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Form and Content: an Introduction to Formal Logic Connecticut College Digital Commons @ Connecticut College Open Educational Resources 2020 Form and Content: An Introduction to Formal Logic Derek D. Turner Connecticut College, [email protected] Follow this and additional works at: https://digitalcommons.conncoll.edu/oer Recommended Citation Turner, Derek D., "Form and Content: An Introduction to Formal Logic" (2020). Open Educational Resources. 1. https://digitalcommons.conncoll.edu/oer/1 This Book is brought to you for free and open access by Digital Commons @ Connecticut College. It has been accepted for inclusion in Open Educational Resources by an authorized administrator of Digital Commons @ Connecticut College. For more information, please contact [email protected]. The views expressed in this paper are solely those of the author. Form & Content Form and Content An Introduction to Formal Logic Derek Turner Connecticut College 2020 Susanne K. Langer. This bust is in Shain Library at Connecticut College, New London, CT. Photo by the author. 1 Form & Content ©2020 Derek D. Turner This work is published in 2020 under a Creative Commons Attribution- NonCommercial-NoDerivatives 4.0 International License. You may share this text in any format or medium. You may not use it for commercial purposes. If you share it, you must give appropriate credit. If you remix, transform, add to, or modify the text in any way, you may not then redistribute the modified text. 2 Form & Content A Note to Students For many years, I had relied on one of the standard popular logic textbooks for my introductory formal logic course at Connecticut College. It is a perfectly good book, used in countless logic classes across the country. But the book is expensive. The for-profit publisher routinely makes minor changes—just enough to justify putting out a new edition, which of course costs more. This also creates a dilemma for instructors: In times past, I’ve had to decide between ordering the soon-to-be out of date edition, which is cheaper and available used, but which students would not be able to sell back, vs. the new edition, which is not available used but which could be resold. A couple of years ago, I lost interest in participating any longer in this sort of system. So I decided to write my own text. Logic is something that should be accessible to anyone and everyone who takes an interest in studying it. There is something a little unseemly about for-profit textbook publishers making money off of students whose interest in taking a logic course makes them a captive audience. One of my goals in writing this book is thus accessibility. My hope is that this book may serve as an engaging, easy-to-read open access alternative. This textbook, I’m sure, has lots of flaws and idiosyncrasies. It’s written in the first instance for my students at Connecticut College, for the particular sort of logic course that I have developed there over the years. If you see problems, or if there are places where the explanation isn’t very clear, please do let me know. Often when you’re studying a textbook and you have trouble understanding something, you might be inclined to blame yourself. But please do not do that here. A text can always be improved (especially if no one is trying to make money from it). So as you study this text, I’d like you to read it with a critical eye even as you’re trying to learn logic. If you see things that could be done better, let me know, and together we might be able to improve the text for the benefit of future students. You’ll find that most of the examples I use are low-stakes and cheesy—some Harry Potter characters, lots of dinosaurs. My dog, Toby, shows up frequently. I want to say up front that I have reasons for preferring low-stakes examples. Many people, when they first approach logic, are really eager to learn how to apply logic in real argumentative contexts. When reasoning about important issues of the day, how can we spot and diagnose bad arguments? And how can we make better ones? One thing I’ve found, however, is that when you’re trying to learn formal logic, especially for the first time, the content is often a distraction. Many people have strong views about issues like immigration, or abortion, or free speech, or whatever it might be. A logic text that’s full of examples involving those and other current matters of political controversy would provoke lots of philosophically rich discussion, but in the course of that discussion the focus would likely drift away from the logic toward the substantive issue that everyone really cares about. However, one of my goals in a logic course is to get you to really care about abstract form—to see it as something glorious and even liberating, as something intrinsically worth studying. I’m convinced that the best way to shine the light on form is to use silly and hopefully fun examples—i.e., silly content—that nobody has much vested interest in. In fact, this is something of a philosophical disagreement that I have with 3 Form & Content other textbook writers. Everyone wants to know how something like logic might be applicable “in real life,” and so other textbooks hit you early with lots of examples involving matters of current interest. Practical applicability really is important, but I’m not convinced that means that it’s helpful to have “real life” examples when you’re first learning logic. By analogy, if you want to learn how to play clawhammer banjo, it might be best not to start out by trying to play a real song. It might be better to start by spending many hours practicing the right-hand frailing technique, which is really hard to learn but (once you master it) unbelievably graceful and efficient. The approach that I take in this text—an approach that emphasizes the relationship between form and content—is loosely inspired by the work of Susanne K. Langer, an amazing philosopher and logic aficionado who taught at Connecticut College. Langer also wrote one of the first introductory textbooks on symbolic logic.1 But she was most famous as a philosopher of art, and especially music. She played the cello, and wrote about music with some authority. Her interest in music was not unrelated to her interest in logic. She saw both as involving the interplay of form and content. Just as you might look at two arguments and find that they both share the same form—modus ponens, say—you might play an A minor chord on a piano and a banjo. Same form, different content. Or if you transpose a song from the key of G to the key of A, the form—the relationships among the notes—stays the same, while the content—the actual notes—is changing. Langer understood that there are many different contexts in life in which we might wish to study the interplay of form and content. Logic is just one example of this, where we’re interested in the form and content of our own thinking. One other thing that animates this book is the conviction that technical vocabulary can be empowering. Most people are better at mastering new technical vocabulary than they realize. I do not watch much baseball, but it is always interesting to see how many technical terms the baseball aficionados in my family have mastered: there are terms for positions (short stop, center field, etc.); terms for types of pitches (fastball, slider); terms for different plays (grounding out, double play, stealing second base); statistical terms (at bats, runs batted in, saves), and a host of other technical concepts with precise definitions. Not only that, but baseball aficionados must learn a complicated set of rules (e.g., if a pitcher throws four balls, the batter walks, etc.). Lots of people master this and other similarly complex systems of technical concepts without even realizing it. Without the concepts, you could not understand or appreciate baseball at all. Surprisingly, when it comes to our own reasoning, many people are in the situation of a person watching a baseball game, but without the benefit of any baseball concepts, with no way to process or grasp what is going on. The fact that so few people have the technical logical concepts that would enable them to think and talk clearly about reasoning in the way that baseball fans (for example) can analyze games with great precision is not the fault of anyone in particular. But it is definitely a kind of collective cultural failing. The good thing is that this failing is pretty easy to remedy. The technical concepts of logic are just as easy to master as the technical concepts of baseball. 1 Susanne K. Langer, An Introduction to Symbolic Logic, 3rd edition. New York: Dover Publications, 1967. The first edition of the book was originally published in 1937. 4 Form & Content And the benefit of studying them is that we no longer have to be alienated from our own reasoning. There are other open educational resource (OER) logic texts out there. You might also wish to consult with Forallx, a wonderful logic text created by P.D. Magnus. One difference between my approach and Magnus’s is that I treat semantic issues along the way, rather than treating formal semantics as a distinct topic later in the text. A team at the University of Calgary has also produced a Calgary remix of Magnus’s text, which is excellent.
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