Science Without Numbers: The Defence of Nominalism (Princeton Legacy Library, 1898)

The description for this book, Science Without Numbers: The Defence of Nominalism, will be forthcoming. According to the doctrine of nominalism, abstract entitiessuch as numbers, functions, and setsdo not exist. The problem this normally poses for a description of the physical world is as any such description must include a physical theory, physical theories are assumed to require mathematics, and mathematics is replete with references to abstract entities. How, then, can nominalism reasonably be maintained? In answer, Hartry Field shows how abstract entities ultimately are dispensable in describing the physical world and that, indeed, we can "do science without numbers." The author also argues that despite the ultimate dispensability of mathematical entities, mathematics remains useful, and that its usefulness can be explained by the nominalist. The explanation of the utility of mathematics does not presuppose that mathematics is true, but only that it is consistent. The argument that the nominalist can freely use mathematics in certain contexts without assuming it to be true appears early on, and it first seems to license only a quite limited use of mathematics. But when combined with the later argument that abstract entities ultimately are dispensable in physical theories, the conclusion emerges that even the most sophisticated applications of mathematics depend only on the assumption that mathematics is consistent and not on the assumption that it is true. Originally published in 2050. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. 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 Contents Preface Preliminary Remarks Why the Utility of Mathematical Entities is Unlike the Utility of Theoretical Entities On Conservativeness First Illustration of Why Mathematical Entities are Useful: Arithmetic Second Illustration of Why Mathematical Entities are Useful: Geometry and Distance Nominalism and the Structure of Physical Space My Strategy for Nominalizing Physics, and its Advantages A Nominalistic Treatment of Newtonian Space-Time A Nominalistic Treatment of Quantities, and a Preview of a Nominalistic Treatment of the Laws involving them Newtonian Gravitational Theory Nominalized Continuity Products and Ratios Signed Products and Ratios Derivatives Second (and Higher) Derivatives Laplaceans Poisson’s Equation Inner Products Gradients Differentiation of Vector Fields The Law of Motion General Remarks Logic and Ontology Notes Index The book description for'Science Without Numbers'is currently unavailable.