Overview
- Offers a novel perspective on the epistemology of science and mathematics
- Describes scientific knowledge as a combination of accurate reference and analytical interpretation
- Includes philosophical case studies drawn from mathematics and cosmology
- Fosters a philosophy of mathematics focused on mathematical practice
- Includes supplementary material: sn.pub/extras
Part of the book series: Studies in Applied Philosophy, Epistemology and Rational Ethics (SAPERE, volume 30)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (8 chapters)
-
Front Matter
-
Back Matter
Keywords
- Langlands Program
- Fermat's Last Theorem
- Andrew Wiles
- Nagelian Theory Reduction
- Cassirer and the Rule of the Series
- Newton vs. Leibniz
- Absolute Time
- Relational Time
- The 3-body Problem
- The Problem of Reference
- Analysis and Representation
- Ampliative vs. Deductive Reasoning
- Math Genie
- Analytic Number Theory
- Algebraic Number Theory
- Complex Analysis
- Differential Equations
- Classical Mechanics and Astronomy
- Modern Cosmology
- Hubble vs. Zwicky
About this book
This book deals with a topic that has been largely neglected by philosophers of science to date: the ability to refer and analyze in tandem. On the basis of a set of philosophical case studies involving both problems in number theory and issues concerning time and cosmology from the era of Galileo, Newton and Leibniz up through the present day, the author argues that scientific knowledge is a combination of accurate reference and analytical interpretation. In order to think well, we must be able to refer successfully, so that we can show publicly and clearly what we are talking about. And we must be able to analyze well, that is, to discover productive and explanatory conditions of intelligibility for the things we are thinking about. The book’s central claim is that the kinds of representations that make successful reference possible and those that make successful analysis possible are not the same, so that significant scientific and mathematical work typically proceeds by means of a heterogeneous discourse that juxtaposes and often superimposes a variety of kinds of representation, including formal and natural languages as well as more iconic modes. It demonstrates the virtues and necessity of heterogeneity in historically central reasoning, thus filling an important gap in the literature and fostering a new, timely discussion on the epistemology of science and mathematics.
Reviews
Authors and Affiliations
Bibliographic Information
Book Title: Starry Reckoning: Reference and Analysis in Mathematics and Cosmology
Authors: Emily Rolfe Grosholz
Series Title: Studies in Applied Philosophy, Epistemology and Rational Ethics
DOI: https://doi.org/10.1007/978-3-319-46690-3
Publisher: Springer Cham
eBook Packages: Religion and Philosophy, Philosophy and Religion (R0)
Copyright Information: Springer International Publishing AG 2016
Hardcover ISBN: 978-3-319-46689-7Published: 15 December 2016
Softcover ISBN: 978-3-319-83562-4Published: 29 April 2018
eBook ISBN: 978-3-319-46690-3Published: 25 November 2016
Series ISSN: 2192-6255
Series E-ISSN: 2192-6263
Edition Number: 1
Number of Pages: XVIII, 187
Number of Illustrations: 15 b/w illustrations
Topics: Epistemology, History of Mathematical Sciences, History and Philosophical Foundations of Physics, Philosophy of Science