Author(s): Hartry H. Field
Year: 1980
Language: English
Pages: 136
Contents......Page 1
Preface......Page 2
Preliminary Remarks......Page 9
1 Why the Utility of Mathematical Entities is Unlike the Utility of Theoretical Entities......Page 15
Appendix: On Conservativeness......Page 24
2 First Illustration of Why Mathematical Entities are Useful: Arithmetic......Page 28
3 Second Illustration of Why Mathematical Entities are Useful: Geometry and Distance......Page 32
4 Nominalism and the Structure of Physical Space......Page 38
5 My Strategy for Nominalizing Physics, and its Advantages......Page 49
6 A Nominalistic Treatment of Newtonian Space-Time......Page 55
7 A Nominalistic Treatment of Quantities, and a Preview of a Nominalistic Treatment of the Laws involving them......Page 63
A. Continuity......Page 67
B. Products and Ratios......Page 70
C. Signed Products and Ratios......Page 74
D. Derivatives......Page 76
E. Second (and Higher) Derivatives......Page 80
F. Laplaceans......Page 82
G. Poisson's Equation......Page 84
H. Inner Products......Page 87
I. Gradients......Page 90
J. Differentiation of Vector Fields......Page 91
K. The Law of Motion......Page 94
L. General Remarks......Page 95
9 Logic and Ontology......Page 98
Notes......Page 113
Index......Page 134
