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Realism in Mathematics

Penelope Maddy

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240358
eISBN:
9780191597978
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/019824035X.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Many mathematicians understand their work as an effort to describe the denizens and features of an abstract mathematical world or worlds. Most philosophers of mathematics consider views of this sort ... More


Jewish Music and Modernity

Philip Bohlman

Published in print:
2008
Published Online:
January 2009
ISBN:
9780195178326
eISBN:
9780199869992
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195178326.001.0001
Subject:
Music, Ethnomusicology, World Music

Is there really such a thing as Jewish music? And does it survive as an expressive practice of worship and identity against modernity? This book poses such questions in new and critical ways by ... More


INVENTING JEWISH MUSIC

Philip V. Bohlman

in Jewish Music and Modernity

Published in print:
2008
Published Online:
January 2009
ISBN:
9780195178326
eISBN:
9780199869992
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195178326.003.0005
Subject:
Music, Ethnomusicology, World Music

As the first of three chapters on the “ontologies” of Jewish music — music’s aesthetic, cultural, and musical identities and capacity to exist in the world of modern Jewish society — this chapter ... More


Setting the Scene: a Response to John Rogerson

KEITH W. WHITELAM

in Understanding the History of Ancient Israel

Published in print:
2007
Published Online:
January 2012
ISBN:
9780197264010
eISBN:
9780191734946
Item type:
chapter
Publisher:
British Academy
DOI:
10.5871/bacad/9780197264010.003.0002
Subject:
Religion, Biblical Studies

John Rogerson's review of works on the history of ancient Israel from Humphrey Prideaux to Martin Noth is a fine illustration of Ecclesiastes' observation (1.9): ‘What has been is what will be, and ... More


CONSTRUCTIVE REVERSE MATHEMATICS: COMPACTNESS PROPERTIES

Hajime Ishihara

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0016
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter proposes a base formal system for constructive reverse mathematics to classify various theorems in intuitionistic, constructive recursive, and classical mathematics by logical ... More


“With All Its Original Stage Enchantment”

Richard Barrios

in A Song in the Dark: The Birth of the Musical Film

Published in print:
2009
Published Online:
February 2010
ISBN:
9780195377347
eISBN:
9780199864577
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195377347.003.0010
Subject:
Music, Popular

Broadway musicals were a ready source for the early musicals, and RKO's smash Rio Rita led the way. Some of the adaptations were close, while others strayed wildly from the originals. Among the ... More


From Voyagers to Martyrs: Toward a Storied History of Mathematics

Amir Alexander

in Circles Disturbed: The Interplay of Mathematics and Narrative

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691149042
eISBN:
9781400842681
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149042.003.0001
Subject:
Mathematics, History of Mathematics

This chapter traces the history of mathematics, from the late sixteenth century to the present, through the lens of mathematical stories. The period is divided into three main epochs and a possible ... More


Objectivity in Mathematical Knowledge

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/9780691167510.003.0009
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter proposes an idea for reconciling the hypothetical conception of mathematics with the traditional idea of the objectivity of mathematical knowledge. The basic notion is that, because new ... More


The complexity of sets

André Nies

in Computability and Randomness

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199230761
eISBN:
9780191710988
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230761.003.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter studies the complexity of sets of natural numbers. There are two interrelated types of complexity, these are computational and descriptive. In both cases, to understand the complexity of ... More


Axioms

Penelope Maddy

in Realism in Mathematics

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240358
eISBN:
9780191597978
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019824035X.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

Pursues the theoretical level of the two‐tiered epistemology of set theoretic realism, the level at which more abstract axioms can be justified by their consequences at more intuitive levels. I ... More


Capitalism as Creative, Chaotic Evolution by Structural Change

Richard M. Goodwin

in Chaotic Economic Dynamics

Published in print:
1990
Published Online:
November 2003
ISBN:
9780198283355
eISBN:
9780191596315
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198283350.003.0001
Subject:
Economics and Finance, Macro- and Monetary Economics

