Logicism, Intuitionism, and Formalism

Logicism, Intuitionism, and Formalism PDF Author: Sten Lindström
Publisher: Springer Science & Business Media
ISBN: 1402089260
Category : Mathematics
Languages : en
Pages : 509

Get Book

Book Description
This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.

Logicism, Intuitionism, and Formalism

Logicism, Intuitionism, and Formalism PDF Author: Sten Lindström
Publisher: Springer Science & Business Media
ISBN: 1402089260
Category : Mathematics
Languages : en
Pages : 509

Get Book

Book Description
This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.

Philosophies of Mathematics

Philosophies of Mathematics PDF Author: Alexander L. George
Publisher: Wiley-Blackwell
ISBN: 9780631195436
Category : Science
Languages : en
Pages : 240

Get Book

Book Description
This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.

Philosophy of Mathematics

Philosophy of Mathematics PDF Author:
Publisher: Elsevier
ISBN: 0080930581
Category : Philosophy
Languages : en
Pages : 735

Get Book

Book Description
One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included

The Britannica Guide to The History of Mathematics

The Britannica Guide to The History of Mathematics PDF Author: Erik Gregersen Associate Editor, Astronomy and Space Exploration
Publisher: The Rosen Publishing Group, Inc
ISBN: 1615301275
Category : Juvenile Nonfiction
Languages : en
Pages : 311

Get Book

Book Description
Traces the origins and development of arithmetic, geometry, trigonometry, analytic geometry, and calculus from the ancient civilizations to the present.

The History of Mathematics

The History of Mathematics PDF Author: Nicholas Faulkner
Publisher: The Rosen Publishing Group, Inc
ISBN: 1680487779
Category : Juvenile Nonfiction
Languages : en
Pages : 346

Get Book

Book Description
This intriguing volume introduces readers to the origins of the mathematical principles they study every day. It covers a wide range of disciplines outlined in curriculum standards and serves as an illuminating companion to their current studies. Readers will learn about the brilliant minds behind some of the breakthroughs in mathematics. They will also enjoy the origin stories of the different disciplines in the field we're so familiar with today. The study of math should go beyond numbers, and this book certainly accomplishes that by giving readers insight into how mathematics came to be.

Logic and Language

Logic and Language PDF Author: B.H. Kazemier
Publisher: Springer Science & Business Media
ISBN: 9401721114
Category : Computers
Languages : en
Pages : 253

Get Book

Book Description


Gnomes in the Fog

Gnomes in the Fog PDF Author: Dennis E. Hesseling
Publisher: Birkhäuser
ISBN: 303487989X
Category : Mathematics
Languages : en
Pages : 448

Get Book

Book Description
The significance of foundational debate in mathematics that took place in the 1920s seems to have been recognized only in circles of mathematicians and philosophers. A period in the history of mathematics when mathematics and philosophy, usually so far away from each other, seemed to meet. The foundational debate is presented with all its brilliant contributions and its shortcomings, its new ideas and its misunderstandings.

Time in Eternity

Time in Eternity PDF Author: Robert John Russell
Publisher: University of Notre Dame Pess
ISBN: 0268091773
Category : Science
Languages : en
Pages : 456

Get Book

Book Description
According to Robert John Russell, one of the foremost scholars on relating Christian theology and science, the topic of “time and eternity” is central to the relation between God and the world in two ways. First, it involves the notion of the divine eternity as the supratemporal source of creaturely time. Second, it involves the eternity of the eschatological New Creation beginning with the bodily Resurrection of Jesus in relation to creaturely time. The key to Russell's engagement with these issues, and the purpose of this book, is to explore Wolfhart Pannenberg’s treatment of time and eternity in relation to mathematics, physics, and cosmology. Time in Eternity is the first book-length exposition of Russell’s unique method for relating Christian theology and the natural sciences, which he calls “creative mutual interaction” (CMI). This method first calls for a reformulation of theology in light of science and then for the delineation of possible topics for research in science drawing on this reformulated theology. Accordingly, Russell first reformulates Pannenberg’s discussion of the divine attributes—eternity and omnipresence—in light of the way time and space are treated in mathematics, physics, and cosmology. This leads him to construct a correlation of eternity and omnipresence in light of the spacetime framework of Einstein’s special relativity. In the process he proposes a new flowing time interpretation of relativity to counter the usual block universe interpretation supported by most physicists and philosophers of science. Russell also replaces Pannenberg’s use of Hegel’s concept of infinity in relation to the divine attributes with the concept of infinity drawn from the mathematics of Georg Cantor. Russell then addresses the enormous challenge raised by Big Bang cosmology to Christian eschatology. In response, he draws on Pannenberg’s interpretation both of the Resurrection as a proleptic manifestation of the eschatological New Creation within history and the present as the arrival of the future. Russell shows how such a reformulated understanding of theology can shed light on possible directions for fundamental research in physics and cosmology. These lead him to explore preconditions in contemporary physics research for the possibility of duration, copresence, retroactive causality, and prolepsis in nature.

Handbook of Epistemology

Handbook of Epistemology PDF Author: I. Niiniluoto
Publisher: Springer Science & Business Media
ISBN: 1402019866
Category : Philosophy
Languages : en
Pages : 1043

Get Book

Book Description
Epistemology or theory of knowledge has always been one of the most important -if not the most important -field of philosophy. New arguments are constantly brought to bear on old views, new variants are marshalled to revive ancient stands, new concepts and distinctions increase the sophistication of epistemogical theories. There are a great many excellent textbooks, monographs as well as anthologies consisting of articles in epistemology. Similarly, there are useful philosophical dictionaries which contain a great number of relatively short entries, and general philosophical handbooks which also touch epistemological issues. This volume of 27 essays grew out from the interest to see a handbook which is devoted entirely to the historical roots and systematic development of theory of knowledge. It is not intended to compete but to supplement the already existing literature. It aims at giving both beginners and more advanced students as well as professionals in epistemology and other areas of philosophy an overview of the central problems and solutions of epistemology. The essays are self-contained and stil often rather extensive discussions of the chosen aspects of knowledge. The contributions presuppose very little familiarity with previous literature and only a few of them require the mastery of even elementary logical notation. This, we hope, makes the volume also accessible to the philosophically interested wider audience. The contributors were asked to provide substantial, up-to-date, self-contained and balanced surveys of the various subareas and more specific topics of epistemology, with reference to literature.

Metaphysics

Metaphysics PDF Author: Jaekwon Kim
Publisher: John Wiley & Sons
ISBN: 1444331027
Category : Philosophy
Languages : en
Pages : 743

Get Book

Book Description
Thoroughly updated, the second edition of this highly successful textbook continues to represent the most comprehensive and authoritative collection of canonical readings in metaphysics. In addition to updated material from the first edition, it presents entirely new sections on ontology and the metaphysics of material objects. One of the most comprehensive and authoritative metaphysics anthologies available – now updated and expanded Offers the most important contemporary works on the central issues of metaphysics Includes new sections on ontology and the metaphysics of material objects, as well as readings on the topics of fictionalism, fundamentality, tropes, vague identity, temporary intrinsics, stage theory, and composition Surpasses other anthologies in its combination of contributions from leading metaphysicians and a younger generation of "rising-stars"