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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

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/9780198566519.003.0001
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

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/9780198566519.003.0005
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


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