Science without numbers : a defence of nominalism / Hartry H. Field.

Format:

Book

Author/Creator:

Field, Hartry H., 1946- author.

Language:

English

Subjects (All):

Science--Philosophy.

Science.

Physical Description:

vi, 111 pages ; 23 cm

Edition:

Second edition.

Place of Publication:

Oxford ; New York, NY : Oxford University Press, 2016.

Summary:

Science Without Numbers caused a stir in philosophy on its original publication in 1980, with its bold nominalist approach to the ontology of mathematics and science. Hartry Field argues that we can explain the utility of mathematics without assuming it true. Part of the argument is that good mathematics has a special feature, "conservativeness", that allows it to be applied to "nominalistic" claims (roughly, those neutral to the existence of mathematical entities) in a way that generates nominalistic consequences more easily without generating any new ones. Field goes on to argue that we can axiomatize physical theories using nominalistic claims only, and that in fact this has advantages over the usual axiomatizations that are independent of nominalism. There has been much debate about the book since it first appeared. It is now reissued in a revised contains a substantial new preface giving the author's current views on the original book and the issues that were raised in the subsequent discussion of it. Book jacket.

Contents:

Preliminary Remarks 1

1 Why the Utility of Mathematical Entities is Unlike the Utility of Theoretical Entities 7

Appendix: On Conservativeness 17

2 First Illustration of Why Mathematical Entities are Useful-Arithmetic 22

3 Second Illustration of Why Mathematical Entities are Useful: Geometry and Distance 26

4 Nominalism and the Structure of Physical Space 31

5 My Strategy for Nominalizing Physics, and its Advantages 42

6 A Nominalistic Treatment of Newtonian Space-Time 47

7 A Nominalistic Treatment of Quantities, and a Preview of a Nominalistic Treatment of the Laws Involving Them 55

8 Newtonian Gravitational Theory Nominalized 61

A Continuity 61

B Products and Ratios 64

C Signed Products and Ratios 68

D Derivatives 70

E Second (and Higher) Derivatives 73

F Laplaceans 76

G Poisson's Equation 78

H Inner Products 81

I Gradients 84

J Differentiation of Vector Fields 85

K The Law of Motion 88

L General Remarks 89

9 Logic and Ontology 92.

ISBN:

0198777914

9780198777915

0198777922

9780198777922

OCLC:

963792531