100 books like The Origin of Concepts

Science has revolutionized the way we live and the way we understand reality, but what accounts for its success? What method sets science apart from other forms of inquiry and ensures that it yields ever-more accurate theories of the world? Strevens argues that the scientific method is not a special kind of logic, like deriving hypotheses from first principles or narrowing hypotheses through falsification, but a simple commitment to arguing with evidence. Strevens shows, with historical case studies, how this commitment is seemingly irrational, as it provides no constraints on what counts as evidence or how evidence should be interpreted, but also incredibly powerful, fostering ingenuity and discovery.

It’s impossible, as a parent, not to marvel at the miracle of learning that occurs in very young children. Indeed, parents have experienced this sense of awe for time immemorial, and some have gone so far as to venture explanations for how it works. John Dewey, the American philosopher and psychologist, argued at the dawn of the twentieth century that children are like young scientists as they go about their day, subtly testing the things and people around them to see how they work. We now know, in no small part due to the work of researchers including The Scientist in the Crib author Alison Gopnik, that Dewey was right. Children are compelled to experiment; what’s more, they make the most of the limited data they produce with a powerful logic invisible to the untrained eye. Parents—but also anyone with a sense of wonder—will find answers to deep mysteries in… show more.

Two skills fundamental to scientific reasoning are inquiry and argument. Inquiry is generating new information, and argument is using that information to justify and evaluate knowledge claims. Kuhn presents a framework for understanding these processes, as well as methods for teaching them. Her insights are grounded in science-education research demonstrating not only why inquiry and argument are challenging but also how they can be improved. Kuhn’s book fundamentally changed how I teach science to others. It provided me a way of organizing and motivating the various research methods I cover in my courses, as tools for building a collective body of knowledge.

If you value science, then you’ve probably puzzled over why other people don’t. Why won’t other people wear masks during a pandemic? Or buy genetically modified foods? Or vaccinate their children. Sinatra and Hofer provide answers by delving deep into the psychology of science denial. They explain the shortcuts we take when searching for scientific information, the misconceptions we hold about scientific knowledge, and the obstacles we face when changing our beliefs and attitudes about scientific topics. From their synthesis of empirical research to their consideration of real-life dilemmas, Sinatra and Hofer provide a compelling account of the public’s fraught relationship with science, as well as practical advice for improving it.

Reuben Hersh is responsible for a revolution in the way we look at mathematics. His main idea is very simple: mathematics is something that is created by human beings. Isn’t that obvious, you say? Not if you believe that mathematics is there even before life itself, that it is built into the nature of reality in some way. In philosophy, this view is called Platonism. Hersh had the radical but obvious idea that if we want to understand what mathematics is we should look at what mathematicians actually do when they create mathematics. Like all great ideas it can be stated very simply but the implications are enormous.  His ideas are what got me started writing my own books about math and science.

Lots of people have a priori ideas about what mathematics is all about but Lakatos had the brilliant idea of looking at what actually happened. His book is all about one famous theorem: “for all regular polyhedra, V – E + F =2, where V is the number of vertices, E is the number of edges, and F is the number of faces.  Think of a cube where V=8, E = 12, F = 6.  

We tend to think that mathematics proceeds from a well-defined hypothesis to conclusion. But that is only the finishing step. Along the way the definitions keep changing as do the hypotheses and even the conclusion. Everything is moving! This is what makes doing mathematics so exciting!

This is another book about the new research into how babies think. I am excited about this research because of its implications for how people learn mathematics and how researchers create math. This book taught me something important about how we all think. Gopnik distinguishes between what she calls flashlight consciousness and lantern consciousness. Flashlight is the way adults think. You focus on one thing at a time and give it your full attention. But babies, she claims, use their minds differently. Their lantern consciousness is unfocused and is aware of the big picture all at once.  

So what happens to lantern consciousness when you grow up? The answer is that creative individuals use it and alternate between lantern and flashlight consciousness. When we are creating or learning something new, we have to drop back to lantern consciousness. Logic comes from flashlight consciousness and, by itself, will never produce anything… show more.

It’s a little weird that this book should find a place on my list. It’s a book about how society has become resistant to anything that is difficult and painful and the kinds of people that we have become as a result. But mathematics is difficult! To understand mathematics you have to think hard, sometimes for a long time. Moreover understanding something hard is discontinuous, it requires a leap to a new way of thinking. You have to start with a problem and this problem might be an ambiguity or a contradiction. A is true and B is true but A and B seem to contradict one another. When you sort out this problem you will have learned something.

The moral here is to embrace things that are difficult if you want to learn significant new things. “No pain, no gain.” You don’t have to worry about some super AI… show more.

Raymond Gibbs is a leading psycholinguist with deep familiarity with theories of conceptual metaphor and their critics. Drawing on evidence from cognitive linguistics and other fields, this book provides a valuable account of the contributions of metaphor to language, thought, action, and culture. Metaphors operate in multimodal experience s well as language. 

Research in cognitive psychology has revealed a lot about human learning and how to make it more effective. Most mathematics students – and indeed their professors – know very little about this research or how to apply it. Weinstein and Sumeracki’s book explains how psychologists generate evidence on learning, gives a basic account of human cognitive processing, explains some strategies for effective learning, and gives tips for applying them. It is not about mathematics and it certainly will not make advanced mathematics simple, but I think that we would all have an easier time if we were more aware of some common misunderstandings about learning and effective ways to improve it.