Metaphysical Myths, Mathematical Practice

The Ontology and Epistemology of the Exact Sciences

Author: Jody Azzouni

Publisher: Cambridge University Press

ISBN: 9780521442237

Category: Mathematics

Page: 249

View: 1580

Jody Azzouni argues in this original and exciting study that mathematical knowledge really is a special kind of knowledge with its own special means of gathering evidence. He analyzes the linguistic pitfalls and misperceptions philosophers in this field are often prone to, and explores the misapplications of epistemic principles from the empirical sciences to the exact sciences. What emerges is a picture of mathematics both sensitive to mathematical practice, and to the ontological and epistemological issues that concern philosophers.

The Oxford Handbook of Metaphysics

Author: Michael J. Loux,Dean W. Zimmerman

Publisher: Oxford University Press on Demand

ISBN: 9780199284221

Category: Philosophy

Page: 724

View: 1867

The Oxford Handbooks series is a major new initiative in academic publishing. Each volume offers an authoritative and up-to-date survey of original research in a particular subject area. Specially commissioned essays from leading figures in the discipline give critical examinations of the progress and direction of debates. Oxford Handbooks provide scholars and graduate students with compelling new perspectives upon a wide range of subjects in the humanities and social sciences. The Oxford Handbook of Metaphysics offers the most authoritative and compelling guide to this diverse and fertile field of philosophy. Twenty-four of the world's most distinguished specialists provide brand-new essays about what kinds of things there are, in what ways they exist, and how they relate to each other. They give the latest word on such topics as identity, modality, time, causation, persons and minds, freedom, and vagueness. The Handbook's unrivalled breadth and depth make it the definitive reference work for students and academics across the philosophical spectrum.

God and Abstract Objects

The Coherence of Theism: Aseity

Author: William Lane Craig

Publisher: Springer

ISBN: 3319553844

Category: Philosophy

Page: 540

View: 2945

This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range of options available to the classical theist for dealing with the challenge of Platonism. It probes in detail the diverse views on the reality of abstract objects and their compatibility with classical theism. It contains a most thorough discussion, rooted in careful exegesis, of the biblical and patristic basis of the doctrine of divine aseity. Finally, it challenges the influential Quinean metaontological theses concerning the way in which we make ontological commitments.

Humanizing Mathematics and its Philosophy

Essays Celebrating the 90th Birthday of Reuben Hersh

Author: Bharath Sriraman

Publisher: Birkhäuser

ISBN: 331961231X

Category: Mathematics

Page: 363

View: 1958

This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.

Truth, Objects, Infinity

New Perspectives on the Philosophy of Paul Benacerraf

Author: Fabrice Pataut

Publisher: Springer

ISBN: 3319459805

Category: Philosophy

Page: 309

View: 1612

This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and epistemology. The book started as a workshop held in Paris at the Collège de France in May 2012 with the participation of Paul Benacerraf. The introduction addresses the methodological point of the legitimate use of so-called “Princess Margaret Premises” in drawing philosophical conclusions from Gödel’s first incompleteness theorem. The book is then divided into three sections. The first is devoted to an assessment of the improved version of the original dilemma of “Mathematical Truth” due to Hartry Field: the challenge to the platonist is now to explain the reliability of our mathematical beliefs given the very subject matter of mathematics, either pure or applied. The second addresses the issue of the ontological status of numbers: Frege’s logicism, fictionalism, structuralism, and Bourbaki’s theory of structures are called up for an appraisal of Benacerraf’s negative conclusions of “What Numbers Could Not Be.” The third is devoted to supertasks and bears witness to the unique standing of Benacerraf’s first publication: “Tasks, Super-Tasks, and Modern Eleatics” in debates on Zeno’s paradox and associated paradoxes, infinitary mathematics, and constructivism and finitism in the philosophy of mathematics. Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the mid 1970’s. A complete chronological bibliography of Benacerraf’s work to 2016 is provided.Essays by Jody Azzouni, Paul Benacerraf, Justin Clarke-Doane, Sébastien Gandon, Brice Halimi, Jon Pérez Laraudogoitia, Mary Leng, Antonio Leòn-Sànchez and Ana Leòn-Mejía, Marco Panza, Fabrice Pataut, Philippe de Rouilhan, Andrea Sereni, and Stewart Shapiro.

A Companion to Relativism

Author: Steven D. Hales

Publisher: John Wiley & Sons

ISBN: 9781444392487

Category: Philosophy

Page: 648

View: 6723

A Companion to Relativism presents original contributions from leading scholars that address the latest thinking on the role of relativism in the philosophy of language, epistemology, ethics, philosophy of science, logic, and metaphysics. Features original contributions from many of the leading figures working on various aspects of relativism Presents a substantial, broad range of current thinking about relativism Addresses relativism from many of the major subfields of philosophy, including philosophy of language, epistemology, ethics, philosophy of science, logic, and metaphysics

New Trends in the History and Philosophy of Mathematics

Author: Tinne Hoff Kjeldsen,Stig Andur Pedersen,Lise Mariane Sonne-Hansen

Publisher: N.A

ISBN: 9788778386069

Category: Mathematics

Page: 161

View: 8101

This book is a collection of papers presented at the conference New Trends in the History and Philosophy of Mathematics held at the University of Roskilde, Denmark, 6-8 August 1998. The purpose of the meeting was to present some of the new ideas on the study of mathematics, its character and the nature of its development. During the last decades work in history and philosophy of mathematics has led to several new original views on mathematics. Both new methods and angles of study have been introduced, and old views of, say, the nature of mathematical theories and proofs have been challenged. For instance, disciplines as etnohistorical studies of mathematics and the sociology of mathematics have resulted in several new insights, and classical historians of mathematics are also experimenting with new perspectives. In a similar way philosophy of mathematics has witnessed rather deep changes. Classical foundational studies have been challenged by new broader perspectives. The aim was to provide a forum within which historians of mathematics, philosophers, and mathematicians could exchange ideas and discuss different new approaches in the history and philosophy of mathematics. The book includes papers by Joan Richards, Henk J. M. Bos, Donald MacKenzie, Arthur Jaffe, Jody Azzouni and Paulus Gerdes. It also includes an extended introduction.

