Gottfried Leibniz was a remarkable thinker who made fundamental contributions not only to philosophy, but also to the development of modern mathematics and science. At the centre of Leibniz's philosophy stands his metaphysics, an ambitious attempt to discover the nature of reality through the use of unaided reason. This volume provides a systematic and comprehensive account of the full range of Leibniz's thought, exploring the metaphysics in detail and showing its subtle and complex relationship to his views on logic, language, physics, and theology. Other chapters examine the intellectual context of his thought and its reception in the eighteenth century. New readers and nonspecialists will find this the most accessible and comprehensive guide to Leibniz currently available. Advanced students and specialists will find a conspectus of recent developments in the interpretation of Leibniz.

This book treats eighteenth-century Italian philosopher Giambattista Vico’s theory of poetic logic for the first time as the originating force in mathematics, transforming instinctive counting and spatial perception into poetic (metaphorical) symbolism that dovetails with the origin of language. It looks at current work on mathematical cognition (from Lakoff and Núñez to Butterworth, Dehaene, and beyond), matching it against the poetic logic paradigm. In a sense, it continues from where Kasner and Newman left off, connecting contemporary research on the mathematical mind to the idea that the products of early mathematics were virtually identical to the first forms of poetic language. As such, this book informs the current research on mathematical cognition from a different angle, by looking back at a still relatively unknown philosopher within mathematics. The aim of this volume is to look broadly at what constitutes the mathematical mind through the Vichian lens of poetic logic. Vico was among the first to suggest that the essential nature of mind could be unraveled indirectly by reconstructing the sources of its “modifications” (his term for “creations”); that is, by examining the creation and function of symbols, words, and all the other uniquely human artifacts—including mathematics—the mind has allowed humans to establish “the world of civil society,” Vico’s term for culture and civilization. The book is of interest to cognitive scientists working on math cognition. It presents the theory of poetic logic as Vico articulated it in his book The New Science, examining its main premises and then applying it to an interpretation of the ongoing work in math cognition. It will also be of interest to the general public, since it presents a history of early mathematics through the lens of an idea that has borne fruit in understanding the origin of language and symbols more broadly.

In this insightful and life-affirming book, Albert Read puts the imagination back at the forefront of our lives as a “muscle” that is boundless in its potential, infinitely rewarding, and central to human achievement. This beautifully written book explores one subject, imagination, through the lens of history and memoir, with some prescriptive aspects to it as well. The author posits that imagination, while elusive, is not just for artists and creatives, it is a muscle—an essential faculty of the mind to be trained and developed over a lifetime. Spanning prehistoric times through to the twenty-first century, from the earliest cave paintings to Leonardo da Vinci’s inventions to Steve Jobs’s approach to office design, it touches on art, music, film, literature, science, and entrepreneurship, to examine how the imagination has evolved—in shape, power, and pace—through the millennia. Albert Read reveals how we can harness the imagination in our day-to-day lives and why, in the new age of technology, it is more pressing than ever that we do so. He explores where to find ideas, how to foster skills in observation and connection, and how to be more attentive to the fluxes of our own minds. After all, as Read expertly outlines, the imagination is our supreme gift, our biggest opportunity, our greatest source of fulfillment and our most vital asset for the future. The book is illustrated throughout with approximately 60 images.

A quarterly review of philosophy.

Presents 33 essays on such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the mathematical way of thinking, the unreasonableness of mathematics, and mathematics as an art. A reprint of volume 3 of the four-volume edition originally published by Simon and Schuster in 1956. Annotation c. Book News, Inc., Portland, OR (booknews.com).