Jump to ContentJump to Main Navigation

You are looking at 1-20 of 29 items

  • Keywords: Russell’s paradox x
Clear All Modify Search

View:

Russell's Principles of Mathematics

Peter Hylton

in Russell, Idealism, and the Emergence of Analytic Philosophy

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240181
eISBN:
9780191597763
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019824018X.003.0007
Subject:
Philosophy, History of Philosophy

The focus of this chapter is on the book mentioned in its title. There, Russell combines the metaphysics of Platonic Atomism with the logic of relations, which he developed on the basis of Peano's ... More


The Logic of Principia Mathematica

Peter Hylton

in Russell, Idealism, and the Emergence of Analytic Philosophy

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240181
eISBN:
9780191597763
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019824018X.003.0010
Subject:
Philosophy, History of Philosophy

Here the concern is with the logic underlying Whitehead and Russell's Principia Mathematica and with the relation of that logic to Russell's underlying metaphysics. The author emphasizes the fact ... More


Introduction

Hartry Field

in Saving Truth From Paradox

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199230747
eISBN:
9780191710933
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230747.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This introductory chapter focuses on Grelling's heterologicality paradox and on Russell's paradox for properties, and surveys the possible strategies for solving them. It also considers objections to ... More


Russell, Idealism, and the Emergence of Analytic Philosophy

Peter Hylton

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240181
eISBN:
9780191597763
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/019824018X.001.0001
Subject:
Philosophy, History of Philosophy

In this book, the author seeks to shed light on the tradition of analytic philosophy by examining one important phase in its formation. This phase is Bertrand Russell's rejection of Absolute ... More


Frege on Extensions of Concepts, From 1884 to 1903 (1984)

TYLER BURGE

in Truth, Thought, Reason: Essays on Frege

Published in print:
2005
Published Online:
May 2010
ISBN:
9780199278534
eISBN:
9780191706943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199278534.003.0008
Subject:
Philosophy, History of Philosophy, Philosophy of Language

This chapter traces historically Frege's uncertainty about how to complete his logicist project by invoking extensions of concepts. The uncertainty is placed in the context of his view that experts ... More


Frege's Account of Classes

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/9780199252619.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

In the Grundlagen, Frege sketched a proof of the basic properties of natural numbers from the numerical equivalence and showed how that equivalence could be proved if numbers were explicitly defined ... More


Temporal Dynamics in Categorization

Michael Spivey

in The Continuity of Mind

Published in print:
2006
Published Online:
September 2007
ISBN:
9780195170788
eISBN:
9780199786831
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195170788.003.0006
Subject:
Psychology, Cognitive Neuroscience

This chapter identifies weaknesses in formal logical approaches to categorization by discussing Russell's Paradox with set theory and the Sorites Paradox, and by tracking the continuous temporal ... 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


Finding a problem

Michael Potter

in Wittgenstein's Notes on Logic

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199215836
eISBN:
9780191721243
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199215836.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter addresses the question of what led Wittgenstein to study philosophy with Russell in Cambridge. Since the narrative of Wittgenstein's life before 1911 is well summarized in available ... More


Meaning and Reference

Wayne A. Davis

in Nondescriptive Meaning and Reference: An Ideational Semantics

Published in print:
2005
Published Online:
February 2006
ISBN:
9780199261659
eISBN:
9780191603099
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199261652.003.0009
Subject:
Philosophy, Philosophy of Language

This chapter focuses on word reference, and shows that the meaning of an expression cannot be identified with its reference to things in the world, rather than its expression of ideas in the mind. It ... More


Collections

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/9780199269730.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter focuses on several different concepts sheltering under one umbrella, and the chapter presses several of these words — set, class, extension, collection — into technical service to ... More


A Puzzle about Time and Thought

Saul A. Kripke

in Philosophical Troubles: Collected Papers, Volume 1

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199730155
eISBN:
9780199918430
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199730155.003.0013
Subject:
Philosophy, General

This chapter analyzes a problem involving time and thought. The problem, quite similar to Russell's paradox, is clear. But in contrast to Russell's paradox, there is nothing in it incompatible with ... More


Core Logic and the Paradoxes

Neil Tennant

in Core Logic

Published in print:
2017
Published Online:
October 2017
ISBN:
9780198777892
eISBN:
9780191823367
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198777892.003.0011
Subject:
Philosophy, Logic/Philosophy of Mathematics

The Law of Excluded Middle is not to be blamed for any of the logico-semantic paradoxes. We explain and defend our proof-theoretic criterion of paradoxicality, according to which the ‘proofs’ of ... More


Paradoxes of Definability, Russell’s Paradox, the Liar

Keith Simmons

in Semantic Singularities: Paradoxes of Reference, Predication, and Truth

Published in print:
2018
Published Online:
July 2018
ISBN:
9780198791546
eISBN:
9780191852923
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791546.003.0005
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

Chapter 5 moves beyond the simple paradoxes discussed in Chapters 2-4. The chapter applies the singularity approach to the traditional paradoxes of definability (or denotation), associated with ... More


The Limits of Representation

José L. Zalabardo

in Representation and Reality in Wittgenstein's Tractatus

Published in print:
2015
Published Online:
August 2015
ISBN:
9780198743941
eISBN:
9780191803949
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198743941.003.0006
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

Wittgenstein’s account of propositional representation imposes limits on what propositions can represent. This chapter explores Wittgenstein’s applications of this result. It considers first ... More


Semantic Singularities: Paradoxes of Reference, Predication, and Truth

Keith Simmons

Published in print:
2018
Published Online:
July 2018
ISBN:
9780198791546
eISBN:
9780191852923
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791546.001.0001
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by the concepts of reference or denotation, predicate extension, and truth. ... More


Whittle’s assault on Cantor’s paradise

Vann McGee

in Oxford Studies in Metaphysics, Volume 9

Published in print:
2015
Published Online:
April 2015
ISBN:
9780198729242
eISBN:
9780191796258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198729242.003.0002
Subject:
Philosophy, Metaphysics/Epistemology

This chapter presents a response to Chapter 1. The arguments put forward in that chapter attempted to drive us from the paradise created by Cantor’s theory of infinite number. The principal complaint ... More


Frege’s Little Theorem and Frege’s Way Out

Roy T. Cook

in Essays on Frege's Basic Laws of Arithmetic

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198712084
eISBN:
9780191780240
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198712084.003.0015
Subject:
Philosophy, Logic/Philosophy of Mathematics

Shortly before the second volume of Basic Laws went to press, Frege appended an Afterword, analyzing the Russell paradox and suggesting an alternate formulation of basic law V. This attempted ‘way ... More


The Myth of the Seven

Stephen Yablo

in Things: Papers on Objects, Events, and Properties

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199266487
eISBN:
9780191594274
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199266487.003.0010
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

Mathematics has been called the one area of inquiry that would retain its point even were the physical world to entirely disappear. This might be heard as an argument for Platonism except that ... More


Russell Reductio Redux

J. P. Studd

in Everything, more or less: A defence of generality relativism

Published in print:
2019
Published Online:
May 2019
ISBN:
9780198719649
eISBN:
9780191788734
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198719649.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

By far and away the strongest argument against there being an absolutely comprehensive domain of quantification comes from the set-theoretic paradoxes. The argument from indefinite extensibility can ... More


View: