The Search For Certainty A Philosophical Account Of Foundations Of Mathematics

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The Search for Certainty : A Philosophical Account of Foundations of Mathematics

Author : Marcus Giaquinto
Publisher : Clarendon Press
ISBN 13 : 0191588172
Total Pages : 302 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis The Search for Certainty : A Philosophical Account of Foundations of Mathematics by : Marcus Giaquinto

Download or read book The Search for Certainty : A Philosophical Account of Foundations of Mathematics written by Marcus Giaquinto and published by Clarendon Press. This book was released on 2002-06-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nineteenth century saw a movement to make higher mathematics rigorous. This seemed to be on the brink of success when it was thrown into confusion by the discovery of the class paradoxes. That initiated a period of intense research into the foundations of mathematics, and with it the birth of mathematical logic and a new, sharper debate in the philosophy of mathematics. The Search for Certainty examines this foundational endeavour from the discovery of the paradoxes to the present. Focusing on Russell's logicist programme and Hilbert's finitist programme, Giaquinto investigates how successful they were and how successful they could be. These questions are set in the context of a clear, non-technical exposition and assessment of the most important discoveries in mathematical logic, above all G--ouml--;del's underivability theorems. More than six decades after those discoveries, Giaquinto asks what our present perspective should be on the question of certainty in mathematics. Taking recent developments into account, he gives reasons for a surprisingly positive response.

The Search for Certainty

Author : Krzysztof Burdzy
Publisher : World Scientific
ISBN 13 : 9814273716
Total Pages : 270 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis The Search for Certainty by : Krzysztof Burdzy

Download or read book The Search for Certainty written by Krzysztof Burdzy and published by World Scientific. This book was released on 2009 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents a radical departure from the current philosophical duopoly in the area of foundations of probability, that is, the frequency and subjective theories. One of the main new ideas is a set of scientific laws of probability. The new laws are simple, intuitive and, last but not least, they agree well with the contents of current textbooks on probability. Another major new claim is that the OC frequency statisticsOCO has nothing in common with the OC frequency philosophy of probability, OCO contrary to popular belief. Similarly, contrary to the general perception, the OC Bayesian statisticsOCO shares nothing in common with the OC subjective philosophy of probability.OCO The book is non-partisan on the scientific side OCo it is supportive of both frequency statistics and Bayesian statistics. On the other hand, it contains well-documented and thoroughly-explained criticisms of the frequency and subjective philosophies of probability. Short reviews of other philosophical theories of probability and basic mathematical methods of probability and statistics are incorporated. The book includes substantial chapters on decision theory and teaching probability, and it is easily accessible to the general audience

Philosophy of Mathematics

Author : Paul Benacerraf
Publisher : Cambridge University Press
ISBN 13 : 1107268133
Total Pages : pages
Book Rating : 4.1/5 (72 download)

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Book Synopsis Philosophy of Mathematics by : Paul Benacerraf

Download or read book Philosophy of Mathematics written by Paul Benacerraf and published by Cambridge University Press. This book was released on 1984-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

What Is Mathematics, Really?

Author : Reuben Hersh
Publisher : Oxford University Press
ISBN 13 : 0198027362
Total Pages : 368 pages
Book Rating : 4.1/5 (98 download)

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Book Synopsis What Is Mathematics, Really? by : Reuben Hersh

Download or read book What Is Mathematics, Really? written by Reuben Hersh and published by Oxford University Press. This book was released on 1997-08-21 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

Philosophical Approaches to the Foundations of Logic and Mathematics

Author : Marcin Trepczyński
Publisher : BRILL
ISBN 13 : 9004445951
Total Pages : 316 pages
Book Rating : 4.0/5 (44 download)

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Book Synopsis Philosophical Approaches to the Foundations of Logic and Mathematics by : Marcin Trepczyński

Download or read book Philosophical Approaches to the Foundations of Logic and Mathematics written by Marcin Trepczyński and published by BRILL. This book was released on 2021-01-25 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philosophical Approaches to the Foundations of Logic and Mathematics consists of eleven articles addressing various aspects of the "roots" of logic and mathematics, their basic concepts and the mechanisms that work in the practice of their use.