Approaches and Methodologies in the Social Sciences

A Pluralist Perspective

Author: Donatella Della Porta,Michael Keating

Publisher: Cambridge University Press

ISBN: 1139474596

Category: Political Science

Page: N.A

View: 3288

A revolutionary textbook introducing masters and doctoral students to the major research approaches and methodologies in the social sciences. Written by an outstanding set of scholars, and derived from successful course teaching, this volume will empower students to choose their own approach to research, to justify this approach, and to situate it within the discipline. It addresses questions of ontology, epistemology and philosophy of social science, and proceeds to issues of methodology and research design essential for producing a good research proposal. It also introduces researchers to the main issues of debate and contention in the methodology of social sciences, identifying commonalities, historic continuities and genuine differences.

Ontology Without Borders

Author: Jody Azzouni

Publisher: Oxford University Press

ISBN: 0190622571

Category: Language Arts & Disciplines

Page: 320

View: 1180

Our experience of objects (and consequently our theorizing about them) is very rich. We perceive objects as possessing individuation conditions. They appear to have boundaries in space and time, for example, and they appear to move independently of a background of other objects or a landscape. In Ontology Without Boundaries Jody Azzouni undertakes an analysis of our concept of object, and shows what about that notion is truly due to the world and what about it is a projection onto the world of our senses and thinking. Location and individuation conditions are our product: there is no echo of them in the world. Features, the ways that objects seem to be, aren't projections. Azzouni shows how the resulting austere metaphysics tames a host of ancient philosophical problems about constitution ("Ship of Theseus," "Sorities"), as well as contemporary puzzles about reductionism. In addition, it's shown that the same sorts of individuation conditions for properties, which philosophers use to distinguish between various kinds of odd abstracta-universals, tropes, and so on, are also projections. Accompanying our notion of an object is a background logic that makes cogent ontological debate about anything from Platonic objects to Bigfoot. Contemporary views about this background logic ("quantifier variance") make ontological debate incoherent. Azzouni shows how a neutral interpretation of quantifiers and quantifier domains makes sense of both philosophical and pre-philosophical ontological debates. Azzouni also shows how the same apparatus makes sense of our speaking about a host of items--Mickey Mouse, unicorns, Martians--that nearly all of us deny exist. It's allowed by what Azzouni shows about the background logic of our ontological debates, as well as the semantics of the language of those debates that we can disagree over the existence of things, like unicorns, without that background logic and semantics forcing ontological commitments onto speakers that they don't have.

The indispensability of mathematics

Author: Mark Colyvan

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 172

View: 7138

The Quine-Putnam indispensability argument in the philosophy of mathematics urges us to place mathematical entities on the same ontological footing as other theoretical entities essential to our best scientific theories. Recently, the argument has come under serious scrutiny, with many influential philosophers unconvinced of its cogency. This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.

Model Theory and the Philosophy of Mathematical Practice

Formalization without Foundationalism

Author: John T. Baldwin

Publisher: Cambridge University Press

ISBN: 1108103014

Category: Science

Page: 352

View: 9150

Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the impact of model theory on contemporary algebraic geometry, number theory, combinatorics, and differential equations. This comprehensive and detailed book will interest logicians and mathematicians as well as those working on the history and philosophy of mathematics.

Educational Perspectives on Mathematics As Semiosis

From Thinking to Interpreting to Knowing

Author: Myrdene Anderson

Publisher: Legas Publishing

ISBN: N.A

Category: Mathematics

Page: 364

View: 3215

Mathematics education research routinely receives the attention of educators, mathematicians, linguists, psychologists, anthropologists, and others. In this volume, the induction of students into mathematical meaning-making is studied through the prism of these several disciplines. What unites all such approaches to pedagogy and to the assessment of pegagogy- and to the subject matter of mathematics itself - is semiotics. Myrdene Anderson teaches at Purdue University, Adalira Saenz-Ludlow teaches at the U of North Carolina, Shea Zetlweger is former chair at Mount Union College, Ohio, Victor V. Cifarelli teaches at the U. ol North Carolina.

Philosophical Logic

Author: Timothy John Smiley

Publisher: British Academy

ISBN: N.A

Category: Language Arts & Disciplines

Page: 158

View: 4520

This edited volume comes out of a one-day conference on philosophical logic at the British Academy in 1996. Philosophical logic covers a number of areas of thought, contrasting with the formal thinking of mathematical logic. Specifically, the essays here are concerned with language, including James Higginbotham, Professor of General Linguistics, Oxford, on 'Higher-Order Logic and Natural Language'.

Logic and Knowledge

Author: Carlo Cellucci,Emily Grosholz,Emiliano Ippoliti

Publisher: Cambridge Scholars Pub

ISBN: N.A

Category: Philosophy

Page: 447

View: 1102

The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VIVII of Platos Republic and Aristotles Prior and Posterior Analytics, to Kants Critique of Pure Reason and Mills A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection of papers by Bertrand Russell (Logic and Knowledge. Essays, 19011950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge. This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors.