Jump to ContentJump to Main Navigation

You are looking at 1-18 of 18 items

  • Keywords: mathematical truth x
Clear All Modify Search

View:

Theist solutions

Brian Leftow

in God and Necessity

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199263356
eISBN:
9780191741777
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199263356.003.0004
Subject:
Philosophy, Philosophy of Religion, Metaphysics/Epistemology

The chapter first displays how Descartes and Leibniz offered contrasting theist approaches to the conflicts — Leibniz’ being in a broad sense Platonic. Theists, it argues, should hold that necessary ... 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


Disagreement and the A Priori

Ralph Wedgwood

in The Nature of Normativity

Published in print:
2007
Published Online:
May 2008
ISBN:
9780199251315
eISBN:
9780191719127
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199251315.003.0012
Subject:
Philosophy, Moral Philosophy

This chapter traces out some implications of this epistemological account. First, it is explained how the account developed in Chapter 10 implies that under favourable conditions, normative truths ... More


On what Possible Worlds could not be (1996)

Robert C. Stalnaker

in Ways a World Might Be: Metaphysical and Anti-Metaphysical Essays

Published in print:
2003
Published Online:
April 2005
ISBN:
9780199251483
eISBN:
9780191602320
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199251487.003.0003
Subject:
Philosophy, Metaphysics/Epistemology

This paper explores the analogy between mathematical Platonism and modal realism, and between Benacerraf’s dilemma and the epistemological objection. It is argued that the parallels and contrasts may ... More


Introduction

Michael D. Resnik

in Mathematics as a Science of Patterns

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198250142
eISBN:
9780191598296
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198250142.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Mathematics has often been described as the ‘Queen of Sciences’, yet philosophical problems arise as soon as one tries to define its subject matter. Anti‐realism concerning mathematical objects has ... More


Arealism

Penelope Maddy

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

Published in print:
2011
Published Online:
May 2011
ISBN:
9780199596188
eISBN:
9780191725395
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199596188.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter returns to the juncture in Chapter II where it was assumed, temporarily, that the historical and continuing inter-relations of pure mathematics with natural science are enough to warrant ... More


Morals

Penelope Maddy

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

Published in print:
2011
Published Online:
May 2011
ISBN:
9780199596188
eISBN:
9780191725395
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199596188.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This concluding chapter draws a pair of morals. First, what's gone before shows that there's a form of objectivity in mathematics that doesn't depend on the existence of mathematical objects or the ... More


Forms of Correspondence: The Intricate Route from Thought to Reality

Gila Sher

in Truth and Pluralism: Current Debates

Published in print:
2013
Published Online:
May 2013
ISBN:
9780195387469
eISBN:
9780199332427
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195387469.003.0008
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Language

The chapter delineates a new approach to truth that falls under the category of ’pluralism within the bounds of correspondence’ and illustrates it with respect to mathematical truth. Mathematical ... More


Possible Worlds Semantics

Charles S. Chihara

in The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic

Published in print:
2001
Published Online:
October 2011
ISBN:
9780199246557
eISBN:
9780191697609
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199246557.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter discusses the philosophical theories and presuppositions of applying possible worlds semantics in order to draw conclusions about matters involving what are called conceptual or broadly ... More


Rationalism Regained 1: The Benacerraf Dilemmas

Robert Hanna

in Cognition, Content, and the A Priori: A Study in the Philosophy of Mind and Knowledge

Published in print:
2015
Published Online:
November 2015
ISBN:
9780198716297
eISBN:
9780191785009
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198716297.003.0006
Subject:
Philosophy, Metaphysics/Epistemology

Chapter 6 re-presents the famous Benacerraf Dilemma, now extended from its original version in the context of mathematical truth and knowledge, to logical truth and knowledge, and then generalized to ... More


Afterword to Part II

Blake D. Dutton

in Augustine and Academic Skepticism: A Philosophical Study

Published in print:
2016
Published Online:
August 2016
ISBN:
9780801452932
eISBN:
9781501703553
Item type:
chapter
Publisher:
Cornell University Press
DOI:
10.7591/cornell/9780801452932.003.0014
Subject:
Classical Studies, Ancient Greek, Roman, and Early Christian Philosophy

This afterword summarizes the main points of Augustine of Hippo's strategy for vindicating the possibility of knowledge against the Academics' denial of that possibility. Augustine puts forward a ... More


A Fundamental Crisis

Giuseppe Primiero

in On the Foundations of Computing

Published in print:
2019
Published Online:
July 2020
ISBN:
9780198835646
eISBN:
9780191873232
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198835646.003.0002
Subject:
Mathematics, Computational Mathematics / Optimization, Logic / Computer Science / Mathematical Philosophy

This chapter reconstructs the historical background of the mathematical foundation of modern computing. At the beginning of the twentieth century,mathematical correctness and truth were under ... More


Platonism and the Apprehensible Truths of Philosophy

Blake D. Dutton

in Augustine and Academic Skepticism: A Philosophical Study

Published in print:
2016
Published Online:
August 2016
ISBN:
9780801452932
eISBN:
9781501703553
Item type:
chapter
Publisher:
Cornell University Press
DOI:
10.7591/cornell/9780801452932.003.0011
Subject:
Classical Studies, Ancient Greek, Roman, and Early Christian Philosophy

This chapter examines how Platonism figures in Augustine of Hippo's views on the apprehensible truths of philosophy. It first considers a passage from the monologue of Against the Academics in which ... More


Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism

Jared Warren

Published in print:
2020
Published Online:
December 2020
ISBN:
9780190086152
eISBN:
9780190086183
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190086152.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

What is the source of logical and mathematical truth? This volume revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source ... More


What Is Conventionalism?

Jared Warren

in Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism

Published in print:
2020
Published Online:
December 2020
ISBN:
9780190086152
eISBN:
9780190086183
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190086152.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter begins by briefly discussing the historical fortunes of conventionalism in logic and mathematics. After this, it clarifies the nature of conventionalism; critically discussing various ... More


Mathematical Determinacy

Jared Warren

in Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism

Published in print:
2020
Published Online:
December 2020
ISBN:
9780190086152
eISBN:
9780190086183
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190086152.003.0010
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter addresses the second major challenge for the extension of conventionalism from logic to mathematics: the richness of mathematical truth. The chapter begins by distinguishing ... More


Second Illustration of Why Mathematical Entities are Useful: Geometry and Distance

Hartry Field

in Science without Numbers

Published in print:
2016
Published Online:
December 2016
ISBN:
9780198777915
eISBN:
9780191823381
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198777915.003.0003
Subject:
Philosophy, Philosophy of Science, Logic/Philosophy of Mathematics

Shows that the use of real numbers in geometry can be accounted for by the conservativeness of mathematics, without assuming the truth of the theory of real numbers. Focuses on Hilbert’s ... More


First Illustration of Why Mathematical Entities are Useful: Arithmetic

Hartry Field

in Science without Numbers

Published in print:
2016
Published Online:
December 2016
ISBN:
9780198777915
eISBN:
9780191823381
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198777915.003.0002
Subject:
Philosophy, Philosophy of Science, Logic/Philosophy of Mathematics

Provides an elementary illustration of the kind of application of mathematics that can be accounted for by the conservativeness of mathematics alone, without invoking the assumption that the ... More


View: