Explanation In Ethics And Mathematics PDF Download
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| Author | : Uri D. Leibowitz |
| Publisher | : Oxford University Press |
| Total Pages | : 256 |
| Release | : 2016-05-26 |
| Genre | : Philosophy |
| ISBN | : 0191084263 |
Download Explanation in Ethics and Mathematics Book in PDF, ePub and Kindle
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.
| Author | : Uri D. Leibowitz |
| Publisher | : Oxford University Press |
| Total Pages | : 268 |
| Release | : 2016 |
| Genre | : Mathematics |
| ISBN | : 0198778597 |
Download Explanation in Ethics and Mathematics Book in PDF, ePub and Kindle
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.
| Author | : Justin Clarke-Doane |
| Publisher | : Oxford University Press |
| Total Pages | : 208 |
| Release | : 2020-03-12 |
| Genre | : Philosophy |
| ISBN | : 0192556800 |
Download Morality and Mathematics Book in PDF, ePub and Kindle
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.
| Author | : John Polkinghorne |
| Publisher | : OUP Oxford |
| Total Pages | : 176 |
| Release | : 2011-05-19 |
| Genre | : Mathematics |
| ISBN | : 0191621897 |
Download Meaning in Mathematics Book in PDF, ePub and Kindle
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 | : Gila Hanna |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 289 |
| Release | : 2009-12-04 |
| Genre | : Education |
| ISBN | : 1441905766 |
Download Explanation and Proof in Mathematics Book in PDF, ePub and Kindle
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.
| Author | : Martin Peterson |
| Publisher | : Oxford University Press |
| Total Pages | : 256 |
| Release | : 2017-06-01 |
| Genre | : Philosophy |
| ISBN | : 0190652276 |
Download The Ethics of Technology Book in PDF, ePub and Kindle
Autonomous cars, drones, and electronic surveillance systems are examples of technologies that raise serious ethical issues. In this analytic investigation, Martin 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. It is primarily the method developed by Peterson for articulating and analyzing the five principles that is novel. He argues that geometric concepts such as points, lines, and planes can be put to work for clarifying the structure and scope of these and other moral principles. This geometric account is based on the Aristotelian dictum that like cases should be treated alike, meaning that the degree of similarity between different cases can be represented as a distance in moral space. The more similar a pair of cases are from a moral point of view, the closer is their location in moral space. A case that lies closer in moral space to a paradigm case for some principle p than to any paradigm for any other principle should be analyzed by applying principle p. The book also presents empirical results from a series of experimental studies in which experts (philosophers) and laypeople (engineering students) have been asked to apply the geometric method to fifteen real-world cases. The empirical findings indicate that experts and laypeople do in fact apply geometrically construed moral principles in roughly, but not exactly, the manner advocates of the geometric method believe they ought to be applied.
| Author | : P. Mancosu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 315 |
| Release | : 2006-03-30 |
| Genre | : Mathematics |
| ISBN | : 1402033354 |
Download Visualization, Explanation and Reasoning Styles in Mathematics Book in PDF, ePub and Kindle
In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.
| Author | : V.A. Lefebvre |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 222 |
| Release | : 2012-12-06 |
| Genre | : Philosophy |
| ISBN | : 9401090513 |
Download Algebra of Conscience Book in PDF, ePub and Kindle
In this book two ethical systems are described in the language of mathematics. Ordinarily mathematics is thought to be a science of quantity. Indeed, manipulation of quantities constitutes much of mathematics. Elementary applied mathematics deals with reckoning and measurement, where concrete quantities are objects of attention, such as counting sheep or weighing corno But the operations on these quantities are performed with the help of symbols, from which concrete referents have been 'abstracted out': 3 + 5 = 8 regardless of whether the symbols stand for numbers of sheep or tons of corno Thus, the first principle that exhibits the power of mathematics is abstraction. It is one ofthe three pillars on which the edifice of mathematics rests. Another pillar is precision. Ordinarily, man communicates by words. W ords serve communication to the extent that they refer to things, events, states of affairs, feelings of the speaker, and so on. These are the meanings attributed to words. Communication is successful to the extent that the meanings coded upon words by the speaker correspond to the meanings decoded by the hearer. As is weH known, the degree ofthis correspondence varies enormously in different contexts of discourse and with the back grounds or attitudes of the speakers and hearers. Mathematics is a language in which the meanings ofthe symbols (the 'words' ofthis language) are absolutely precise. This precision is achieved by abstraction. Abstract terms are defined by their relations to other terms and by nothing else.
| Author | : Justin Clarke-Doane |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 219 |
| Release | : 2020-03-12 |
| Genre | : Mathematics |
| ISBN | : 0198823665 |
Download Morality and Mathematics Book in PDF, ePub and Kindle
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.
| Author | : Paul Ernest |
| Publisher | : Springer |
| Total Pages | : 377 |
| Release | : 2018-06-09 |
| Genre | : Education |
| ISBN | : 3319777602 |
Download The Philosophy of Mathematics Education Today Book in PDF, ePub and Kindle
This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future.
