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Author: Bonnie Gold
Publisher: MAA
ISBN: 9780883855676
Category : Mathematics
Languages : en
Pages : 392
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Book Description
Sixteen original essays exploring recent developments in the philosophy of mathematics, written in a way mathematicians will understand.
Author: Bonnie Gold
Publisher: MAA
ISBN: 9780883855676
Category : Mathematics
Languages : en
Pages : 392
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Book Description
Sixteen original essays exploring recent developments in the philosophy of mathematics, written in a way mathematicians will understand.
Author: M. Jablonowski
Publisher: Springer
ISBN: 0230288596
Category : Business & Economics
Languages : en
Pages : 147
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Book Description
This book identifies the pitfalls of applying precautionary strategies to high-stakes risks that have already become entrenched. Precaution must be applied on a precautionary basis, considering alternative paths to progress that maintain natural risk levels. This requires a radical rethinking of the way we define and achieve progress.
Author: Fenner Stanley Tanswell
Publisher: Cambridge University Press
ISBN: 1009325132
Category : Philosophy
Languages : en
Pages : 158
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Book Description
This Element looks at the contemporary debate on the nature of mathematical rigour and informal proofs as found in mathematical practice. The central argument is for rigour pluralism: that multiple different models of informal proof are good at accounting for different features and functions of the concept of rigour. To illustrate this pluralism, the Element surveys some of the main options in the literature: the 'standard view' that rigour is just formal, logical rigour; the models of proofs as arguments and dialogues; the recipe model of proofs as guiding actions and activities; and the idea of mathematical rigour as an intellectual virtue. The strengths and weaknesses of each are assessed, thereby providing an accessible and empirically-informed introduction to the key issues and ideas found in the current discussion.
Author: Gila Hanna
Publisher: Springer Science & Business Media
ISBN: 9400721293
Category : Education
Languages : en
Pages : 468
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Book Description
*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
Author: Andreas J. Stylianides
Publisher: Springer
ISBN: 3319709968
Category : Education
Languages : en
Pages : 298
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Book Description
This book explores new trends and developments in mathematics education research related to proof and proving, the implications of these trends and developments for theory and practice, and directions for future research. With contributions from researchers working in twelve different countries, the book brings also an international perspective to the discussion and debate of the state of the art in this important area. The book is organized around the following four themes, which reflect the breadth of issues addressed in the book: • Theme 1: Epistemological issues related to proof and proving; • Theme 2: Classroom-based issues related to proof and proving; • Theme 3: Cognitive and curricular issues related to proof and proving; and • Theme 4: Issues related to the use of examples in proof and proving. Under each theme there are four main chapters and a concluding chapter offering a commentary on the theme overall.
Author: Catarina Dutilh Novaes
Publisher: Cambridge University Press
ISBN: 1108846246
Category : Philosophy
Languages : en
Pages : 287
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Book Description
This comprehensive account of the concept and practices of deduction is the first to bring together perspectives from philosophy, history, psychology and cognitive science, and mathematical practice. Catarina Dutilh Novaes draws on all of these perspectives to argue for an overarching conceptualization of deduction as a dialogical practice: deduction has dialogical roots, and these dialogical roots are still largely present both in theories and in practices of deduction. Dutilh Novaes' account also highlights the deeply human and in fact social nature of deduction, as embedded in actual human practices; as such, it presents a highly innovative account of deduction. The book will be of interest to a wide range of readers, from advanced students to senior scholars, and from philosophers to mathematicians and cognitive scientists.
Author: Bharath Sriraman
Publisher: Springer Nature
ISBN: 3031408462
Category :
Languages : en
Pages : 3221
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Book Description
Author: Elizabeth G. Price
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111027244
Category : Religion
Languages : en
Pages : 474
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Book Description
When debating the need for prophets, Muslim theologians frequently cited an objection from a group called the Barāhima – either a prophet conveys what is in accordance with reason, so they would be superfluous, or a prophet conveys what is contrary to reason, so they would be rejected. The Barāhima did not recognise prophecy or revelation, because they claimed that reason alone could guide them on the right path. But who were these Barāhima exactly? Were they Brahmans, as their title would suggest? And how did they become associated with this highly incisive objection to prophecy? This book traces the genealogy of the Barāhima and explores their profound impact on the evolution of Islamic theology. It also charts the pivotal role that the Kitāb al-Zumurrud played in disseminating the Barāhima’s critiques and in facilitating an epistemological turn in the wider discourse on prophecy (nubuwwa). When faced with the Barāhima, theologians were not only pressed to explain why rational agents required the input of revelation, but to also identify an epistemic gap that only a prophet could fill. A debate about whether humans required prophets thus evolved into a debate about what humans could and could not know by their own means.
Author: Jens Erik Fenstad
Publisher: Springer
ISBN: 3319729748
Category : Philosophy
Languages : en
Pages : 138
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Book Description
This book explains exactly what human knowledge is. The key concepts in this book are structures and algorithms, i.e., what the readers “see” and how they make use of what they see. Thus in comparison with some other books on the philosophy (or methodology) of science, which employ a syntactic approach, the author’s approach is model theoretic or structural. Properly understood, it extends the current art and science of mathematical modeling to all fields of knowledge. The link between structure and algorithms is mathematics. But viewing “mathematics” as such a link is not exactly what readers most likely learned in school; thus, the task of this book is to explain what “mathematics” should actually mean. Chapter 1, an introductory essay, presents a general analysis of structures, algorithms and how they are to be linked. Several examples from the natural and social sciences, and from the history of knowledge, are provided in Chapters 2–6. In turn, Chapters 7 and 8 extend the analysis to include language and the mind. Structures are what the readers see. And, as abstract cultural objects, they can almost always be seen in many different ways. But certain structures, such as natural numbers and the basic theory of grammar, seem to have an absolute character. Any theory of knowledge grounded in human culture must explain how this is possible. The author’s analysis of this cultural invariance, combining insights from evolutionary theory and neuroscience, is presented in the book’s closing chapter. The book will be of interest to researchers, students and those outside academia who seek a deeper understanding of knowledge in our present-day society.
Author: O. Bueno
Publisher: Springer
ISBN: 0230245196
Category : Philosophy
Languages : en
Pages : 330
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Book Description
Thirteen promising young researchers write on what they take to be the right philosophical account of mathematics and discuss where the philosophy of mathematics ought to be going. New trends are revealed, such as an increasing attention to mathematical practice, a reassessment of the canon, and inspiration from philosophical logic.
