The art of logic in an illogical world

The Art of Logic is a book that I would say is important for a lot of people to read, but is emotionally weighted so that many of those people will dismiss large portions of it by default. It's fundamentally an introduction to first-order logic with a variety of ways to apply it to real-life discussions, but Cheng usually takes examples from her own opinions to help explain the applications and she's pretty blatantly what most Americans would describe as a leftist. I mean, I agree with most of her opinions and the logic behind them and it's interesting to see many of the arguments abstracted and developed, but explaining implications by arguing that "being white implies being privileged" is maybe a bit too much of a hot topic to belong well in what feels like an introduction book.

As an introduction to abstract logical systems, this book covers pretty much all the usual topics in a quick and straightforward way. It's nice to take a look at these systems without staring at truth tables for hours. My one complaint is that, as stated above, the examples are pretty heavily weighted to "leftist" arguments, but in terms of establishing how the logical operations work they're all well explained. In fact, over the course of the book and through explaining additional logical operations, Cheng develops some of these examples over time to be more robust and better explain where detractors tend to trip up on their side of the issue. She not only argues that "being white implies being privileged," but she talks about common counter-arguments and how they are or are not logically sound.

The most interesting parts of the book are her discussions of analogies and emotions. Of course, as humans, emotions play heavily into the way we see the world and the way we form arguments about our opinions. An interesting statement that gets repeated a few times is that "emotions are always true." They aren't an argument, or even an opinion, but the way we feel about an issue often informs how we form an opinion and how capable we are of defending that opinion. At some point in following our beliefs through to their roots, we come to core axioms defined largely based on emotion; we believe that governments should help their people, or we believe that every is fundamentally on their own, often not because of a purely rational reason but because that's just the way we feel. When our axioms don't align, we end up in arguments. An argument about universal healthcare may not really be about effectiveness or costs or morality, but about how we view the government's role in our lives. It's interesting to see Cheng break down examples to the point that it's obvious to the reader that, sometimes, you just have to agree to disagree.

The way she explains how to make analogies is also pretty interesting. It's not enough to pick an analogy that seems to make the same argument that you're making; you have to find something that makes the same argument as your "opponent" sees it, and it has to be something that they can connect to emotionally. Comparing white privilege over black people in society may not play well if you compare it to someone's relationship with their boss, especially if they like their boss, but it might make a bigger impact if you compare it to the way a white man feels when they walk into an asian supermarket and don't really understand what the hell they're doing and everyone else seems mildly annoyed by their existence. It's about picking an appropriate level of abstraction, where a white man probably doesn't understand power differentials based on race or gender but might understand them if you make a different analogy based on some place where they do feel that difference.

Now, there are a few other ways I think this book could have been put together better. In a lot of earlier chapters there are references to later chapters (as in, "we'll cover this in more detail in chapter 15") and there are enough of them that it's sort of irritating to read. If it's an important topic and comes up repeatedly earlier in the book, it should probably be properly covered earlier in the book. Additionally, while she does briefly cover a couple of fallacies like strawmen (which she occasionally constructs to demonstrate some logical operation, although it makes sense in those situations) she doesn't seem to cover as many as this book could probably use. Appealing to emotion is covered in quite a bit more detail while rational arguments are considered less useful since people sometimes ignore logic, thus making the book feel a bit moot by the end of it. I'd say my biggest criticism is that this book feels like it's targeted towards people who already try to make rational arguments in the way that western society tries to make them. If you don't think this sounds like a useful book, you're probably one of the people who should be trying to read and understand it. I found it useful as a review and application of the logic classes I took in university; if you already have basically no idea how a logical argument is formed, I'm not sure this book would be very useful. It's a fairly good book that constantly feels like it's not reaching the people that most need it, and it taints the experience in a way that I can rant about for a few paragraphs and still feel like I haven't explained properly.

So basically, I think that everyone should read this book or something like it, and if you don't think that you want or need to I would especially recommend it even though it feels a bit like spitting in the ocean.