The Laws of Thought: The Quest for a Mathematical Theory of the Mind

Can human thought be accurately described in a mathematical model? asks Griffiths (Algorithms to Live By), a psychology and computer science professor at Princeton, in this entertaining and information-rich exploration. Griffiths discusses how three frameworks for formalizing thought—rules and symbols, neural networks, and probability theory—can be combined to understand how the mind works, an idea that has strong implications for AI. Starting with mathematician and philosopher Gottfried Wilhelm Leibniz’s attempts in the 17th century to reduce logical reasonings to calculations, Griffiths details efforts throughout history to codify cognition, particularly with respect to language acquisition and development. He explains the challenges of each framework (reducing thought to rules and symbols, for example, doesn’t capture how the same set of facts can lead to different interpretations) and how the other frameworks can address those challenges and come together to form a more complete understanding of human cognition. Throughout, he points out differences between human minds and AI systems, such as the fact that AI requires massive amounts of data to solve problems whereas humans can learn from small amounts of information. Griffiths discusses academic history and abstruse mathematical concepts with ease, punctuating rarefied concepts with relatable metaphors and personal asides. Readers will enjoy this lively, enlightening work. (Feb.)