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Introduction to Part II

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/9780198239529.003.0009
Subject:
Philosophy, Ancient Philosophy, Philosophy of Science

Part II investigates two Hellenistic models of spatial magnitude, time, and motion — models that can be seen as conceptual alternatives to the Aristotelian model considered in some detail in Part I. ... More


Simple Shapes: Vision and Concepts

Marcus Giaquinto

in Visual Thinking in Mathematics

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199285945
eISBN:
9780191713811
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285945.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter focuses on the cognitive resources needed for basic geometry. It argues that the initial geometrical concepts of basic shapes depend on the way we perceive those shapes. In having ... More


Basic Geometrical Knowledge

Marcus Giaquinto

in Visual Thinking in Mathematics

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199285945
eISBN:
9780191713811
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285945.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter shows how we might come by a simple geometrical belief without inferring it from other beliefs, in a way that is consonant with the apparent obviousness and cogency of the acquired ... More


Geometrical Discovery by Visualizing

Marcus Giaquinto

in Visual Thinking in Mathematics

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199285945
eISBN:
9780191713811
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285945.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter shows how, using basic beliefs, one can go on to make a geometrical discovery by visual means in a non-empirical manner. It focuses on a simple example in order to illustrate the general ... More


Egypt and Mesopotamia

Victor J. Katz and Karen Hunger Parshall

in Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691149059
eISBN:
9781400850525
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149059.003.0002
Subject:
Mathematics, History of Mathematics

This chapter explores the beginnings of algebra in Egypt and Mesopotamia. They are the earliest civilizations to have left written mathematical records, and they date back thousands of years. From ... More


The Ancient Greek World

Victor J. Katz and Karen Hunger Parshall

in Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691149059
eISBN:
9781400850525
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149059.003.0003
Subject:
Mathematics, History of Mathematics

This chapter focuses on the mathematicians of Ancient Greece; more specifically, on the elements of geometrical algebra present in the works of Euclid and Apollonius, as well as the propositions of ... More


Ancient Greek Mathematics: A Role for Diagrams

José Ferreirós

in Mathematical Knowledge and the Interplay of Practices

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167510
eISBN:
9781400874002
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167510.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter focuses on the ancient Greek tradition of geometrical proof in light of recent studies by Kenneth Manders and others. It advances the view that the borderline of elementary mathematics ... More


<i>GL</i>(<i>n</i>) × <i>GL</i>(<i>n</i>) × … × <i>GL</i>(<i>n</i>) Examples

Nicholas M. Katz

in Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153308
eISBN:
9781400842704
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153308.003.0021
Subject:
Mathematics, Number Theory

This chapter investigates the question which begings as follows. Suppose we have a geometrically irreducible middle extension sheaf G on 𝔾ₘ/k which is pure of weight zero, such that the object N := ... More


The Inscrutability of Intrinsic Content

John Foster

in A World for Us: The Case for Phenomenalistic Idealism

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199297139
eISBN:
9780191711398
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199297139.003.0002
Subject:
Philosophy, Moral Philosophy

The realist view of the physical world represents it as something whose existence is logically independent of the human mind and philosophically fundamental. If we retain allegiance to this view, ... More


Locke on Powers: The Geometrical Model

Walter Ott

in Causation and Laws of Nature in Early Modern Philosophy

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199570430
eISBN:
9780191722394
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570430.003.0021
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

Locke's ontology of relations and powers points to an alternative to the occasionalists' cognitive model of causality. So far, though, this is all it has done; it remains to be seen just how Locke ... More


Diagram‐Based Geometric Practice

Kenneth Manders

in The Philosophy of Mathematical Practice

Published in print:
2008
Published Online:
February 2010
ISBN:
9780199296453
eISBN:
9780191711961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296453.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter provides a survey of issues about diagrams in traditional geometrical reasoning. After briefly refuting several common philosophical objections, and giving a sketch of diagram-based ... More


The Euclidean Diagram (1995)

Kenneth Manders

in The Philosophy of Mathematical Practice

Published in print:
2008
Published Online:
February 2010
ISBN:
9780199296453
eISBN:
9780191711961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296453.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is ... More


Reflections on the Purity of Method in Hilbert's Grundlagen der Geometrie

Michael Hallett

in The Philosophy of Mathematical Practice

Published in print:
2008
Published Online:
February 2010
ISBN:
9780199296453
eISBN:
9780191711961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296453.003.0009
Subject:
Philosophy, Logic/Philosophy of Mathematics

In the Conclusion to his Grundlagen der Geometrie of 1899, Hilbert stated that the concern with ‘purity of method’ is nothing more than a ‘subjective interpretation’ of the demand for a careful ... More


Anion-topology approach

Sergry V. Krivovichev

in Structural Crystallography of Inorganic Oxysalts

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199213207
eISBN:
9780191707117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213207.003.0004
Subject:
Physics, Crystallography

This chapter deals with description of dense 2-D topologies using the concept of anion-topology introduced by P. C. Burns and co-authors for the analysis of uranyl layered structures. Anion ... More


Sources of Paradigm Uniformity

Luigi Burzio

in Paradigms in Phonological Theory

Published in print:
2004
Published Online:
February 2010
ISBN:
9780199267712
eISBN:
9780191708213
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199267712.003.0004
Subject:
Linguistics, Phonetics / Phonology

This chapter argues that paradigm uniformity (PU) effects ultimately show that, while the move towards parallelism initiated by OT was much on the right track, the degree of parallelism in the system ... More


Contrast theory

G. A. D. Briggs and O. V. Kolosov

in Acoustic Microscopy: Second Edition

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199232734
eISBN:
9780191716355
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232734.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

Reflection acoustic microscopy of solid surfaces is generally dominated by interference between a specularly reflected wave and reflected waves associated with excitation of Rayleigh waves in the ... More


Historical developments 1

ANDRÉ AUTHIER

in Dynamical Theory of X-Ray Diffraction

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198528920
eISBN:
9780191713125
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528920.003.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter provides a historical introduction to X-ray dynamical diffraction. It starts with an account of Ewald's thesis on the dispersion of light and of the famous experiment of the diffraction ... More


Geometrical theory of X-ray diffraction

ANDRÉ AUTHIER

in Dynamical Theory of X-Ray Diffraction

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198528920
eISBN:
9780191713125
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528920.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter describes a concise summary of the geometrical theory of X-ray diffraction, which is not the main topic of the book. The amplitude diffracted by a periodic electron distribution is ... More


Neutrino Oscillations In Matter

Carlo Giunti and Chung W. Kim

in Fundamentals of Neutrino Physics and Astrophysics

Published in print:
2007
Published Online:
January 2010
ISBN:
9780198508717
eISBN:
9780191708862
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508717.003.0009
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the physics of neutrino oscillations in matter and explains effective potentials in matter, evolution of neutrino flavours, the MSW effect, slab approximation, parametric ... More


A Philosopher Looks at Tool Use and Causal Understanding

James Woodward

in Tool Use and Causal Cognition

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199571154
eISBN:
9780191731259
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199571154.003.0002
Subject:
Psychology, Developmental Psychology, Evolutionary Psychology

This chapter presents a kind of typology of different sorts of abilities that might be associated with the notion of causal understanding, the acquisition of causal beliefs, causally informed action ... More


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