Mathematics and metaphilosophy Justin Clarke-Doane

Format:

Book

Author/Creator:

Clarke-Doane, Justin, author.

Series:

Cambridge elements. Elements in the philosophy of mathematics

Cambridge elements : elements in the philosophy of mathematics

Language:

English

Subjects (All):

Mathematics--Philosophy.

Mathematics.

Pluralism.

Realism.

Objectivism (Philosophy).

pluralism.

Physical Description:

1 online resource

Place of Publication:

Cambridge, United Kingdom New York, NY Cambridge University Press 2022

Summary:

This Element discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs ('the justificatory challenge'), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the challenge to explain their reliability ('the reliability challenge'), arises to the extent that we could have easily had different beliefs. The Element shows that mathematical facts are not, in general, empirically accessible, contra Quine, and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is unmysterious. The Element concludes with a complementary 'pluralism' about modality, logic and normative theory, highlighting its surprising implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap's pragmatism, transposed to the key of realism

Contents:

Cover

Title page

Copyright page

Mathematics and Metaphilosophy

Contents

Introduction

1 Self-evidence, Analyticity, and Intuition

1.1 Two Kinds of Axiom

1.2 Self-evidence

1.3 Analyticity

1.4 Reflective Equilibrium

1.5 Conclusion

2 Observation and Indispensability

2.1 The Web of Belief

2.2 Nominalistic Science

2.3 The Problem of Metalogic

2.4 Conclusion

3 Connection, Contingency, and Pluralism

3.1 Clarifying the Challenge

3.2 Connection

3.3 Counterfactual Dependence

3.4 Contingency

3.5 Mathematical Pluralism

4 Modality, Logic, and Normativity

4.1 Generalizing

4.2 Modal Pluralism

4.3 Logical Pluralism

4.4 Indefinite Extensibility and Perspectivalism

4.5 Realist Carnapianism

Conclusions

References

Acknowledgments

Notes:

Includes bibliographical references

Description based on online resource; title from digital title page (viewed on June 23, 2022)

ISBN:

9781108995405

1108995403

9781108993937

1108993931

OCLC:

1331792967

Access Restriction:

Restricted for use by site license