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Author: Stewart Shapiro Publisher: OUP Oxford ISBN: 0192893068 Category : Philosophy Languages : en Pages : 323
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: Geoffrey Hellman Publisher: Cambridge University Press ISBN: 110863074X Category : Science Languages : en Pages : 167
Book Description
The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the Element considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives.
Author: Peter van Inwagen Publisher: Taylor & Francis ISBN: 1000938298 Category : Philosophy Languages : en Pages : 299
Book Description
In Do Numbers Exist? Peter van Inwagen and William Lane Craig take opposite sides on whether there are abstract objects, such as numbers and properties. Craig argues that there are no abstract objects, whereas Van Inwagen argues that there are. Their exchange explores various arguments about the existence and nature of abstract objects. They focus especially on whether our ordinary and scientific thought and talk commit us to abstract objects, surveying the options available to us and the objections each faces. The debate covers central problems and methods in metaphysics, and also delves into theological questions raised by abstract objects. Key Features: Showcases the presentation and defense of two points of view on the existence of abstract objects, from two of the world’s leading philosophers Presents definitions in an easily accessible form Provides frequent summaries of previously covered material Includes a glossary of all specialized vocabulary
Author: Hartry Field Publisher: Oxford University Press ISBN: 0191083771 Category : Philosophy Languages : en Pages : 176
Book Description
Science Without Numbers caused a stir in philosophy on its original publication in 1980, with its bold nominalist approach to the ontology of mathematics and science. Hartry Field argues that we can explain the utility of mathematics without assuming it true. Part of the argument is that good mathematics has a special feature ("conservativeness") that allows it to be applied to "nominalistic" claims (roughly, those neutral to the existence of mathematical entities) in a way that generates nominalistic consequences more easily without generating any new ones. Field goes on to argue that we can axiomatize physical theories using nominalistic claims only, and that in fact this has advantages over the usual axiomatizations that are independent of nominalism. There has been much debate about the book since it first appeared. It is now reissued in a revised contains a substantial new preface giving the author's current views on the original book and the issues that were raised in the subsequent discussion of it.
Author: Geoffrey Hellman Publisher: Clarendon Press ISBN: 019152011X Category : Philosophy Languages : en Pages : 172
Book Description
Geoffrey Hellman presents a detailed interpretation of mathematics as the investigation of structural possibilities, as opposed to absolute, Platonic objects. After dealing with the natural numbers and analysis, he extends his approach to set theory, and shows how to dispense with a fixed universe of sets. Finally, he addresses problems of application to the physical world.
Author: Øystein Linnebo Publisher: Princeton University Press ISBN: 069120229X Category : Mathematics Languages : en Pages : 214
Book Description
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: Edward Kasner Publisher: Courier Corporation ISBN: 0486320278 Category : Mathematics Languages : en Pages : 400
Book Description
With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.
Author: Jim Holt
Author: Jim Holt
Author: Stewart Shapiro
Author: Geoffrey Hellman
Author: Peter van Inwagen
Author: Hartry Field
Author: George Lakoff
Author: Geoffrey Hellman
Author: Øystein Linnebo
Author: Bertrand Russell
Author: Edward Kasner