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Author : Bertrand Russell
Publisher :
Page : 224 pages
File Size : 15,90 MB
Release : 1920
Category : Mathematics
ISBN :
Author : Mark Colyvan
Publisher : Cambridge University Press
Page : 199 pages
File Size : 44,70 MB
Release : 2012-06-14
Category : Mathematics
ISBN : 0521826020
A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.
Author : Bertrand Russell
Publisher :
Page : 0 pages
File Size : 15,2 MB
Release : 1963
Category : Mathematics
ISBN :
Author : David Bostock
Publisher : John Wiley & Sons
Page : 345 pages
File Size : 12,35 MB
Release : 2009-03-09
Category : Mathematics
ISBN : 1405189924
Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era. Offers beginning readers a critical appraisal of philosophical viewpoints throughout history Gives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism Provides readers with a non-partisan discussion until the final chapter, which gives the author's personal opinion on where the truth lies Designed to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals
Author : Stewart Shapiro
Publisher : OUP Oxford
Page : 323 pages
File Size : 16,95 MB
Release : 2000-07-13
Category : Philosophy
ISBN : 0192893068
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 : Joel David Hamkins
Publisher : MIT Press
Page : 350 pages
File Size : 20,83 MB
Release : 2021-03-09
Category : Mathematics
ISBN : 0262542234
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.
Author : Alfred North Whitehead
Publisher :
Page : 688 pages
File Size : 27,65 MB
Release : 1910
Category : Logic, Symbolic and mathematical
ISBN :
Author : Øystein Linnebo
Publisher : Princeton University Press
Page : 214 pages
File Size : 44,18 MB
Release : 2020-03-24
Category : Mathematics
ISBN : 069120229X
A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.
Author : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 27,5 MB
Release : 2004-01-15
Category : Philosophy
ISBN : 0191556432
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Author : Bertrand Russell
Publisher : W. W. Norton & Company
Page : 580 pages
File Size : 34,20 MB
Release : 1996
Category : Mathematics
ISBN : 9780393314045
Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical--that what is commonly called mathematics is simply later deductions from logical premises.