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Space, Time, and Stuff

Frank Arntzenius

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199696604
eISBN:
9780191738333
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199696604.001.0001
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

Much of this book can be seen as an attempt to show that physics is geometry, an attempt to show that the fundamental structure of the physical world is purely geometrical structure. Along the way, ... More


What is Special Relativity?

Harvey R. Brown

in Physical Relativity: Space-time structure from a dynamical perspective

Published in print:
2005
Published Online:
September 2006
ISBN:
9780199275830
eISBN:
9780191603914
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199275831.003.0008
Subject:
Philosophy, Philosophy of Science

This chapter begins with a discussion of Minkowski's geometrization of special relativity (SR). It then discusses Minkowski space-time, what absolute geometry explains, and special relativity. It is ... More


The Longest Journey: Bertrand Russell

Bas C. van Fraassen

in Scientific Representation: Paradoxes of Perspective

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199278220
eISBN:
9780191707926
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199278220.003.00010
Subject:
Philosophy, Philosophy of Mind, Philosophy of Science

The first sustained, rigorous development of a structuralist view of science appeared in the writings of Bertrand Russell, where the philosophical motivation precedes a precise formulation drawing on ... More


Transcendental‐Phenomenological Idealism: Husserl and Weyl

Thomas Ryckman

in The Reign of Relativity: Philosophy in Physics 1915-1925

Published in print:
2005
Published Online:
April 2005
ISBN:
9780195177176
eISBN:
9780199835324
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195177177.003.0005
Subject:
Philosophy, Philosophy of Science

Weyl’s major contributions in the spring of 1918 to the general theory of relativity and to constructive analysis reveal the influence of Husserl’s transcendental-phenomenological idealism. The known ... More


Weyl's “Purely Infinitesimal” Constitution of Field Physics

Thomas Ryckman

in The Reign of Relativity: Philosophy in Physics 1915-1925

Published in print:
2005
Published Online:
April 2005
ISBN:
9780195177176
eISBN:
9780199835324
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195177177.003.0006
Subject:
Philosophy, Philosophy of Science

It is shown how Weyl intertwined phenomenological analysis and mathematical construction in building the foundation of his “pure infinitesimal geometry” underlying gravitation and electromagnetism. ... More


The Shape of Space II: Curved Space?

Nick Huggett

in Everywhere and Everywhen: Adventures in Physics and Philosophy

Published in print:
2010
Published Online:
May 2010
ISBN:
9780195379518
eISBN:
9780199776559
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195379518.003.0007
Subject:
Philosophy, Philosophy of Science

One can readily imagine a curved surface, but the very idea of a curved 3‐dimensional space may seem impossible; indeed, until ‘non‐Euclidean’ geometry was developed in the nineteenth century, such ... More


Looking for Geometry

Nick Huggett

in Everywhere and Everywhen: Adventures in Physics and Philosophy

Published in print:
2010
Published Online:
May 2010
ISBN:
9780195379518
eISBN:
9780199776559
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195379518.003.0008
Subject:
Philosophy, Philosophy of Science

One can readily imagine a curved surface, but the very idea of a curved 3‐dimensional space may seem impossible; indeed, until ‘non‐Euclidean’ geometry was developed in the nineteenth century, such ... More


Pictorial Perspective and the Indexical

Bas C. van Fraassen

in Scientific Representation: Paradoxes of Perspective

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199278220
eISBN:
9780191707926
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199278220.003.0004
Subject:
Philosophy, Philosophy of Mind, Philosophy of Science

The connection between perspective and the indexical shows up in the sciences, for example, when talk of frames of reference is conducted in terms of observers (whose frames they are, so to speak). ... More


 There goes the neighbourhood...

Frank Arntzenius

in Space, Time, and Stuff

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199696604
eISBN:
9780191738333
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199696604.003.0002
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

In this chapter it is argued that one cannot specify the state of the contents of a classical world, i.e. the state of matter and fields which is governed by classical physics, space-time point by ... More


 Calculus as geometry

Frank Arntzenius

in Space, Time, and Stuff

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199696604
eISBN:
9780191738333
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199696604.003.0008
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

This chapter argues that calculus, the theory of differentiation and integration that permeates modern science, can be formulated as a purely geometric theory, which does not entail the existence of ... More


Logic and Mathematics

Jr. Henry E. Kyburg

in Science & Reason

Published in print:
1991
Published Online:
October 2011
ISBN:
9780195062533
eISBN:
9780199853038
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195062533.003.0002
Subject:
Philosophy, Philosophy of Science

This chapter discusses the philosophy and logic behind the mathematical ideas of first-order logic, metalanguages, arithmetic, and geometry. It familiarizes the reader to these mathematical ideas, ... More


1921: “Critical or Empiricist Interpretation of the New Physics?”

