Set Theory And Its Philosophy A Critical Introduction PDF EPUB Download

Set Theory And Its Philosophy A Critical Introduction also available in docx and mobi. Read Set Theory And Its Philosophy A Critical Introduction online, read in mobile or Kindle.

Set Theory and Its Philosophy

A Critical Introduction

Author: Michael D. Potter

Publisher: University of Hawaii Press

ISBN:

Category: Mathematics

Page: 345

View: 838

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Set Theory and its Philosophy

A Critical Introduction

Author: Michael Potter

Publisher: Clarendon Press

ISBN:

Category: Philosophy

Page: 360

View: 865

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

An Aristotelian Realist Philosophy of Mathematics

Mathematics as the Science of Quantity and Structure

Author: J. Franklin

Publisher: Springer

ISBN:

Category: Mathematics

Page: 308

View: 843

Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

Cognitive Set Theory

Author: Alec Rogers

Publisher: ArborRhythms

ISBN:

Category: Psychology

Page:

View: 615

Badiou's 'Being and Event'

A Reader's Guide

Author: Christopher Norris

Publisher: Bloomsbury Publishing

ISBN:

Category: Philosophy

Page: 336

View: 828

Alain Badiou's Being and Event is the most original and significant work of French philosophy to have appeared in recent decades. It is the magnum opus of a thinker who is widely considered to have re-shaped the character and set new terms for the future development of philosophy in France and elsewhere. This book has been written very much with a view to clarifying Badiou's complex and demanding work for non-specialist readers. It offers guidance on philosophical and intellectual context, key themes, reading the text, reception and influence; and further reading.

Objectivity, Realism, and Proof

FilMat Studies in the Philosophy of Mathematics

Author: Francesca Boccuni

Publisher: Springer

ISBN:

Category: Science

Page: 344

View: 780

This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge. The essays collected here explore the semantic and epistemic problems raised by different kinds of mathematical objects, by their characterization in terms of axiomatic theories, and by the objectivity of both pure and applied mathematics. They investigate controversial aspects of contemporary theories such as neo-logicist abstractionism, structuralism, or multiversism about sets, by discussing different conceptions of mathematical realism and rival relativistic views on the mathematical universe. They consider fundamental philosophical notions such as set, cardinal number, truth, ground, finiteness and infinity, examining how their informal conceptions can best be captured in formal theories. The philosophy of mathematics is an extremely lively field of inquiry, with extensive reaches in disciplines such as logic and philosophy of logic, semantics, ontology, epistemology, cognitive sciences, as well as history and philosophy of mathematics and science. By bringing together well-known scholars and younger researchers, the essays in this collection – prompted by the meetings of the Italian Network for the Philosophy of Mathematics (FilMat) – show how much valuable research is currently being pursued in this area, and how many roads ahead are still open for promising solutions to long-standing philosophical concerns. Promoted by the Italian Network for the Philosophy of Mathematics – FilMat

Derrida, Badiou and the Formal Imperative

Author: Christopher Norris

Publisher: A&C Black

ISBN:

Category: Philosophy

Page: 240

View: 515

In this path-breaking study Christopher Norris proposes a transformed understanding of the much-exaggerated differences between analytic and continental philosophy. While keeping the analytic tradition squarely in view his book focuses on the work of Jacques Derrida and Alain Badiou, two of the most original and significant figures in the recent history of ideas. Norris argues that these thinkers have decisively reconfigured the terrain of contemporary philosophy and, between them, pointed a way beyond some of those seemingly intractable issues that have polarised debate on both sides of the notional rift between the analytic and continental traditions. In particular his book sets out to show - against the received analytic wisdom - that continental philosophy has its own analytic resources and is capable of bringing some much-needed fresh insight to bear on problems in philosophy of language, logic and mathematics. Norris provides not only a unique comparative account of Derrida's and Badiou's work but also a remarkably wide-ranging assessment of their joint contribution to philosophy's current - if widely resisted - potential for self-transformation.

Great Events from History

The 20th century, 1901-1940

Author: Robert F. Gorman

Publisher: Salem PressInc

ISBN:

Category: History

Page: 3453

View: 211

Presents essays arranged in chronological order on key world events that occurred in such areas as politics, science, medicine, communications, literature, music, philosophy, and international affairs during the first forty years of the twentieth century.

Deleuze and the Fold: A Critical Reader

Author: Sjoerd van Tuinen

Publisher: Palgrave MacMillan

ISBN:

Category: Philosophy

Page: 263

View: 179

This collection of essays presents a thorough explication of one of Deleuze's most difficult works, 'The Fold.'

Proof, Logic, and Formalization

Author: Michael Detlefsen

Publisher: Psychology Press

ISBN:

Category: Mathematics

Page: 241

View: 750

The mathematical proof is the most important form of justification in mathematics. It is not, however, the only kind of justification for mathematical propositions. The existence of other forms, some of very significant strength, places a question mark over the prominence given to proof within mathematics. This collection of essays, by leading figures working within the philosophy of mathematics, is a response to the challenge of understanding the nature and role of the proof.

Best Books