## Identity in Physics: A Historical, Philosophical, and Formal Analysis

*Steven French and Décio Krause*

- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199278244
- eISBN:
- 9780191603952
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199278245.001.0001
- Subject:
- Philosophy, Philosophy of Science

Drawing on philosophical accounts of identity and individuality, as well as the histories of both classical and quantum physics, this book explores two alternative metaphysical approaches to quantum ... More

## Plural Predication

*Thomas McKay*

- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199278145
- eISBN:
- 9780191707971
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199278145.001.0001
- Subject:
- Philosophy, Philosophy of Language

Plural predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These ... More

## The Mathematics of Non-Individuality

*Steven French and Décio Krause*

### in Identity in Physics: A Historical, Philosophical, and Formal Analysis

- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199278244
- eISBN:
- 9780191603952
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199278245.003.0007
- Subject:
- Philosophy, Philosophy of Science

This chapter presents the theory of quasi-sets, and argues that this offers an appropriate set-theoretic formalism for non-individual quantum objects. The basic idea is that in a quasi-set, there may ... More

## The Logic of Quanta

*Steven French and Décio Krause*

### in Identity in Physics: A Historical, Philosophical, and Formal Analysis

- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199278244
- eISBN:
- 9780191603952
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199278245.003.0009
- Subject:
- Philosophy, Philosophy of Science

This chapter begins with a philosophically-oriented outline of quantum field theory that looks at the different ways in which a quantum field can be constructed. The difficulties in articulating a ... More

## CONSTRUCTIVE SET THEORIES AND THEIR CATEGORY-THEORETIC MODELS

*Alex Simpson*

### 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/9780198566519.003.0003
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter advocates a pragmatic approach to constructive set theory, using axioms based solely on set-theoretic principles that are directly relevant to (constructive) mathematical practice. The ... More

## TOWARD A MINIMALIST FOUNDATION FOR CONSTRUCTIVE MATHEMATICS

*Maria Emilia Maietti and Giovanni Sambin*

### 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/9780198566519.003.0006
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

The two main views in modern constructive mathematics usually associated with constructive type theory and topos theory are compatible with the classical view, but they are incompatible with each ... More

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

*Laura Crosilla and Peter Schuster (eds)*

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566519
- eISBN:
- 9780191713927
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566519.001.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

Constructive mathematics is a vital area of research which has gained special attention in recent years due to the distinctive presence of computational content in its theorems. This characteristic ... More

## Set Theory and The Philosophy of Mathematics

*Graham Priest*

### in In Contradiction

- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0011
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter discusses certain aspects of naive set theory, that is, set theory in which the abstraction scheme holds for all formulas of the language of set theory, and some of its implications for ... More

## Set Theoretic Paradoxes

*Graham Priest*

### in In Contradiction

- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0003
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

In this chapter it is argued that the standard paradoxes of set theory are also dialetheias. In particular, it argues that Zermelo Fraenkel set theory does not provide a satisfactory solution to ... More

## PRESHEAF MODELS FOR CONSTRUCTIVE SET THEORIES

*Nicola Gambino*

### 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/9780198566519.003.0004
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter introduces new kinds of models for constructive set theories based on categories of presheaves. It concentrates on categories of classes rather than sets, following the lines of ... More

## Set Theory and its Philosophy: A Critical Introduction

*Michael Potter*

- Published in print:
- 2004
- Published Online:
- September 2011
- ISBN:
- 9780199269730
- eISBN:
- 9780191699443
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269730.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This book presents a philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. The book offers an ... More

## INTRODUCTION

*Laura Crosilla and Peter Schuster*

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566519
- eISBN:
- 9780191713927
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566519.003.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This introductory chapter sets the stage for the following chapters. It first discusses the issue of foundational systems for constructive mathematical practice, and expresses the desire for a closer ... More

## The Problem of Conceptual Understanding

*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/9780691167510.003.0010
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter considers one of the most intriguing questions that philosophy of mathematics in practice must, sooner or later, confront: how understanding of mathematics is obtained. In particular, it ... More

## Mathematics without Numbers: Towards a Modal-Structural Interpretation

*Geoffrey Hellman*

- Published in print:
- 1993
- Published Online:
- November 2003
- ISBN:
- 9780198240341
- eISBN:
- 9780191597664
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198240341.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to ... More

## UNIVERSES IN TOPOSES

*Thomas Streicher*

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566519
- eISBN:
- 9780191713927
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566519.003.0005
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses a notion of universe in toposes, which from a logical point of view gives rise to an extension of Higher Order Intuitionistic Arithmetic (HAH). In this way, one can construct ... More

## Set Theory, Model Theory, and Computability Theory

*Wilfrid Hodges*

### in The Development of Modern Logic

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780195137316
- eISBN:
- 9780199867912
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195137316.003.0032
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter surveys set theory, model theory, and computability theory: how they first emerged from the foundations of mathematics, and how they have developed since. There are any amounts of ... More

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

*Penelope Maddy*

- Published in print:
- 2011
- Published Online:
- May 2011
- ISBN:
- 9780199596188
- eISBN:
- 9780191725395
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199596188.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

Mathematics depends on proofs, and proofs have to begin somewhere, from some fundamental assumptions. Chapter I traces the historical rise of pure mathematics and the development of set theory, ... More

## Mathematical Prelude: A Selective Introduction to Logic and Set Theory for Social Scientists

*Gary Goertz and James Mahoney*

### in A Tale of Two Cultures: Qualitative and Quantitative Research in the Social Sciences

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149707
- eISBN:
- 9781400845446
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149707.003.0002
- Subject:
- Sociology, Social Research and Statistics

This chapter considers some key ideas from logic and set theory as they relate to qualitative research in the social sciences, including ideas concerning necessary and sufficient conditions. It also ... More

## Autocommentary on the First Edition

*Graham Priest*

### in In Contradiction

- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0020
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter charts some of the developments that have taken place since the first edition of this book was published, including areas where the author's views have been revised. It does this by ... More

## Mathematics and Make‐Believe

*Mary Leng*

### in Mathematics and Reality

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199280797
- eISBN:
- 9780191723452
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199280797.003.0007
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter presents in detail Kendall L. Walton's account of metaphor as prop‐oriented make‐believe, and discusses how this account can be used to provide an anti‐realist account of the ideal ... More