Thomas Ryckman

in The Reign of Relativity: Philosophy in Physics 1915-1925

Published in print:
2005
Published Online:
April 2005
ISBN:
9780195177176
eISBN:
9780199835324
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195177177.003.0003
Subject:
Philosophy, Philosophy of Science

Mortiz Schlick’s article of this title was highly influential in convincing several generations of philosophers that GTR outrightly falsified any variety of Kantian epistemology. In fact, the ... More


The Quantum Model: Spatial Magnitude

Michael J. White

in The Continuous and the Discrete: Ancient Physical Theories from a Contemporary Perspective

Published in print:
1992
Published Online:
October 2011
ISBN:
9780198239529
eISBN:
9780191679940
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198239529.003.0005
Subject:
Philosophy, Ancient Philosophy, Philosophy of Science

This chapter discusses the quantum model of spatial magnitude. There are two forms of the doctrine that spatial magnitude is constituted of quanta. According to the weaker form, it is a physical fact ... More


Quasars, Causality, and Geometry: A Scientific Controversy That Did not Occur

Wesley C. Salmon

in Causality and Explanation

Published in print:
1998
Published Online:
November 2003
ISBN:
9780195108644
eISBN:
9780199833627
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195108647.003.0026
Subject:
Philosophy, Philosophy of Science

Shows how the failure of astrophysicists to honor the distinction between causal processes and pseudoprocesses vitiates much of the discussion of quasars since their discovery in 1963. In this case, ... More


Mathematics

Peter R. Anstey

in John Locke and Natural Philosophy

Published in print:
2011
Published Online:
May 2011
ISBN:
9780199589777
eISBN:
9780191725487
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199589777.003.0007
Subject:
Philosophy, History of Philosophy, Philosophy of Science

This chapter argues that from the early drafts of the Essay to the Essay itself, Locke held to the view that the truths of mathematics are made true by things in the world or ways the world could be. ... More


Demonstration

Peter R. Anstey

in John Locke and Natural Philosophy

Published in print:
2011
Published Online:
May 2011
ISBN:
9780199589777
eISBN:
9780191725487
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199589777.003.0008
Subject:
Philosophy, History of Philosophy, Philosophy of Science

This chapter argues that Locke's theory of demonstration as the perception of the agreement or disagreement of ideas, is a pre‐linguistic account of reasoning that does not concern relations between ... More


Second Illustration of Why Mathematical Entities are Useful: Geometry and Distance

Hartry Field

in Science without Numbers

Published in print:
2016
Published Online:
December 2016
ISBN:
9780198777915
eISBN:
9780191823381
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198777915.003.0003
Subject:
Philosophy, Philosophy of Science, Logic/Philosophy of Mathematics

Shows that the use of real numbers in geometry can be accounted for by the conservativeness of mathematics, without assuming the truth of the theory of real numbers. Focuses on Hilbert’s ... More


My Strategy for Nominalizing Physics, and its Advantages

Hartry Field

in Science without Numbers

Published in print:
2016
Published Online:
December 2016
ISBN:
9780198777915
eISBN:
9780191823381
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198777915.003.0005
Subject:
Philosophy, Philosophy of Science, Logic/Philosophy of Mathematics

Suggests that the Hilbert theory of geometry, and its representation and uniqueness theorems, provide a general model of how physical theories are to be nominalized. Several features of Hilbert’s ... More


Husserl on the Origins of Geometry

Ian Hacking

in Science and the Life-World: Essays on Husserl's Crisis of European Sciences

Published in print:
2009
Published Online:
June 2013
ISBN:
9780804756044
eISBN:
9780804772945
Item type:
chapter
Publisher:
Stanford University Press
DOI:
10.11126/stanford/9780804756044.003.0004
Subject:
Philosophy, Philosophy of Science

This chapter examines the foundations of mathematics, focusing on The Origin of Geometry, an appendix to the Crisis. It notes that Husserl is one of those philosophers who is awed by mathematics, ... More


Universality and Spatial Form

Rodolphe Gasché

in Science and the Life-World: Essays on Husserl's Crisis of European Sciences

Published in print:
2009
Published Online:
June 2013
ISBN:
9780804756044
eISBN:
9780804772945
Item type:
chapter
Publisher:
Stanford University Press
DOI:
10.11126/stanford/9780804756044.003.0007
Subject:
Philosophy, Philosophy of Science

This chapter examines the paradox concerning philosophical and scientific universality. It argues that Husserl's Crisis can be correctly understood as a critique of universality, more particularly of ... More


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