Author : Chris John Pincock
Publisher : Ann Arbor, Mich. : University Microfilms International
Page : 644 pages
File Size : 47,68 MB
Release : 2002
Category :
ISBN :
Author : Erich H. Reck
Publisher : Oxford University Press
Page : 469 pages
File Size : 22,36 MB
Release : 2020
Category : Mathematics
ISBN : 0190641223
This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.
Author : Erich H. Reck
Publisher : Oxford University Press
Page : 320 pages
File Size : 29,98 MB
Release : 2020-05-06
Category : Philosophy
ISBN : 0190641231
Recently, debates about mathematical structuralism have picked up steam again within the philosophy of mathematics, probing ontological and epistemological issues in novel ways. These debates build on discussions of structuralism which began in the 1960s in the work of philosophers such as Paul Benacerraf and Hilary Putnam; going further than these previous thinkers, however, these new debates also recognize that the motivation for structuralist views should be tied to methodological developments within mathematics. In fact, practically all relevant ideas and methods have roots in the structuralist transformation that modern mathematics underwent in the 19th and early 20th centuries. This edited volume of new essays by top scholars in the philosophy of mathematics explores this previously overlooked 'pre-history' of mathematical structuralism. The contributors explore this historical background along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics, such as Dedekind, Hilbert, and Bourbaki, who are responsible for the introduction of new number systems, algebras, and geometries that transformed the landscape of mathematics. Second, they reexamine a range of philosophical reflections by mathematically inclined philosophers, like Russell, Cassirer, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism. Overall, the essays in this volume show not only that the pre-history of mathematical structuralism is much richer than commonly appreciated, but also that it is crucial to take into account this broader intellectual history for enriching current debates in the philosophy of mathematics. The insights included in this volume will interest scholars and students in the philosophy of mathematics, the philosophy of science, and the history of philosophy.
Author : Geoffrey Hellman
Publisher : Cambridge University Press
Page : 167 pages
File Size : 28,7 MB
Release : 2018-11-29
Category : Science
ISBN : 110863074X
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 : Charles S. Chihara
Publisher : Clarendon Press
Page : 395 pages
File Size : 35,94 MB
Release : 2003-11-20
Category : Philosophy
ISBN : 0191533106
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 are applied 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 how such 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 nominalistic outlook 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.
Author : Stewart Shapiro
Publisher : Oxford University Press
Page : 296 pages
File Size : 14,10 MB
Release : 1997-08-07
Category : Philosophy
ISBN : 0198025459
Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.
Author : Mustafa Emre Civelek
Publisher : Lulu.com
Page : 120 pages
File Size : 46,72 MB
Release : 2018-03-12
Category : Business & Economics
ISBN : 1609621298
Structural Equation Modeling is a statistical method increasingly used in scientific studies in the fields of Social Sciences. It is currently a preferred analysis method, especially in doctoral dissertations and academic researches. Many universities do not include this method in the curriculum, so students and scholars try to solve these problems using books and internet resources. This book aims to guide the researcher in a way that is free from math expressions. It teaches the steps of a research program using structured equality modeling practically. For students writing theses and scholars preparing academic articles, this book aims to analyze systematically the methodology of studies conducted using structural equation modeling methods in the social sciences. In as simple language as possible, it conveys basic information. It consists of two parts: the first gives basic concepts of structural equation modeling, and the second gives examples of applications.
Author : Geoffrey Hellman
Publisher : Clarendon Press
Page : 172 pages
File Size : 39,85 MB
Release : 1989-10-12
Category : Philosophy
ISBN : 019152011X
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 : Michael D. Resnik
Publisher : Clarendon Press
Page : 300 pages
File Size : 28,48 MB
Release : 1997-07-31
Category : Philosophy
ISBN : 0191519006
Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defence of realism about the metaphysics of mathematics—the view that mathematics is about things that really exist. Resnik's distinctive philosophy of mathematics is here presented in an accessible and systematic form: it will be of value not only to specialists in this area, but to philosophers, mathematicians, and logicians interested in the relationship between these three disciplines, or in truth, realism, and epistemology.
Author : Otávio Bueno
Publisher : Oxford University Press
Page : 276 pages
File Size : 36,47 MB
Release : 2018
Category : Mathematics
ISBN : 0198815042
How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? Bueno and French offer a new approach to the puzzle of the applicability of mathematics, through a detailed examination of a series of case studies from the history of twentieth-century physics.