Philosophy of Mathematics

Author : Ahmet Cevik
Publisher : CRC Press
ISBN 13 : 1000468801
Total Pages : 352 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Philosophy of Mathematics by : Ahmet Cevik

Download or read book Philosophy of Mathematics written by Ahmet Cevik and published by CRC Press. This book was released on 2021-11-09 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. "Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature." - Mark Balaguer, California State University, Los Angeles "There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy." - Michele Friend, George Washington University and CNRS, Lille, France

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Author : Paolo Mancosu
Publisher : Oxford University Press, USA
ISBN 13 : 0195132440
Total Pages : 290 pages
Book Rating : 4.1/5 (951 download)

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Book Synopsis Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century by : Paolo Mancosu

Download or read book Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century written by Paolo Mancosu and published by Oxford University Press, USA. This book was released on 1999 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century p. 8 1.1 The Quaestio de Certitudine Mathematicarum p. 10 1.2 The Quaestio in the Seventeenth Century p. 15 1.3 The Quaestio and Mathematical Practice p. 24 2. Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity p. 34 2.1 Magnitudes, Ratios, and the Method of Exhaustion p. 35 2.2 Cavalieri's Two Methods of Indivisibles p. 38 2.3 Guldin's Objections to Cavalieri's Geometry of Indivisibles p. 50 2.4 Guldin's Centrobaryca and Cavalieri's Objections p. 56 3. Descartes' Geometrie p. 65 3.1 Descartes' Geometrie p. 65 3.2 The Algebraization of Mathematics p. 84 4. The Problem of Continuity p. 92 4.1 Motion and Genetic Definitions p. 94 4.2 The "Causal" Theories in Arnauld and Bolzano p. 100 4.3 Proofs by Contradiction from Kant to the Present p. 105 5. Paradoxes of the Infinite p. 118 5.1 Indivisibles and Infinitely Small Quantities p. 119 5.2 The Infinitely Large p. 129 6. Leibniz's Differential Calculus and Its Opponents p. 150 6.1 Leibniz's Nova Methodus and L'Hopital's Analyse des Infiniment Petits p. 151 6.2 Early Debates with Cluver and Nieuwentijt p. 156 6.3 The Foundational Debate in the Paris Academy of Sciences p. 165 Appendix Giuseppe Biancani's De Mathematicarum Natura p. 178 Notes p. 213 References p. 249 Index p. 267.

Philosophy and Foundations of Mathematics

Author : A. Heyting
Publisher : Elsevier
ISBN 13 : 1483278158
Total Pages : 644 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Philosophy and Foundations of Mathematics by : A. Heyting

Download or read book Philosophy and Foundations of Mathematics written by A. Heyting and published by Elsevier. This book was released on 2014-05-12 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examines mathematics and experience and mathematics and logic. Topics include denumerably unfinished sets, continuum problem, logic of relations, consistency proofs for formal systems independent of their interpretation, infinite numbers, and problems of space and time. The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.

In Quest of Certainty

Author : Stefan Andersson
Publisher : Stockholm, Sweden : Almqvist & Wiksell
ISBN 13 :
Total Pages : 218 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis In Quest of Certainty by : Stefan Andersson

Download or read book In Quest of Certainty written by Stefan Andersson and published by Stockholm, Sweden : Almqvist & Wiksell. This book was released on 1994 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Isaac Newton on Mathematical Certainty and Method

Author : Niccolò Guicciardini
Publisher : MIT Press
ISBN 13 : 0262013177
Total Pages : 449 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Isaac Newton on Mathematical Certainty and Method by : Niccolò Guicciardini

Download or read book Isaac Newton on Mathematical Certainty and Method written by Niccolò Guicciardini and published by MIT Press. This book was released on 2009 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: An analysis of Newton's mathematical work, from early discoveries to mature reflections, and a discussion of Newton's views on the role and nature of mathematics.

Philosophy of Mathematics

Author : Gerhard Preyer
Publisher : Walter de Gruyter
ISBN 13 : 3110323680
Total Pages : 184 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Philosophy of Mathematics by : Gerhard Preyer

Download or read book Philosophy of Mathematics written by Gerhard Preyer and published by Walter de Gruyter. This book was released on 2013-05-02 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: One main interest of philosophy is to become clear about the assumptions, premisses and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is acheivable or necessary like the articles in the firt part of the publication show. Also the role of formal derivations, the role of the concept of apriority, and the intuitions of mathematical principles and properties need to be discussed. The second part is a contribution on nominalistic and platonistic views in mathematics, like the "indispensability argument" of W. v. O. Quine H. Putnam and the "makes no difference argument" of A. Baker. Not only in retrospect, the third part shows the problems of Mill, Frege's and the unity of mathematics and Descartes's contradictional conception of mathematical essences. Together, these articles give us a hint into the relationship between mathematics and world, that is, one of the central problems in philosophy of mathematics and philosophy of science.

