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## 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

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