Jump to ContentJump to Main Navigation

You are looking at 1-20 of 130 items

  • Keywords: axioms x
Clear All Modify Search

View:

Set Theory: Boolean-Valued Models and Independence Proofs

John L. Bell

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568520
eISBN:
9780191717581
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568520.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This is the third edition of a well-known graduate textbook on Boolean-valued models of set theory. The aim of the first and second editions was to provide a systematic and adequately motivated ... More


Mathematical Justifications are Not Infinitely Various

Neil Tennant

in Changes of Mind: An Essay on Rational Belief Revision

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199655755
eISBN:
9780191742125
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199655755.003.0010
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter gives a suitably texturized proof of a deep result in mathematical logic by Harvey Friedman, which was produced on request. It states that every extant mathematical theory (by virtue of ... More


It stands alone

Louis A. Girifalco

in The Universal Force: Gravity - Creator of Worlds

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199228966
eISBN:
9780191711183
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228966.003.0016
Subject:
Physics, History of Physics

The theory of relativity is unique and is based on very simple ideas. In fact, it has only one fundamental premise and one physical fact. The premise is that the laws of physics must be the same ... 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


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


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


Conclusions: A New Basis for Interpreting the Mysteries

ROGER BECK

in The Religion of the Mithras Cult in the Roman Empire: Mysteries of the Unconquered Sun

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199216130
eISBN:
9780191712128
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199216130.003.0012
Subject:
Classical Studies, Ancient Religions

This concluding chapter revisits the summary description of the religion of the Mithras cult proposed in Chapter 1.


Problems

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/9780199651443.003.0006
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

Russell’s attempt to obey the Vicious Circle Principle must lead to the conclusion that there are only countably many propositional functions, but this conflicts with his axiom of reducibility. So we ... More


Among

Thomas J. McKay

in Plural Predication

Published in print:
2006
Published Online:
January 2007
ISBN:
9780199278145
eISBN:
9780191707971
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199278145.003.0007
Subject:
Philosophy, Philosophy of Language

This chapter develops some axioms that express the fundamental features of the among relationship. It shows that although among is interdefinable with one of on one understanding of the one of ... 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


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


Computing Changes in Belief

Neil Tennant

in Changes of Mind: An Essay on Rational Belief Revision

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199655755
eISBN:
9780191742125
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199655755.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter introduces the basic ideas involved in our formal modeling of belief schemes as finite dependency networks. The chapter emphasizes the epistemological motivation for using each formal ... 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


What Would a Scientific Economics Look Like?

MICHAEL JOFFE

in Evidence, Inference and Enquiry

Published in print:
2011
Published Online:
January 2013
ISBN:
9780197264843
eISBN:
9780191754050
Item type:
chapter
Publisher:
British Academy
DOI:
10.5871/bacad/9780197264843.003.0016
Subject:
Sociology, Methodology and Statistics

This chapter compares biology with the practices of economics to determine the extent to which mainstream economic theory can be regarded as ‘scientific’. This survey of practice in the two ... More


Implementation of the Extension of the Truth Theory to Quantifiers

Ernest Lepore and Kirk Ludwig

in Donald Davidson's Truth-Theoretic Semantics

Published in print:
2007
Published Online:
May 2008
ISBN:
9780199290932
eISBN:
9780191710445
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199290932.003.0004
Subject:
Philosophy, Philosophy of Language

This chapter gives a small informal theory for a language fragment including quantifiers in illustration. The discussion in subsequent chapters takes place, then, in this new framework in which the ... More


The Tractatus

Michael Potter

in Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap

Published in print:
2002
Published Online:
May 2007
ISBN:
9780199252619
eISBN:
9780191712647
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199252619.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

Ludwig Wittgenstein studied with Russell in Cambridge from 1911 to 1913, and wrote the Tractatus while on active service in the Austrian army during the First World War. Large parts of the book are ... More


Ramsey

Michael Potter

in Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap

Published in print:
2002
Published Online:
May 2007
ISBN:
9780199252619
eISBN:
9780191712647
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199252619.003.0009
Subject:
Philosophy, Logic/Philosophy of Mathematics

Frank Ramsey was involved in preparing the English translation of the Tractatus as an undergraduate at Cambridge. He developed an account of the theory of types which avoided the difficulties ... 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


THE DUALITY OF CLASSICAL AND CONSTRUCTIVE NOTIONS AND PROOFS

Sara Negri and Jan Von Plato

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/9780198566519.003.0009
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

The method of converting mathematical axioms into rules of sequent calculus reveals a perfect duality between classical and constructive basic notions, such as equality and apartness, and between the ... More


ITERATED BOOLEAN EXTENSIONS, MARTIN'S AXIOM, AND SOUSLIN'S HYPOTHESIS

John L. Bell

in Set Theory: Boolean-Valued Models and Independence Proofs

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568520
eISBN:
9780191717581
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568520.003.0007
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

The technique of iterating Boolean extensions is introduced in this chapter and applied to prove the independence of Souslin’s hypothesis concerning the structure of densely ordered sets.


View: