## 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

## 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

## 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

## 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

## 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

## Quantifying Chaos

*Robert C. Hilborn*

### in Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

- Published in print:
- 2000
- Published Online:
- January 2010
- ISBN:
- 9780198507239
- eISBN:
- 9780191709340
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507239.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter explores various means of quantifying the degree of chaotic behaviour of both numerically generated time series and time series from real experiments. These methods include Lyapunov ... More

## All Things Must Pass Away

*Joshua Spencer*

### in Oxford Studies in Metaphysics volume 7

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199659081
- eISBN:
- 9780191745201
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199659081.003.0003
- Subject:
- Philosophy, Metaphysics/Epistemology

One plausible thesis, stated using plural quantification, is that there are some things that are all things. Although widely accepted, in this chapter it is argued that that thesis is false. The ... More

## Cosmological Arguments

*Herman Philipse*

### in God in the Age of Science?: A Critique of Religious Reason

- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199697533
- eISBN:
- 9780191738470
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199697533.003.0012
- Subject:
- Philosophy, Philosophy of Religion, Metaphysics/Epistemology

Inductive cosmological arguments are prima facie more promising for the natural theologian than deductive arguments, such as the Kalam cosmological argument, which is not sound. In the cosmological ... More