Description
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
Table of Contents
1: Why the Utility of Mathematical Entities is Unlike the Utility of Theoretical Entities Appendix: On Conservativeness 2: First Illustration of Why Mathematical Entities are Useful: Arithmetic 3: Second Illustration of Why Mathematical Entities are Useful: Geometry and Distance 4: Nominalism and the Structure of Physical Space 5: My Strategy for Nominalizing Physics, and its Advantages 6: A Nominalistic Treatment of Newtonian Space-Time 7: A Nominalistic Treatment of Quantities, and a Preview of a Nominalistic Treatment of the Laws Involving them 8: Newtonian Gravitational Theory Nominalized 9: Logic and Ontology
