed I was quoting Stevie Smith on the forums (“I was too far out all my life, not waving but drowning”).
But I really like logic, so when I saw ClassCentral’s tweet about this, I signed up.
First off, though it’s intended for beginners, I don’t think it’s the best choice for a first logic class. There’s just too much verbiage. Secondly, it’s not the best course for those who wish to audit, since there are very few exercises on this side of the paywall, and logic is, like math, something that requires practice. Third, it requires additional software; a textbook/manual is included, but it’s still not the best choice for anyone who doesn’t have a fairly high comfort level with figuring out how new programs work (since it’s part of the Computer Science curriculum, that was probably a given in the mooc design). Fourth, and I realize this sounds petty but it was somewhat serious, I had a lot of trouble seeing some of the video material, particularly screen shots of sentences from Tarsky’s World (blurry to begin with, so enlarging only goes so far) and handwritten notes. I was working on a 17” screen; anyone working on a phone would need a microscope.
On the plus side, the software – Tarski’s World, where all the worlds are named after philosophers – is a pretty cool way to play with and test statements. And, while the forums were dead (the only questions were technical issues, and there was no discussion of the logic at all), it was a pleasant surprise that one of the professors, Dave, was on hand to field problems (I caught some unbalanced parentheses, for instance).
A great deal of empnasis is placed on the idea of what certain statements say about the world, and what’s truth functional and what isn’t, the differences between tautologies, logical truth, tautological consequence and equivalence. This is where all the verbiage comes in. I’m not sure it’s productive, since I still don’t think I actually understand what they were trying to convey.
Still, I found the gold nugget: normal forms, and especially prenex form. But there’s a caveat: I had no idea what prenex form was from listening to the course videos, so I went hunting on Youtube and found a couple of playlists that were very helpful. Once I knew what Dave and John were talking about, I could understand what they were talking about. Since there weren’t many examples (two, in fact, one very easy and one very complicated), I’m going to need more practice, but it looks like there’s some out there. And, let me tell you, putting things into prenex form is the coolest thing since logic trees. Alas, it’s kind of a silly thing to get hooked on, since it’s a means to an end rather than an end in itself, but it is fun.
I probably sound like I didn’t care for this course at all, but that isn’t the case. The FOL-to-English translation exercises reminded me a bit of the first couple of weeks of Keith Devlin’s Intro to Mathematical Thinking (also a Stanford course), which I loved. I think, if I were to take it again, I’d want to pay the $50 so I could find out if the exercises I was doing were turning out right. But the real test is in the follow-up course, “Language, Proof, and Logic”: It seems to cover most of the same territory, but over 15 weeks. Will I dare to take yet another Stanford logic course? Maybe. I have a full plate for the moment, but we’ll see.