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Author: Christopher Pincock
Publisher: OUP USA
Published: 2012-01-13
Total Pages: 347
ISBN-13: 0199757100
DOWNLOAD EBOOK →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. Pincock tackles this perennial question by asking how mathematics contributes to the success of our best scientific representations.
Author: Roman Frigg
Publisher: Springer Nature
Published: 2020-09-02
Total Pages: 250
ISBN-13: 3030451534
DOWNLOAD EBOOK →This monograph offers a critical introduction to current theories of how scientific models represent their target systems. Representation is important because it allows scientists to study a model to discover features of reality. The authors provide a map of the conceptual landscape surrounding the issue of scientific representation, arguing that it consists of multiple intertwined problems. They provide an encyclopaedic overview of existing attempts to answer these questions, and they assess their strengths and weaknesses. The book also presents a comprehensive statement of their alternative proposal, the DEKI account of representation, which they have developed over the last few years. They show how the account works in the case of material as well as non-material models; how it accommodates the use of mathematics in scientific modelling; and how it sheds light on the relation between representation in science and art. The issue of representation has generated a sizeable literature, which has been growing fast in particular over the last decade. This makes it hard for novices to get a handle on the topic because so far there is no book-length introduction that would guide them through the discussion. Likewise, researchers may require a comprehensive review that they can refer to for critical evaluations. This book meets the needs of both groups.
Author: Christopher Pincock
Publisher: Oxford University Press
Published: 2012-01-13
Total Pages: 352
ISBN-13: 0190208570
DOWNLOAD EBOOK →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: James Nguyen
Publisher: Cambridge University Press
Published: 2022-09-01
Total Pages: 154
ISBN-13: 1009007343
DOWNLOAD EBOOK →This Element presents a philosophical exploration of the notion of scientific representation. It does so by focussing on an important class of scientific representations, namely scientific models. Models are important in the scientific process because scientists can study a model to discover features of reality. But what does it mean for something to represent something else? This is the question discussed in this Element. The authors begin by disentangling different aspects of the problem of representation and then discuss the dominant accounts in the philosophical literature: the resemblance view and inferentialism. They find them both wanting and submit that their own preferred option, the so-called DEKI account, not only eschews the problems that beset these conceptions, but further provides a comprehensive answer to the question of how scientific representation works. This title is also available as Open Access on Cambridge Core.
Author: Insa Lawler
Publisher: Taylor & Francis
Published: 2022-12-13
Total Pages: 429
ISBN-13: 1000782034
DOWNLOAD EBOOK →This volume assembles cutting-edge scholarship on scientific understanding, scientific representation, and their delicate interplay. Featuring several articles in an engaging ‘critical conversation’ format, the volume integrates discussions about understanding and representation with perennial issues in the philosophy of science, including the nature of scientific knowledge, idealizations, scientific realism, scientific inference, and scientific progress. In the philosophy of science, questions of scientific understanding and scientific representation have only recently been put in dialogue with each other. The chapters advance these discussions from a variety of fresh perspectives. They range from case studies in physics, chemistry, and neuroscience to the representational challenges of machine learning models; from special forms of representation such as maps and topological models to the relation between understanding and explanation; and from the role of idealized representations to the role of representation and understanding in scientific progress. Scientific Understanding and Representation will appeal to scholars and advanced students working in philosophy of science, philosophy of physics, philosophy of mathematics, and epistemology.
Author: Patrick Suppes
Publisher: Stanford Univ Center for the Study
Published: 2002
Total Pages: 536
ISBN-13: 9781575863337
DOWNLOAD EBOOK →A fundamental reason for using formal methods in the philosophy of science is the desirability of having a fixed frame of reference that may be used to organize the variety of doctrines at hand. This book—Patrick Suppes's major work, and the result of several decades of research—examines how set-theoretical methods provide such a framework, covering issues of axiomatic method, representation, invariance, probability, mechanics, and language, including research on brain-wave representations of words and sentences. This is a groundbreaking, essential text from a distinguished philosopher.