As in meteorology, prediction in economics is hampered by highly irregular, chaotic dynamics. A two‐sector model is employed to examine the complementary growth theories of Schumpeter and Keynes ... More


The Contradiction (i): The Problem

David Bostock

in Russell's Logical Atomism

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199651443
eISBN:
9780191741197
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199651443.003.0002
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

The chapter gives some background on the mathematical achievements of Cantor and Dedekind, and describes how Russell aimed to show that all mathematics can be derived from a purely logical starting ... More


Georg Cantor’s Paradise, Metaphysics, and Husserlian Logic

Claire Ortiz Hill

in Categories of Being: Essays on Metaphysics and Logic

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199890576
eISBN:
9780199980031
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199890576.003.0010
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

This chapter deals with the discussion that was going on among set theorists and logicians at the end of the nineteenth century and at the beginning of the twentieth century. Logical experimentation ... More


Binding Matter, Unbinding God

Stephen H. Webb

in Jesus Christ, Eternal God: Heavenly Flesh and the Metaphysics of Matter

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199827954
eISBN:
9780199919468
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199827954.003.0004
Subject:
Religion, Theology

Aristotle's position on the eternity of matter posited a profound challenge to theology, as did the Greek philosophical conviction that matter is infinite (which Aristotle exceptionally did not ... More


Cardinals

Michael Potter

in Set Theory and its Philosophy: A Critical Introduction

Published in print:
2004
Published Online:
September 2011
ISBN:
9780199269730
eISBN:
9780191699443
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199269730.003.0014
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter studies the concept of equinumerosity introduced in § 4.8 by means of the following definition: two sets are said to be equinumerous if there is a one-to-one correspondence between them. ... More


Naturalism in Mathematics

Penelope Maddy

Published in print:
2000
Published Online:
November 2003
ISBN:
9780198250753
eISBN:
9780191597961
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198250754.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

It is well known that certain natural statements of set theory, like Cantor's continuum hypothesis (CH), cannot be proved or disproved on the basis of the standard axioms (Zermelo–Fraenkel with ... More


Absolute infinity

Graham Priest

in Beyond the Limits of Thought

Published in print:
2002
Published Online:
October 2011
ISBN:
9780199254057
eISBN:
9780191698194
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199254057.003.0009
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter examines the relevance of mathematician and philosopher George Cantor's views on infinity to the contradictions in the limits of thought. Cantor's work has clarified with an ... More


The Letters of Menakhem-Mendl and Sheyne-Sheyndl and Motl, the Cantor's Son

Sholem Aleichem

Published in print:
2002
Published Online:
October 2013
ISBN:
9780300092462
eISBN:
9780300128635
Item type:
book
Publisher:
Yale University Press
DOI:
10.12987/yale/9780300092462.001.0001
Subject:
Religion, Judaism

This book presents an outstanding new translation of two favorite comic novels by the preeminent Yiddish writer Sholem Aleichem. The Letters of Menakhem-Mendl and Sheyne-Sheyndl portrays a tumultuous ... More


The Development of Analysis: A Case Study

Philip Kitcher

in The Nature of Mathematical Knowledge

Published in print:
1985
Published Online:
November 2003
ISBN:
9780195035414
eISBN:
9780199833368
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195035410.003.0011
Subject:
Philosophy, Logic/Philosophy of Mathematics

Concludes with a more sustained look at a single part of the history of mathematics, the development of analysis from the seventeenth century to the work of Dedekind, Cantor and Frege. The discussion ... More


The Church Orders: An Introduction

Joseph Herl

in Worship Wars in Early Lutheranism Choir, Congregation and Three Centuries of Conflict

Published in print:
2008
Published Online:
January 2010
ISBN:
9780195365849
eISBN:
9780199864263
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195365849.003.0003
Subject:
Music, History, Western

Lutheran agendas and church orders—documents containing regulations concerning church life, doctrine, and the liturgy—present a complex tapestry of liturgical life among early Lutherans. It included ... More


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