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Constructibility

Constructibility
Author: Keith J. Devlin
Publisher: Cambridge University Press
Total Pages: 438
Release: 2017-03-16
Genre: Computers
ISBN: 110716835X

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A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.


The Axiom of Constructibility

The Axiom of Constructibility
Author: K. J. Devlin
Publisher: Springer
Total Pages: 105
Release: 2006-11-15
Genre: Mathematics
ISBN: 354037034X

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A Structural Account of Mathematics

A Structural Account of Mathematics
Author: Charles S. Chihara
Publisher: Clarendon Press
Total Pages: 395
Release: 2004
Genre: Language Arts & Disciplines
ISBN: 0199267537

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Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems areapplied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true.Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show howsuch systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalisticoutlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings.A Structural Account of Mathematics will be required reading for anyone working in this field.


Constructibility and Mathematical Existence

Constructibility and Mathematical Existence
Author: Charles S. Chihara
Publisher: Oxford University Press
Total Pages: 299
Release: 1990
Genre: Mathematics
ISBN: 0198248172

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Concerned with the problem of existence in mathematics, this volume develops a mathematical system in which there are no existence assertions but only assertions of constructibility. It explores the philosophical implications of such an approach in the writings of Field, Burgess, Maddy and Kitcher.


Sat2000

Sat2000
Author: Ian Gent
Publisher:
Total Pages: 568
Release: 2000
Genre: Computer algorithms
ISBN: 9784274903632

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Interpreting Godel

Interpreting Godel
Author: Juliette Kennedy
Publisher: Cambridge University Press
Total Pages: 293
Release: 2014-08-21
Genre: Literary Collections
ISBN: 1107002664

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In this groundbreaking volume, leading philosophers and mathematicians explore Kurt Gödel's work on the foundations and philosophy of mathematics.


Descartes and His Contemporaries

Descartes and His Contemporaries
Author: Roger Ariew
Publisher: University of Chicago Press
Total Pages: 280
Release: 1995-10-15
Genre: Philosophy
ISBN: 9780226026299

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Before publishing his landmark Meditations in 1641, Rene Descartes sent his manuscript to many leading thinkers to solicit their objections to his arguments. He included these objections, along with his own detailed replies, as part of the first edition. This unusual strategy gave Descartes a chance to address criticisms in advance and to demonstrate his willingness to consider diverse viewpoints—critical in an age when radical ideas could result in condemnation by church and state, or even death. Descartes and his Contemporaries recreates the tumultuous intellectual community of seventeenth-century Europe and provides a detailed, modern analysis of the Meditations in its historical context. The book's chapters examine the arguments and positions of each of the objectors—Hobbes, Gassendi, Arnauld, Morin, Caterus, Bourdin, and others whose views were compiled by Mersenne. They illuminate Descartes' relationships to the scholastics and particularly the Jesuits, to Mersenne's circle with its debates about the natural sciences, to the Epicurean movements of his day, and to the Augustinian tradition. Providing a glimpse of the interactions among leading 17th-century intellectuals as they grappled with major philosophical issues, this book sheds light on how Descartes' thought developed and was articulated in opposition to the ideas of his contemporaries.


Basic Set Theory

Basic Set Theory
Author: Azriel Levy
Publisher: Courier Corporation
Total Pages: 418
Release: 2012-06-11
Genre: Mathematics
ISBN: 0486150739

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Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.