Mathematics and Its Logics

Mathematics and Its Logics
Author :
Publisher : Cambridge University Press
Total Pages : 296
Release :
ISBN-10 : 9781316999608
ISBN-13 : 1316999602
Rating : 4/5 (602 Downloads)

Book Synopsis Mathematics and Its Logics by : Geoffrey Hellman

Download or read book Mathematics and Its Logics written by Geoffrey Hellman and published by Cambridge University Press. This book was released on 2021-02-04 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extendability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic.


Mathematics and Its Logics Related Books

Mathematics and Its Logics
Language: en
Pages: 296
Authors: Geoffrey Hellman
Categories: Science
Type: BOOK - Published: 2021-02-04 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appe
Mathematics in Philosophy
Language: en
Pages: 367
Authors: Charles D. Parsons
Categories: Mathematics
Type: BOOK - Published: 2018-08-06 - Publisher: Cornell University Press

DOWNLOAD EBOOK

This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics. A common point o
Essays on mathematical and philosophical logic
Language: en
Pages: 462
Authors: Jaakko Hintikka
Categories: Logic
Type: BOOK - Published: 1976 - Publisher:

DOWNLOAD EBOOK

Philosophy of Mathematics in the Twentieth Century
Language: en
Pages: 365
Authors: Charles Parsons
Categories: Philosophy
Type: BOOK - Published: 2014-03-10 - Publisher: Harvard University Press

DOWNLOAD EBOOK

In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past ce
18 Unconventional Essays on the Nature of Mathematics
Language: en
Pages: 346
Authors: Reuben Hersh
Categories: Mathematics
Type: BOOK - Published: 2006-01-16 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physic