Uncountable : a philosophical history of number and humanity from antiquity to the present

著者

    • Nirenberg, David
    • Nirenberg, Ricardo L.

書誌事項

Uncountable : a philosophical history of number and humanity from antiquity to the present

David Nirenberg and Ricardo L. Nirenberg

University of Chicago Press, 2021

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注記

Includes bibliographical references and index

Summary: "From the time of Pythagoras, we have been tempted to treat numbers as the ultimate or only truth. This book tells the history of that habit of thought. But more, it argues that the logic of counting sacrifices much of what makes us human, and that we have a responsibility to match the objects of our attention to the forms of knowledge that do them justice. Humans have extended the insights and methods of number and mathematics to more and more aspects of the world, even to their gods and their religions.Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity.But the rules of mathematics do not strictly apply to many things-from elementary particles to people-in the world.By subjecting such things to the laws of logic and mathematics, we gain some kinds of knowledge, but we also lose others. How do our choices about what parts of the world to subject to the logics of mathematics affect how we live and how we die?This question is rarely asked, bu

収録内容

  • Introduction: Playing with Pebbles
  • World War Crisis
  • The Greeks: A Protohistory of Theory
  • Plato, Aristotle, and the Future of Western Thought
  • Monotheism's Math Problem
  • From Descartes to Kant: An Outrageously Succinct History of Philosophy
  • What Numbers Need: Or, When Does 2 + 2 = 4?
  • Physics (and Poetry): Willing Sameness and Difference
  • Axioms of Desire: Economics and the Social Sciences
  • Killing Time
  • Ethical Conclusions

内容説明・目次

内容説明

Our knowledge of mathematics has structured much of what we think we know about ourselves as individuals and communities, shaping our psychologies, sociologies, and economies. In pursuit of a more predictable and more controllable cosmos, we have extended mathematical insights and methods to more and more aspects of the world. Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity. Yet, in the process, are we losing sight of the human? When we apply mathematics so broadly, what do we gain and what do we lose, and at what risk to humanity? These are the questions that David and Ricardo L. Nirenberg ask in Uncountable, a provocative account of how numerical relations became the cornerstone of human claims to knowledge, truth, and certainty. There is a limit to these number-based claims, they argue, which they set out to explore. The Nirenbergs, father and son, bring together their backgrounds in math, history, literature, religion, and philosophy, interweaving scientific experiments with readings of poems, setting crises in mathematics alongside world wars, and putting medieval Muslim and Buddhist philosophers in conversation with Einstein, Schroedinger, and other giants of modern physics. The result is a powerful lesson in what counts as knowledge and its deepest implications for how we live our lives.

目次

Introduction: Playing with Pebbles 1 World War Crisis 2 The Greeks: A Protohistory of Theory 3 Plato, Aristotle, and the Future of Western Thought 4 Monotheism's Math Problem 5 From Descartes to Kant: An Outrageously Succinct History of Philosophy 6 What Numbers Need: Or, When Does 2 + 2 = 4? 7 Physics (and Poetry): Willing Sameness and Difference 8 Axioms of Desire: Economics and the Social Sciences 9 Killing Time 10 Ethical Conclusions Acknowledgments Notes Bibliography Index of Names

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