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Author: J. Franklin
Publisher: Springer
ISBN: 1137400730
Category : Mathematics
Languages : en
Pages : 316
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Book Description
Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.
Author: Bertrand Russell
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 224
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Book Description
Author: David Corfield
Publisher: Cambridge University Press
ISBN: 1139436392
Category : Philosophy
Languages : en
Pages : 300
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Book Description
In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.
Author: Fernando Zalamea
Publisher: National Geographic Books
ISBN: 0956775012
Category : Philosophy
Languages : en
Pages : 0
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Book Description
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830–1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the “real mathematics” of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the “making of mathematics.” In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.
Author: Stewart Shapiro
Publisher: OUP Oxford
ISBN: 0192893068
Category : Philosophy
Languages : en
Pages : 323
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Book Description
Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.
Author: J. Franklin
Publisher: Springer
ISBN: 1137400730
Category : Mathematics
Languages : en
Pages : 316
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Book Description
Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.
Author: Jordan Ellenberg
Publisher: Penguin Press
ISBN: 1594205221
Category : Mathematics
Languages : en
Pages : 480
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Book Description
A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.
Author: Morris Kline
Publisher: Courier Corporation
ISBN: 0486136310
Category : Mathematics
Languages : en
Pages : 514
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Book Description
Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.
Author: Jan Westerhoff
Publisher: Oxford University Press
ISBN: 0192587188
Category : Philosophy
Languages : en
Pages : 352
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Book Description
Does the real world, defined as a world of objects that exist independent of human interests, concerns, and cognitive activities, really exist? Jan Westerhoff argues that we have good reason to believe it does not. His discussion considers four main facets of the idea of the real world, ranging from the existence of a separate external and internal world (comprising various mental states congregated around a self), to the existence of an ontological foundation that grounds the existence of all the entities in the world, and the existence of an ultimately true theory that provides a final account of all there is. As Westerhoff discusses the reasons for rejecting the postulation of an external world behind our representations, he asserts that the internal world is not as epistemically transparent as is usually assumed, and that there are good reasons for adopting an anti-foundational account of ontological dependence. Drawing on conclusions from the ancient Indian philosophical system of Madhyamaka Buddhism, Westerhoff defends his stance in a purely Western philosophical framework, and affirms that ontology, and philosophy more generally, need not be conceived as providing an ultimately true theory of the world.
Author: James Robert Brown
Publisher: Psychology Press
ISBN: 0415122759
Category : Mathematics
Languages : en
Pages : 181
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Book Description
Philosophy of Mathematicsis clear and engaging, and student friendly The book discusses the great philosophers and the importance of mathematics to their thought. Among topics discussed in the book are the mathematical image, platonism, picture-proofs, applied mathematics, Hilbert and Godel, knots and notation definitions, picture-proofs and Wittgenstein, computation, proof and conjecture.
Author: Brian Clegg
Publisher: Macmillan
ISBN: 1250081041
Category : Mathematics
Languages : en
Pages : 303
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Book Description
Presents an accessible, in-depth look at the history of numbers and their applications in life and science, from math's surreal presence in the virtual world to the debates about the role of math in science.
