Triptych: Foundations of Logic

Part of what I want to accomplish with this blog, and my mission to read an introductory textbook in every subject I claim to be interested in, is to map out my own ignorance. It's easy to convince yourself of your own imaginary expertise in a subject if you've never been forced outside of your comfort zone within that subject. I notice that a lot of people haven't been forced outside of their comfort zone on the subject of logic.

Many people who have done a bit of programming, a bit of maths and read a few Wikipedia articles on logical fallacies seem to fancy themselves experts on logic. A lot of these people are very vocal on the internet. I used to be one of them and I'm very, very sorry. In more recent years I'd found these people frustrating to look at, mostly because I'd done a bit more maths and read a bit beyond the Wikipedia articles, but I didn't have a particularly high horse to climb on.

By accident rather than design, over the past few months I've wound up completing something of a foundations-of-logic triptych, studying a coherent body of knowledge on three different fronts. It started with Lepore's Meaning and Argument, which I've mentioned previously. Then for unrelated reasons I ended up working through the Coursera Think Again: How to Reason and Argue MOOC, and Doug Walton's Informal Logic: A Pragmatic Approach.

Meaning and Argument

This is something of a misnomer as far as book titles go, as it doesn't really cover anything about meaning in the sense of semantics. I got hold of it on the recommendation of the Less Wrong Best Textbooks list. It is primarily an introductory text on formal logic, covering propositional, categorical and first-order logic, as well as use of logic-tree techniques to validate deductive arguments. It doesn't cover inductive logic. It excels at presenting a large number of exercises for drilling oneself in translating natural language into logical notation, as well as manipulating that notation and evaluating it for deductive validity. A very strong emphasis of the book is demonstrating the resistance natural language exhibits to being systematically translated in this manner.

Informal Logic: A Pragmatic Approach

Whereas the previous text dealt with formal logic as an abstract set of relationships between propositions, this text, as its title suggests, covers informal logic in the familiar environment of human discourse. It primarily concerns itself with the purpose of different types of dialogue, pragmatics, different categories and subcategories of informal argument, and in particular distinguishing cases where these categories of argument are and are not fallacious. This book strikes me as a very pleasing antidote to anyone who first sees a list of logical fallacies and thinks "woah! I'm totally going to win me some arguments with these!" In fact, it almost seems to be written for this specific purpose. It is not the easiest book to read from cover to cover. Previous versions had the subtitle "a handbook for logical argumentation", and the reference/handbookiness of it is very apparent. While it is very fit for purpose in terms of ironing out one's understanding of informal fallacies, I would recommend it only until I find something more readable.

Think Again: How to Reason and Argue

The goals of this course are wide but not lofty. It is a very broad introduction to a selection of topics surrounding reasoning and the formation and evaluation of arguments. I can't even remember why I started watching the video lectures, but I very quickly found myself charmed by the course instructors Walter Sinnott-Armstrong and Ram Neta. Their deliveries were warm and entertaining, and I found myself watching video after video. I skipped quite a few of the videos on subjects I'd covered in detail elsewhere, and watched most of them at 1.5x speed. In my case this was very much a gap-filling exercise, but over such a broad area there were quite a lot of gaps.

Think Again covers the linguistic foundations of arguments, formal logic up to first-order (along with a lot of drilling exercises, which I didn't really bother with off the back of Meaning and Argument, but which strike me as potentially useful), inductive arguments, causal and probabilistic reasoning, various categories of fallacious reasoning and processes of refutation. This was my first introduction to Walter Sinnott-Armstrong, whose academic work involves practical ethics and the evolutionary basis of morality. Off the back of this course I obtained his textbook, and while I've only flipped through it, the first half seems structurally similar to the Think Again course, only a lot less MOOCy and in much greater depth.

This triptych has definitely given me a much stronger position of meta-knowledge on various concepts and activities that get labelled "logic", though at some point I should take a more comprehensive introduction to mathematical logic and make it a tetraptych ((This is totally a real word. I just looked it up.)). Off the back of it, I'm probably going to investigate Walter Sinnott-Armstrong's other philosophical work, and I'm motivated to investigate the linguistics/pragmatics angle in more depth; I've been sitting on O'Grady's Contemporary Linguistics for about a year.

The triptych format (approaching a subject from three different sources) seems like a good format for building a solid subject foundation, so I may very well employ it again in future.

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