Lectures on the Philosophy of Mathematics

Lectures on the Philosophy of Mathematics

Author: Joel David Hamkins

Publisher: MIT Press

Published: 2021-03-09

Total Pages: 350

ISBN-13: 0262542234

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An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.


Uncountable

Uncountable

Author: David Nirenberg

Publisher: University of Chicago Press

Published: 2021-10-20

Total Pages: 429

ISBN-13: 022664698X

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"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, but it is urgent, because the sciences built upon those laws now govern so much of our knowledge, from physics to psychology.Number and Knowledge sets out to ask it. In chapters proceeding chronologically from Ancient Greek philosophy and the rise of monotheistic religions to the emergence of modern physics and economics, the book traces how ideals, practices, and habits of thought formed over millennia have turned number into the foundation-stone of human claims to knowledge and certainty.But the book is also a philosophical and poetic exhortation to take responsibility for that history, for the knowledge it has produced, and for the many aspects of the world and of humanity that it ignores or endangers.To understand what can be counted and what can't is to embrace the ethics of purposeful knowing"--


Iron

Iron

Author: Perry Fairfax Nursey

Publisher:

Published: 1850

Total Pages: 548

ISBN-13:

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The First Knowledge Economy

The First Knowledge Economy

Author: Margaret C. Jacob

Publisher: Cambridge University Press

Published: 2014-01-09

Total Pages: 269

ISBN-13: 1107044014

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Provocative new account of the importance of knowledge to the economic transformation of western Europe during the Industrial Revolution.


Categories for the Working Philosopher

Categories for the Working Philosopher

Author: Elaine M. Landry

Publisher: Oxford University Press

Published: 2017

Total Pages: 486

ISBN-13: 019874899X

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This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these areas.