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.
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