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Mathematics and Physical Reality

Geoffrey Hellman

in Mathematics without Numbers: Towards a Modal-Structural Interpretation

Published in print:
1993
Published Online:
November 2003
ISBN:
9780198240341
eISBN:
9780191597664
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198240341.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

Strategies for extending the modal‐structural approach to applications of mathematics are explored. The basic idea is to entertain what relationships would hold between a non‐mathematical system of ... More


Mathematics in application

Penelope Maddy

in Second Philosophy: A Naturalistic Method

Published in print:
2007
Published Online:
January 2009
ISBN:
9780199273669
eISBN:
9780191706264
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199273669.003.0024
Subject:
Philosophy, Logic/Philosophy of Mathematics

Turning now to the role of mathematics in natural science, this chapter takes up a number of themes. First, the Quine/Putnam idea that the indispensability of mathematics for much of science confirms ... More


Varying Interpretations

Christopher Pincock

in Mathematics and Scientific Representation

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199757107
eISBN:
9780199932313
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199757107.003.0004
Subject:
Philosophy, Philosophy of Science

Another kind of scientific representation is obtained when a scientist links representations using some shared mathematics. This sort of situation is quite different from the acausal representations ... More


The Indispensability of Mathematics

Mark Colyvan

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195137545
eISBN:
9780199833139
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/019513754X.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Looks at the Quine–Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical ... More


Applying Mathematics: Two Models

Jody Azzouni

in Deflating Existential Consequence: A Case for Nominalism

Published in print:
2004
Published Online:
January 2005
ISBN:
9780195159882
eISBN:
9780199834990
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195159888.003.0009
Subject:
Philosophy, Logic/Philosophy of Mathematics

Several applications of mathematics to empirical domains are described, including a small portion of Newtonian mechanics. The simplest case is one where a nonmathematical empirical description of the ... More


Time Series Analysis

Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray

in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691151687
eISBN:
9781400848911
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151687.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter summarizes the fundamental concepts and tools for analyzing time series data. Time series analysis is a branch of applied mathematics developed mostly in the fields of signal processing ... More


The Problem

Penelope Maddy

in Defending the Axioms: On the Philosophical Foundations of Set Theory

Published in print:
2011
Published Online:
May 2011
ISBN:
9780199596188
eISBN:
9780191725395
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199596188.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

Proper understanding of contemporary set theory requires a clear sense of how it came to be what it is and the mathematical roles it is designed to play. This chapter traces the rise of pure ... More


Quantum Chemistry qua Applied Mathematics: Approximation Methods and Crunching Numbers

Kostas Gavroglu and Ana Simões

in Neither Physics nor Chemistry: A History of Quantum Chemistry

Published in print:
2011
Published Online:
August 2013
ISBN:
9780262016186
eISBN:
9780262298759
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262016186.003.0004
Subject:
History, History of Science, Technology, and Medicine

In Britain, John Edward Lennard-Jones, Douglas Rayner Hartree, and Charles Alfred Coulson played important roles in expanding the domain of applied mathematics to include quantum chemistry. This ... More


Academic Mathematics in France before 1699: The Administrative Turn at the Académie Royale des Sciences

J.B. Shank

in Before Voltaire: The French Origins of "Newtonian" Mechanics, 1680-1715

Published in print:
2018
Published Online:
May 2019
ISBN:
9780226509297
eISBN:
9780226509327
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226509327.003.0003
Subject:
History, History of Science, Technology, and Medicine

Chapter 3 completes Part I's assessment of the culture of French academic mathematics begun in Chapter 2. It focuses on the institutional and social developments that turned the Académie Royale des ... More


Why Empirically Indispensable Mathematical Doctrine and (Some) Scientific Law Must Be Taken as True: Preliminary Considerations

Jody Azzouni

in Deflating Existential Consequence: A Case for Nominalism

Published in print:
2004
Published Online:
January 2005
ISBN:
9780195159882
eISBN:
9780199834990
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195159888.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

A version of the indispensability of the truth of applied mathematical doctrine and empirical scientific law is established in this and the next chapter. This chapter begins the argument with a ... More


The Game Theory Phenomenon

Paul Erickson

in The World the Game theorists Made

Published in print:
2015
Published Online:
May 2016
ISBN:
9780226097039
eISBN:
9780226097206
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226097206.003.0001
Subject:
History, History of Science, Technology, and Medicine

Writing about game theory’s past presents several historiographical challenges. At least prior to its prominent appearances in economics since the 1980s, game theory does not correlate neatly with ... More


A Second Pilgrim’s Progress

Mark Wilson

in Physics Avoidance: and other essays in conceptual strategy

Published in print:
2017
Published Online:
December 2017
ISBN:
9780198803478
eISBN:
9780191841651
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198803478.003.0009
Subject:
Philosophy, Philosophy of Science, Philosophy of Language

Influenced by Quine, self-styled naturalist projects within the philosophy of mathematics rest upon simplistic conceptions of linguistic reference and how the inferential tools of applied mathematics ... More


Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

John A. Adam

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691148373
eISBN:
9781400885404
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691148373.001.0001
Subject:
Mathematics, Applied Mathematics

This book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. It includes discussions of how ocean waves are refracted around ... More


Kitcher against the Platonists

Gideon Rosen

in The Philosophy of Philip Kitcher

Published in print:
2016
Published Online:
June 2016
ISBN:
9780199381357
eISBN:
9780199381371
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199381357.003.0002
Subject:
Philosophy, General, Philosophy of Science

Gideon Rosen discusses Kitcher’s recent critique of platonism and defense of formalism. Kitcher argues that any view that attributes a subject matter to mathematics, including platonism, has no good ... More


Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691142173
eISBN:
9781400842650
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142173.001.0001
Subject:
Mathematics, Applied Mathematics

Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important ... More


Eli’s Impact: A Case Study

Charles Fefferman

Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)

in Advances in Analysis: The Legacy of Elias M. Stein

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159416
eISBN:
9781400848935
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159416.003.0002
Subject:
Mathematics, Numerical Analysis

This chapter illustrates the continuing powerful influence of Eli Stein's ideas. It starts by recalling his ideas on Littlewood–Paley theory, as well as several major developments in pure and applied ... More


Scientific Method

Marjorie Senechal

in I Died for Beauty: A Biography of Dorothy Wrinch

Published in print:
2012
Published Online:
March 2015
ISBN:
9780199732593
eISBN:
9780190254353
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:osobl/9780199732593.003.0008
Subject:
History, History of Science, Technology, and Medicine

This chapter describes Dot's work with Harold Jeffreys. Like Dot, Harold was drawn to applied mathematics, first to astronomy, then to geophysics, the earth. Like Dot, he was drawn to the philosophy ... More


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