Columbia Companion to Twentieth-Century Philosophies

Author : Constantin V. Boundas
Publisher : Columbia University Press
ISBN 13 : 023114203X
Total Pages : 754 pages
Book Rating : 4.2/5 (311 download)

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Book Synopsis Columbia Companion to Twentieth-Century Philosophies by : Constantin V. Boundas

Download or read book Columbia Companion to Twentieth-Century Philosophies written by Constantin V. Boundas and published by Columbia University Press. This book was released on 2007 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: Columbia Companion to Twentieth-Century Philosophies is the first guide to cover both the Anglo-American analytic and European Continental traditions. The first section features Nicholas Rescher writing on neoidealism, Josephine Donovan commenting on feminist philosophy, Tyler Burge discussing the philosophy of language and mind, and Robert Hanna reflecting on Kant's legacy. The second section presents Jean Grondin on hermeneutics, Leonard Lawlor on phenomenology, Charles Scott on postmodernism, and Babette Babich on the philosophy of science. The volume also covers logical positivism, naturalism, pragmatism, aesthetics, existentialism, Marxism, the Frankfurt School, structuralism, psychoanalysis, political philosophy, ethics, and the philosophy of religion. The final section addresses concurrent trends in Indian, Chinese, Japanese, and African philosophy, and a comprehensive introduction by Constantin V. Boundas not only provides a thorough outline of the problems and issues of the analytic and Continental traditions but also boldly challenges the conviction that the two approaches must be rivals. Offering an unusually panoramic perspective, the Columbia Companion to Twentieth-Century Philosophies enables readers to encounter foundational materials on their own terms.

Pluralism in Mathematics: A New Position in Philosophy of Mathematics

Author : Michèle Friend
Publisher : Springer Science & Business Media
ISBN 13 : 9400770588
Total Pages : 297 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Pluralism in Mathematics: A New Position in Philosophy of Mathematics by : Michèle Friend

Download or read book Pluralism in Mathematics: A New Position in Philosophy of Mathematics written by Michèle Friend and published by Springer Science & Business Media. This book was released on 2013-11-20 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy’s Naturalism, Shapiro’s Structuralism and Formalism. In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry. In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a strong warning to treat the word ‘pluralism’ with care.

The Philosophy of Mathematical Practice

Author : Paolo Mancosu
Publisher : OUP Oxford
ISBN 13 : 0191559091
Total Pages : 460 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis The Philosophy of Mathematical Practice by : Paolo Mancosu

Download or read book The Philosophy of Mathematical Practice written by Paolo Mancosu and published by OUP Oxford. This book was released on 2008-06-19 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment - such as visualization, explanation, and understanding - can nonetheless be subjected to philosophical analysis. The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representation systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.

Introducing Philosophy of Mathematics

Author : Michele Friend
Publisher : Routledge
ISBN 13 : 1317493796
Total Pages : 217 pages
Book Rating : 4.3/5 (174 download)

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Book Synopsis Introducing Philosophy of Mathematics by : Michele Friend

Download or read book Introducing Philosophy of Mathematics written by Michele Friend and published by Routledge. This book was released on 2014-12-05 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

Origins and Varieties of Logicism

Author : Francesca Boccuni
Publisher : Taylor & Francis
ISBN 13 : 1000508110
Total Pages : 419 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Origins and Varieties of Logicism by : Francesca Boccuni

Download or read book Origins and Varieties of Logicism written by Francesca Boccuni and published by Taylor & Francis. This book was released on 2021-11-29 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a plurality of perspectives on the historical origins of logicism and on contemporary developments of logicist insights in philosophy of mathematics. It uniquely provides up-to-date research and novel interpretations on a variety of intertwined themes and historical figures related to different versions of logicism. The essays, written by prominent scholars, are divided into three thematic sections. Part I focuses on major authors like Frege, Dedekind, and Russell, providing a historical and theoretical exploration of such figures in the philosophical and mathematical milieu in which logicist views were first expounded. Part II sheds new light on the interconnections between these founding figures and a number of influential other traditions, represented by authors like Hilbert, Husserl, and Peano, as well as on the reconsideration of logicism by Carnap and the logical empiricists. Finally, Part III assesses the legacy of such authors and of logicist themes for contemporary philosophy of mathematics, offering new perspectives on highly debated topics—neo-logicism and its extension to accounts of ordinal numbers and set-theory, the comparison between neo-Fregean and neo-Dedekindian varieties of logicism, and the relation between logicist foundational issues and empirical research on numerical cognition—which define the prospects of logicism in the years to come. This book offers a comprehensive account of the development of logicism and its contemporary relevance for the logico-philosophical foundations of mathematics. It will be of interest to graduate students and researchers working in philosophy of mathematics, philosophy of logic, and the history of analytic philosophy.

An Introduction to the Philosophy of Mathematics

Author : Mark Colyvan
Publisher : Cambridge University Press
ISBN 13 : 1107377005
Total Pages : 199 pages
Book Rating : 4.1/5 (73 download)

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Book Synopsis An Introduction to the Philosophy of Mathematics by : Mark Colyvan

Download or read book An Introduction to the Philosophy of Mathematics written by Mark Colyvan and published by Cambridge University Press. This book was released on 2012-06-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.