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.
Oxford Studies in Metaethics is the only publication devoted exclusively to original philosophical work in the foundations of ethics. It provides an annual selection of much of the best new scholarship being done in the field. Its broad purview includes work being done at the intersection of ethical theory and metaphysics, epistemology, philosophy of language, and philosophy of mind. The essays included in the series provide an excellent basis for understanding recent developments in the field; those who would like to acquaint themselves with the current state of play in metaethics would do well to start here.
Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics. The chapters are written by some of the world's finest mathematicians, mathematical physicists and philosophers of mathematics, each giving their perspective on this fascinating debate. Every chapter is followed by a short response from another member of the author team, reinforcing the main theme and raising further questions. Accessible to anyone interested in what mathematics really means, and useful for mathematicians and philosophers of science at all levels, Meaning in Mathematics offers deep new insights into a subject many people take for granted.
Author: Christopher Pincock
Publisher: Oxford University Press
Release Date: 2012-01-13
Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a scientific representation. Several different sorts of contributions from mathematics are then articulated. Pincock argues that each contribution can be understood as broadly epistemic, so that what mathematics ultimately contributes to science is best connected with our scientific knowledge. In the second part of the book, Pincock critically evaluates alternative approaches to the role of mathematics in science. These include the potential benefits for scientific discovery and scientific explanation. A major focus of this part of the book is the indispensability argument for mathematical platonism. Using the results of part one, Pincock argues that this argument can at best support a weak form of realism about the truth-value of the statements of mathematics. The book concludes with a chapter on pure mathematics and the remaining options for making sense of its interpretation and epistemology. Thoroughly grounded in case studies drawn from scientific practice, this book aims to bring together current debates in both the philosophy of mathematics and the philosophy of science and to demonstrate the philosophical importance of applications of mathematics.
Author: Paolo Mancosu
Publisher: Oxford University Press on Demand
Release Date: 2008-06-19
This book gives a coherent and unified presentation of a new direction of work in philosophy of mathematics. This new approach in philosophy of mathematics requires extensive attention to mathematical practice and provides philosophical analyses of important novel characteristics of contemporary (twentieth century) mathematics and of many aspects of mathematical activity-such as visualization, explanation, understanding etc.-- which escape purely formal logicaltreatment.The book consists of a lengthy introduction by the editor and of eight chapters written by some of the very best scholars in this area. Each chapter consists of a short introduction to the general topic of the chapter and of a longer research article in the very same area. Theeight topics selected represent a broad spectrum of the contemporary philosophical reflection on different aspects of mathematical practice: Diagrammatic reasoning and representational systems; Visualization; Mathematical Explanation; Purity of Methods; Mathematical Concepts; Philosophical relevance of category theory; Philosophical aspects of computer science in mathematics; Philosophical impact of recent developments in mathematical physics.
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: Thomas Nagel
Publisher: Oxford University Press, USA
Release Date: 1997
"...[a] subtle, compact, and forceful book.... is a work of philosophical reflection...a significant contribution to the culture wars of our time."--New York Review of Books "...a ringing defense of the rationalist conception of reason...a book that should be read and pondered in this golden age of subjectivism."--Colin McGinn, The New Republic
Author: Mark Colyvan
Publisher: Cambridge University Press
Release Date: 2012-06-14
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.
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.
In Aristotle's teleological view of the world, natural things come to be and are present for the sake of some function or end (for example, wings are present in birds for the sake of flying). Whereas much of recent scholarship has focused on uncovering the (meta-)physical underpinnings of Aristotle's teleology and its contrasts with his notions of chance and necessity, this book examines Aristotle's use of the theory of natural teleology in producing explanations of natural phenomena. Close analyses of Aristotle's natural treatises and his Posterior Analytics show what methods are used for the discovery of functions or ends that figure in teleological explanations, how these explanations are structured, and how well they work in making sense of phenomena. The book will be valuable for all who are interested in Aristotle's natural science, his philosophy of science, and his biology.