Jump to ContentJump to Main Navigation

You are looking at 1-12 of 12 items

  • Keywords: foundations of mathematics x
Clear All Modify Search

View:

Pure Mathematics

E. Brian Davies

in Science in the Looking Glass: What Do Scientists Really Know?

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199219186
eISBN:
9780191711695
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219186.003.0005
Subject:
Physics, History of Physics

This chapter seeks to demolish the myth that mathematics is uniquely free of controversy, and therefore a guaranteed source of objective and eternal knowledge. Topics discussed include the origins of ... More


Tolerance and Analyticity in Carnap's Philosophy of Mathematics

Michael Friedman

in Future Pasts: The Analytic Tradition in Twentieth Century Philosophy

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195139167
eISBN:
9780199833214
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019513916X.003.0011
Subject:
Philosophy, History of Philosophy

This essay is an interpretation of Carnap’s principle of tolerance in his 1934 Logical Syntax of Language, as expressed in his philosophy of mathematics. Friedman argues that Carnap’s deepest ... More


Frege on Knowing the Third Realm (1992)

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/9780199278534.003.0009
Subject:
Philosophy, History of Philosophy, Philosophy of Language

Frege regarded the foundations of mathematics as self-evident. He maintained that reason could enable one to know of the existence and nature of both mind-independent abstract objects, such as the ... More


Wittgenstein and Intuitionism

Robert J. Fogelin

in Philosophical Interpretations

Published in print:
1992
Published Online:
November 2003
ISBN:
9780195071627
eISBN:
9780199833221
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019507162X.003.0015
Subject:
Philosophy, General

This essay explores one important strain that runs through Wittgenstein's Remarks on the Foundations of Mathematics: his commitment to themes characteristic of the intuitionist movement in logic and ... 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


Mathematics Based on Fuzzy Logic

Radim Bělohlávek, Joseph W. Dauben, and George J. Klir

in Fuzzy Logic and Mathematics: A Historical Perspective

Published in print:
2017
Published Online:
June 2017
ISBN:
9780190200015
eISBN:
9780190200039
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190200015.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics, General

Mathematical reasoning is governed by the laws of classical logic, based on the principle of bivalence. With the acceptance of intermediate truth degrees, the situation changed substantially. This ... More


Parameterisation

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/9780199254057.003.0011
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter examines the relevance of mathematician Frank Ramsey's essay The Foundations of Mathematics to the contradictions in the limits of thought. Ramsey has provided the most acute early ... More


Unfolding FOLDS: A Foundational Framework for Abstract Mathematical Concepts

Jean-Pierre Marquis

in Categories for the Working Philosopher

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198748991
eISBN:
9780191811593
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198748991.003.0008
Subject:
Philosophy, History of Philosophy

FOLDS, first-order logic with dependent sorts, has been introduced by the logician Michael Makkai as a foundational framework to capture the abstract nature of contemporary mathematical concepts. In ... More


The Logical Must: Wittgenstein on Logic

Penelope Maddy

Published in print:
2014
Published Online:
August 2014
ISBN:
9780199391752
eISBN:
9780199391776
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199391752.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics, General

This book is an examination of Wittgenstein’s philosophy of logic, early and late, undertaken from an austere naturalistic perspective called ‘‘Second Philosophy’’. On a generally metaphysical ... More


Turing, Wittgenstein, and Emergence

Juliet Floyd

in Philosophy of Emerging Media: Understanding, Appreciation, Application

Published in print:
2015
Published Online:
March 2016
ISBN:
9780190260743
eISBN:
9780190277772
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780190260743.003.0014
Subject:
Philosophy, Philosophy of Language

Emerging media are a product of the digital world that Alan Turing fathered. In 1936 Turing transformed the ancient notion of algorithm—by the 1920s central to mathematical logic—into the idea of a ... More


The mathematical practice of definitions by abstraction from Euclid to Frege (and beyond)

Paolo Mancosu

in Abstraction and Infinity

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198746829
eISBN:
9780191809095
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198746829.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics, History of Philosophy

The first chapter is devoted to showing that, contrary to what Frege intimates in the Grundlagender Arithmetik, abstraction principles were quite widespread in the mathematical practice that preceded ... More


Rule-Following and Logic

Penelope Maddy

in The Logical Must: Wittgenstein on Logic

Published in print:
2014
Published Online:
August 2014
ISBN:
9780199391752
eISBN:
9780199391776
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199391752.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics, General

Like the Second Philosopher, the later Wittgenstein also rejects the priority of sense. In Philosophical Investigations and Remarks on the Foundations of Mathematics, the famous rule-following ... More


View: