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The Case for Mathematical Realism

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...

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Doubts About Realism

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...

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The Elusive Distinction Between Mathematics and Natural Science

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....

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Holism: Evidence in Science and Mathematics

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...

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Introduction

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...

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

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...

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Mathematical Objects as Positions in Patterns

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...

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Patterns and Mathematical Knowledge

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...

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Positing Mathematical Objects

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,...

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Recent Attempts at Blunting the Indispensability Thesis

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...

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What Is Mathematical Realism?

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...

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What Is Structuralism? and Other Questions

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...