Book

Mathematics as a Science of Patterns

Michael D. Resnik

Published in print December 1999 | ISBN: 9780198250142
Published online November 2003 | e-ISBN: 9780191598296 | DOI: https://dx.doi.org/10.1093/0198250142.001.0001
Mathematics as a Science of Patterns

Results | All related links for this item | 1-12 of 12 results for: Return to index card »


Refine by type

Refine by product

 

The Case for Mathematical Realism

Michael D. Resnik.

in Mathematics as a Science of Patterns

December 1999; p ublished online November 2003 .

Chapter. Subjects: Philosophy of Mathematics and Logic. 3970 words.

The application of mathematics to science and the enormous success that derives from it is, perhaps, the strongest evidence in favour of mathematical realism. Quine and Putnam have taken...

Go to Oxford Scholarship Online »  abstract

Doubts About Realism

Michael D. Resnik.

in Mathematics as a Science of Patterns

December 1999; p ublished online November 2003 .

Chapter. Subjects: Philosophy of Mathematics and Logic. 5790 words.

One of the strongest motivations for being an anti‐realist with regard to mathematics is the difficulty in formulating a plausible realist epistemology, given that there seems to be a lack...

Go to Oxford Scholarship Online »  abstract

The Elusive Distinction Between Mathematics and Natural Science

Michael D. Resnik.

in Mathematics as a Science of Patterns

December 1999; p ublished online November 2003 .

Chapter. Subjects: Philosophy of Mathematics and Logic. 4175 words.

It is commonly believed that the epistemology of mathematics must be different from the epistemology of science because their objects are different in kind, i.e. metaphysically different....

Go to Oxford Scholarship Online »  abstract

Holism: Evidence in Science and Mathematics

Michael D. Resnik.

in Mathematics as a Science of Patterns

December 1999; p ublished online November 2003 .

Chapter. Subjects: Philosophy of Mathematics and Logic. 10115 words.

I present a theory of justification for mathematical beliefs that is both non‐foundationalist, in that it claims that some mathematics must be justified indirectly in terms of its...

Go to Oxford Scholarship Online »  abstract

Introduction

Michael D. Resnik.

in Mathematics as a Science of Patterns

December 1999; p ublished online November 2003 .

Chapter. Subjects: Philosophy of Mathematics and Logic. 2530 words.

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...

Go to Oxford Scholarship Online »  abstract

The Local Conception of Mathematical Evidence: Proof, Computation, and Logic

Michael D. Resnik.

in Mathematics as a Science of Patterns

December 1999; p ublished online November 2003 .

Chapter. Subjects: Philosophy of Mathematics and Logic. 14811 words.

The fact that mathematics is ordinarily practised as an autonomous science with its own, peculiar type of evidence constituted mainly by deductive reasoning (proofs and computations) is...

Go to Oxford Scholarship Online »  abstract

Mathematical Objects as Positions in Patterns

Michael D. Resnik.

in Mathematics as a Science of Patterns

December 1999; p ublished online November 2003 .

Chapter. Subjects: Philosophy of Mathematics and Logic. 9031 words.

It is usual to regard mathematical objects as entities that can be identified, characterized, and known in isolation. In this chapter, I propose a contrasting view according to which...

Go to Oxford Scholarship Online »  abstract

Patterns and Mathematical Knowledge

Michael D. Resnik.

in Mathematics as a Science of Patterns

December 1999; p ublished online November 2003 .

Chapter. Subjects: Philosophy of Mathematics and Logic. 7162 words.

I present a hypothetical account of how the ancients might have come to introduce mathematical objects in order to describe patterns, and I explain how working with patterns can generate...

Go to Oxford Scholarship Online »  abstract

Positing Mathematical Objects

Michael D. Resnik.

in Mathematics as a Science of Patterns

December 1999; p ublished online November 2003 .

Chapter. Subjects: Philosophy of Mathematics and Logic. 8596 words.

If, as I grant, mathematical objects are abstract entities existing outside of space and time, and if the idea of supernaturally grasping abstract entities is scientifically unacceptable,...

Go to Oxford Scholarship Online »  abstract

Recent Attempts at Blunting the Indispensability Thesis

Michael D. Resnik.

in Mathematics as a Science of Patterns

December 1999; p ublished online November 2003 .

Chapter. Subjects: Philosophy of Mathematics and Logic. 11648 words.

The indispensability thesis maintains both that using mathematical terms and assertions is an indispensable part of scientific practice and that this practice commits science to...

Go to Oxford Scholarship Online »  abstract

What Is Mathematical Realism?

Michael D. Resnik.

in Mathematics as a Science of Patterns

December 1999; p ublished online November 2003 .

Chapter. Subjects: Philosophy of Mathematics and Logic. 12196 words.

Talk of truth plays a major role in formulating realism, to the point that realist theories are often criticized by attacking the correspondence theory of truth that they are presumed to...

Go to Oxford Scholarship Online »  abstract

What Is Structuralism? and Other Questions

Michael D. Resnik.

in Mathematics as a Science of Patterns

December 1999; p ublished online November 2003 .

Chapter. Subjects: Philosophy of Mathematics and Logic. 12051 words.

I explore the relation between structuralism and other theses that I have presented in the rest of the book, in particular, my holism, realism about mathematical objects, and the...

Go to Oxford Scholarship Online »  abstract