Author: Wenceslao J. Gonzalez
Publisher: Springer Science & Business Media
Published: 2014-02-19
Total Pages: 233
ISBN-13: 9400778384
DOWNLOAD EBOOK →This book analyzes Bas van Fraassen’s characterization of representation and models in science. In this regard, it presents the philosophical coordinates of his approach and pays attention to his structural empiricism as a framework for his views on scientific representations and models. These are developed here through two new contributions made by van Fraassen. In addition, there are analyses of the relation between models and reality in his approach, where the complexity of this conception is considered in detail. Furthermore, there is an examination of scientific explanation and epistemic values judgments. This volume includes a wealth of bibliographical information on his philosophy and relevant philosophical issues. Bas van Fraassen is a key figure in contemporary philosophy of science, as the prestigious Hempel Award shows. His views on scientific representation offer new ideas on how it should be characterized, and his conception of models shows a novelty that goes beyond other empiricists’ approaches of recent times. Both aspects — the characterization of scientific representation and the conception of models in science — are part of a deliberate attempt to forge a “structural empiricism,” an alternative to structural realism based on an elaborated version of empiricism.
Author: Pavel I. Etingof
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 240
ISBN-13: 0821853511
DOWNLOAD EBOOK →Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Author: Kaur Berinderjeet
Publisher: World Scientific
Published: 2017-04-12
Total Pages: 396
ISBN-13: 9813224231
DOWNLOAD EBOOK →This book contributes towards the literature in the field of mathematics education, specifically on aspects of empowering learners of mathematics. The book, comprising eighteen chapters, written by renowned researchers in mathematics education, provides readers with approaches and applicable classroom strategies to empower learners of mathematics. The chapters in the book can be classified into four sections. The four sections focus on how learners could be empowered in their learning, cognitive and affective processes, through mathematical content, purposefully designed mathematical tasks, whilst developing 21st century competencies. Contents: Empowering Mathematics Learners (Berinderjeet Kaur & Lee Ngan Hoe)Empowering Learning in an Algebra Class: The Case of Expansion and Factorisation (Chua Boon Liang)Facilitating Students' Mathematical Noticing (Tan Liang Soon & Hang Kim Hoo)Empowering Junior College Students through the Educational Use of Graphics Calculators (Barry Kissane)Understanding Future Teachers' Mathematical Knowing to Overcome Double Discontinuities (Hyungmi Cho & Oh Nam Kwon)Developing Student Voice in the Mathematics Classroom (Glenda Anthony & Roberta Hunter)Empowering Mathematics Learners through Effective Memory Strategies (Wong Khoon Yoong)Empower Primary School Pupils to Use Representations to Solve Process Problems (Yeo Kai Kow Joseph)Empowering Mathematics Learners with Metacognitive Strategies in Problem Solving (Loh Mei Yoke & Lee Ngan Hoe)Mathematical Problem Solving: An Approach to Empowering Students in the Mathematics Classroom (Toh Tin Lam)Empowering Mathematics Learners through Exploratory Tasks (Ariyadi Wijaya)Use of Open and Guided Investigative Tasks to Empower Mathematics Learners (Joseph B W Yeo)Using Representations to Develop Mathematical Thinking (Palanisamy K Veloo & Parmjit Singh)Empowering Teachers to Use Open-Ended Real-World Tasks in Primary Mathematics Classrooms (Ng Kit Ee Dawn)ACISK Framework — A Tool for Empowering Mathematics Learners to be Self-Directed (Wong Lai Fong & Berinderjeet Kaur)Empowering Students through Inquiry (Steve Thornton)Developing Self-Regulated Learners in the Primary Mathematics Classroom (Cheng Lu Pien & Teong Ying Xi Theodora)Empowering Students' Learning through Mathematical Modelling (Chun Ming Eric Chan, Rashidah Vapumarican, Kaiwen Vanessa Oh, Huanjia Tracey Liu & Yew Hwee Seah) Readership: Graduate students, researchers, practitioners and teachers in mathematics.
Author: Emily R. Grosholz
Publisher:
Published: 1991
Total Pages: 172
ISBN-13: 9781280809743
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