Explanation In Ethics And Mathematics
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Explanation In Ethics And Mathematics
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Author : Uri D. Leibowitz
language : en
Publisher: Oxford University Press
Release Date : 2016-05-26
Explanation In Ethics And Mathematics written by Uri D. Leibowitz and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-26 with Philosophy categories.
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. The first--debunking arguments--aims to put pressure on realism by emphasising the seeming redundancy of mathematical or moral entities when it comes to explaining our judgements. In the moral realm this challenge has been made by Gilbert Harman and Sharon Street; in the mathematical realm it is known as the 'Benacerraf-Field' problem. The second strategy--indispensability arguments--aims to provide support for realism by emphasising the seeming intellectual indispensability of mathematical or moral entities, for example when constructing good explanatory theories. This strategy is associated with Quine and Putnam in mathematics and with Nicholas Sturgeon and David Enoch in ethics. Explanation in Ethics and Mathematics addresses these issues through an explicitly comparative methodology which we call the 'companions in illumination' approach. By considering 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. For good measure, two further companions for illumination are also broached: the philosophy of chance and the philosophy of religion. Collectively, these comparisons light up new questions, arguments, and problems of interest to scholars interested in realism in any area.
Morality And Mathematics
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Author : Justin Clarke-Doane
language : en
Publisher: Oxford University Press
Release Date : 2020-03-12
Morality And Mathematics written by Justin Clarke-Doane and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-12 with Philosophy categories.
To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the genealogy of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together -- and for a surprising reason. Moral questions, insofar as they are practical, are objective in a sense that mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of factual areas like logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage.
Explanation And Proof In Mathematics
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Author : Gila Hanna
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-04
Explanation And Proof In Mathematics written by Gila Hanna and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-04 with Education categories.
In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece. Proof as bearers of mathematical knowledge. Bridging knowing and proving in mathematical reasoning. The role of mathematics in long-term cognitive development of reasoning. Proof as experiment in the work of Wittgenstein. Relationships between mathematical proof, problem-solving, and explanation. Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
Morality And Mathematics
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Author : Justin Clarke-Doane
language : en
Publisher:
Release Date : 2020
Morality And Mathematics written by Justin Clarke-Doane and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
Are there moral facts? Are there mathematical facts? Many say yes to the latter but no to the former. Justin Clarke-Doane argues that the situation is much more subtle: although there are no real moral facts, morality is objective in a paradigmatic respect. Conversely, while there are real mathematical facts, mathematics fails to be objective.
The Ethics Of Technology
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Author : Martin Peterson
language : en
Publisher: Oxford University Press
Release Date : 2017
The Ethics Of Technology written by Martin Peterson and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Philosophy categories.
In this analytically oriented work, Peterson articulates and defends five moral principles for addressing ethical issues related to new and existing technologies: the cost-benefit principle, the precautionary principle, the sustainability principle, the autonomy principle, and the fairness principle.
Truth Objects Infinity
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Author : Fabrice Pataut
language : en
Publisher: Springer
Release Date : 2017-01-27
Truth Objects Infinity written by Fabrice Pataut and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-27 with Philosophy categories.
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 León-Sánchez and Ana C. León-Mejía, Marco Panza, Fabrice Pataut, Philippe de Rouilhan, Andrea Sereni, and Stewart Shapiro.
An Introduction To The Philosophy Of Mathematics
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Author : Mark Colyvan
language : en
Publisher: Cambridge University Press
Release Date : 2012-06-14
An Introduction To The Philosophy Of Mathematics written by Mark Colyvan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-14 with Mathematics categories.
A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.
Mathematics And Scientific Representation
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Author : Christopher Pincock
language : en
Publisher: Oxford University Press
Release Date : 2012-01-13
Mathematics And Scientific Representation written by Christopher Pincock and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-13 with Philosophy categories.
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.
Mathematics Without Apologies
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Author : Michael Harris
language : en
Publisher: Princeton University Press
Release Date : 2017-05-30
Mathematics Without Apologies written by Michael Harris and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-30 with Mathematics categories.
An insightful reflection on the mathematical soul What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.
The Metaethics Of Constitutional Adjudication
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Author : Bosko Tripkovic
language : en
Publisher: Oxford University Press
Release Date : 2017-12-22
The Metaethics Of Constitutional Adjudication written by Bosko Tripkovic and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-22 with Law categories.
In this book Bosko Tripkovic develops a theory of value-based arguments in constitutional adjudication. In contrast to the standard question of constitutional theory that asks whether the courts get moral answers wrong, it asks a more fundamental question of whether the courts get the morality itself wrong. Tripkovic argues for an antirealist conception of value -one that does not presuppose the existence of mind-independent moral truths- and accounts for the effect this ought to have on existing value-based arguments made by constitutional courts. The book identifies three dominant types of value-based arguments in comparative constitutional practice: arguments from constitutional identity, common sentiment, and universal reason, and explains why they fail as self-standing approaches to moral judgment. It then suggests that the appropriate moral judgments emerge from the dynamics between practical confidence, which denotes the inescapability of the self and the evaluative attitudes it entails, and reflection, which denotes the process of challenging and questioning these attitudes. The book applies the notions of confidence and reflection to constitutional reasoning and maintains that the moral inquiry of the constitutional court ought to depart from the emotive intuitions of the constitutional community and then challenge these intuitions through reflective exposure to different perspectives in order to better understand and develop the underlying constitutional identity. The book casts new light on common constitutional dilemmas and allows us to envisage new ways of resolving them.