Logic Primer

"I chose Logic Primer by Colin Allen and Michael Hand for the reason that I taught from it for over a decade at the University of York. One of the interesting things about teaching logic at a university is that no logic teacher at a university is happy with anyone else’s textbook. This is why there are so many logic textbooks: everyone gets hyper-frustrated with the text they’re teaching and ends up writing their own. Now, I’m quite lazy, and I didn’t. I stuck to this book, though actually I changed it in lots of ways. When I teach with it, I reorder it, I delete sections, I add in new sections and new definitions of terms, so in practice the students are learning from my annotated version of the text. But this is why so many logic textbooks are written. The solution to that problem has arisen in our Web 2.0. I’ll mention it for reference, namely that there is now a logic textbook which is open-source and freely editable, called forallx . It’s online, and more and more logic teachers are saying ‘I’ll take that, and I can edit it in any way I like and use it.’ Anyone can freely access not only the original version of the text, but also any of its modifications. So there’s a Cambridge version of this textbook, a York version, a Calgary version, a SUNY version, a UBC version and probably many more I don’t know about. But the underlying formal language and system is the same in all of those. “Effectively, formal logic is a very general form of algebra” Let me go back to Logic Primer and why I like it so much. I like it because it doesn’t explain anything. Allen and Hand say, in the preface, that it’s intended to be used in conjunction with someone giving lectures who’ll do the explanations. They say they don’t really think you can learn logic from this book alone. I think that’s false—I’ve known students who failed to turn up to all my lectures who still managed to do well in the exam by teaching themselves from this book! This book presents a formal system of logic in its clearest, most structured form. I’ll just read from the preface, where they describe what they do: “The text consists of definitions, examples, comments and exercises.” As you go through the text, every paragraph is labeled as either a definition, an example, a comment or an exercise. Exactly. And if your mind is prepared to engage with that structure, then absolutely everything you need to learn logic is there. If something doesn’t work, if you keep getting an exercise wrong, you can go back to the definition and ask yourself, ‘Did I use the definition correctly?’ These definitions are incredibly carefully crafted. They’re not crafted to be easy to understand; they’re crafted to make sure that everything works perfectly if you follow the definitions strictly. Exactly. Most logic textbooks try to soften the blow of what a formal language is like, and how explicit and rulebound it is, by giving lots of examples, by trying to make it feel natural and comfortable. Many logic lecturers do the same: they’re worried that people are going to be put off, and so they try to say, ‘It’s OK, this isn’t too far out of your comfort zone’. Whereas this book, Logic Primer , doesn’t have any of that at all. It just says, ‘Here it is, bare bones, follow the rules, it’ll all work.’ All that is gone from this book. If you’re teaching from it, it’s great because you can put in as much or as little of that as you want. And if you’re wanting to teach yourself logic, you’ve got everything you need and nothing that you might not need in there. So that’s a really nice feature of it. The type of logic in this book—there are different types of formal logic, usually categorized by their proof system, i.e. how you manage to prove things in that logic—is called a natural deduction proof system. You might think that means it feels very natural when you use it. It doesn’t. The way you prove something in this system is you start with your premises and you end with your conclusion. All the bits in between can feel very unnatural, because it’s formal logic and you have to follow these very strict rules. Interestingly, the authors didn’t invent a new system—they used one that was in a previous textbook, E. J. Lemmon’s Beginning Logic , which was first published in 1965 and was the standard textbook in Oxford for a very long time. But it’s turgid. So, there are two books that you could use to learn exactly the same set of rules. (I’ll come back to this idea that there might be different rules and systems in my fifth choice.)"