Author: Uri D. Leibowitz
Publisher: Oxford University Press
Release Date: 2016-06-02
How far should our realism extend? For many years philosophers of mathematics and philosophers of ethics have worked independently to address the question of how best to understand the entities apparently referred to by mathematical and ethical talk. But the similarities between their endeavours are not often emphasised. This book provides that emphasis. In particular, it focuses on two types of argumentative strategies that have been deployed in both areas:debunking arguments, and indispensability arguments. Explanation in Ethics and Mathematics considers how argumentative strategies in the philosophy of mathematics might apply to the philosophy of ethics,and vice versa. The papers collected here break new ground in both areas, and illuminate new questions, arguments, and problems of interest to scholars working on realism in any area.
Author: Hilary PUTNAM
Publisher: Harvard University Press
Release Date: 2004
In this brief book one of the most distinguished living American philosophers takes up the question of whether ethical judgments can properly be considered objective--a question that has vexed philosophers over the past century. Reviewing what he deems the disastrous consequences of ontology's influence on analytic philosophy--in particular, the contortions it imposes upon debates about the objective of ethical judgments--Putnam proposes abandoning the very idea of ontology.
Author: Marc Lange
Publisher: Oxford University Press
Release Date: 2016-10-18
Not all scientific explanations work by describing causal connections between events or the world's overall causal structure. Some mathematical proofs explain why the theorems being proved hold. In this book, Marc Lange proposes philosophical accounts of many kinds of non-causal explanations in science and mathematics. These topics have been unjustly neglected in the philosophy of science and mathematics. One important kind of non-causal scientific explanation is termed explanation by constraint. These explanations work by providing information about what makes certain facts especially inevitable - more necessary than the ordinary laws of nature connecting causes to their effects. Facts explained in this way transcend the hurly-burly of cause and effect. Many physicists have regarded the laws of kinematics, the great conservation laws, the coordinate transformations, and the parallelogram of forces as having explanations by constraint. This book presents an original account of explanations by constraint, concentrating on a variety of examples from classical physics and special relativity. This book also offers original accounts of several other varieties of non-causal scientific explanation. Dimensional explanations work by showing how some law of nature arises merely from the dimensional relations among the quantities involved. Really statistical explanations include explanations that appeal to regression toward the mean and other canonical manifestations of chance. Lange provides an original account of what makes certain mathematical proofs but not others explain what they prove. Mathematical explanation connects to a host of other important mathematical ideas, including coincidences in mathematics, the significance of giving multiple proofs of the same result, and natural properties in mathematics. Introducing many examples drawn from actual science and mathematics, with extended discussions of examples from Lagrange, Desargues, Thomson, Sylvester, Maxwell, Rayleigh, Einstein, and Feynman, Because Without Cause's proposals and examples should set the agenda for future work on non-causal explanation.
Author: John Allen Paulos
Release Date: 2013-05-29
From the author of the national bestseller Innumeracy, a delightful exploration and explanation of mathematical concepts from algebra to zero in easily accessible alphabetical entries. "Paulos . . . does for mathematics what The Joy of Sex did for the boudoir. . . ."--Washington Post Book World. First time in paperback.
Author: Francisco J. Ayala
Publisher: Academic Press
Release Date: 2016-07-21
Evolution, Explanation, Ethics and Aesthetics: Towards a Philosophy of Biology focuses on the dominant biological topic of evolution. It deals with the prevailing philosophical themes of how to explain the adaptation of organisms, the interplay of chance and necessity, and the recurrent topics of emergence, reductionism, and progress. In addition, the extensively treated topic of how to explain human nature as a result of natural processes and the encompassed issues of the foundations of morality and the brain-to-mind transformation is discussed. The philosophy of biology is a rapidly expanding field, not more than half a century old at most, and to a large extent is replacing the interest in the philosophy of physics that prevailed in the first two-thirds of the twentieth century. Few texts available have the benefit of being written by an eminent biologist who happens to be also a philosopher, as in this work. This book is a useful resource for seminar courses and college courses on the philosophy of biology. Researchers, academics, and students in evolutionary biology, behavior, genetics, and biodiversity will also be interested in this work, as will those in human biology and issues such as ethics, religion, and the human mind, along with professional philosophers of science and those concerned with such issues as whether evolution is compatible with religion and/or where morality comes from. Presents the unique perspective of a distinguished biologist with extensive experience in the field who has published much about the subject in a wide variety of journals and edited volumes Covers the philosophical issues related to evolution and biology in an approachable and readable style Includes the most up-to-date treatment of this burgeoning, exciting field within biology Provides the ideal guide for researchers, academics, and students in evolutionary biology, behavior, genetics, and biodiversity
Author: Paul Ernest
Release Date: 2016-07-15
This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.
Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.
The hidden brain is the voice in our ear when we make the most important decisions in our lives—but we’re never aware of it. The hidden brain decides whom we fall in love with and whom we hate. It tells us to vote for the white candidate and convict the dark-skinned defendant, to hire the thin woman but pay her less than the man doing the same job. It can direct us to safety when disaster strikes and move us to extraordinary acts of altruism. But it can also be manipulated to turn an ordinary person into a suicide terrorist or a group of bystanders into a mob. In a series of compulsively readable narratives, Shankar Vedantam journeys through the latest discoveries in neuroscience, psychology, and behavioral science to uncover the darkest corner of our minds and its decisive impact on the choices we make as individuals and as a society. Filled with fascinating characters, dramatic storytelling, and cutting-edge science, this is an engrossing exploration of the secrets our brains keep from us—and how they are revealed.
Author: Katarzyna de Lazari-Radek
Publisher: Oxford University Press, USA
Release Date: 2014
Tests the views and metaphor of 19th-century utilitarian philosopher Henry Sidgwick against a variety of contemporary views on ethics, determining that they are defensible and thus providing a defense of objectivism in ethics and of hedonistic utilitarianism.
The purpose of the book is to establish a common language for, and understanding of, embodiment as it applies to mathematical thinking, and to link mathematics education research to recent work in gesture studies, cognitive linguistics and the theory of embodied cognition. Just as in past decades, mathematics education experienced a "turn to the social" in which sociocultural factors were explored, in recent years there has been a nascent "turn to the body." An increasing number of researchers and theorists in mathematics education have become interested in the fact that, although mathematics may be socially constructed, this construction is not arbitrary or unconstrained, but rather is rooted in, and shaped by, the body. All those who engage with mathematics, whether at an elementary or advanced level, share the same basic biological and cognitive capabilities, as well as certain common physical experiences that come with being humans living in a material world. In addition, the doing and communicating of mathematics is never a purely intellectual activity: it involves a wide range of bodily actions, from committing inscriptions to paper or whiteboard, to speaking, listening, gesturing and gazing. This volume will present recent research on gesture and mathematics, within a framework that addresses several levels of mathematical development. The chapters will begin with contributions that examine early mathematical and protomathematical knowledge, for example, the conservation of volume and counting. The role of gesture in teaching and learning arithmetic procedures will be addressed. Core concepts and tools from secondary level mathematics will be investigated, including algebra, functions and graphing. And finally, research into the embodied understanding of advanced topics in geometry and calculus will be presented. The overall goal for the volume is to acknowledge the multimodal nature of mathematical knowing, and to contribute to the creation of a model of the interactions and mutual influences of bodily motion, spatial thinking, gesture, speech and external inscriptions on mathematical thinking, communication and learning. The intended audience is researchers and theorists in mathematics education as well as graduate students in the field.
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.
Author: David Boonin
Publisher: Oxford University Press, USA
Release Date: 2014
David Boonin presents a new account of the non-identity problem: a puzzle about our obligations to people who do not yet exist. He provides a critical survey of solutions to the problem that have been proposed, and concludes by developing an unorthodox alternative solution, one that differs fundamentally from virtually every other approach.