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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.
Saving Truth from Paradox is an ambitious investigation into
paradoxes of truth and related issues, with occasional forays into
notions such as vagueness, the nature of validity, and the Godel
incompleteness theorems. Hartry Field presents a new approach to
the paradoxes and provides a systematic and detailed account of the
main competing approaches.
Hartry Field presents a selection of thirteen of his most important essays on a set of related topics at the foundations of philosophy; one essay is previously unpublished, and eight are accompanied by substantial new postscripts. Five of the essays are primarily about truth, meaning, and propositional attitudes, five are primarily about semantic indeterminacy and other kinds of 'factual defectiveness' in our discourse, and three are primarily about issues concerning objectivity, especially in mathematics and in epistemology. This influential work by a key figure in contemporary philosophy will reward the attention of any philosopher interested in language, epistemology, or mathematics.
Hartry Field presents a selection of thirteen of his most important essays on a set of related topics at the foundations of philosophy; one essay is previously unpublished, and eight are accompanied by substantial new postscripts. Five of the essays are primarily about truth, meaning, and propositional attitudes, five are primarily about semantic indeterminacy and other kinds of 'factual defectiveness' in our discourse, and three are primarily about issues concerning objectivity, especially in mathematics and in epistemology. This influential work by a key figure in contemporary philosophy will reward the attention of any philosopher interested in language, epistemology, or mathematics.
Saving Truth from Paradox is an ambitious investigation into
paradoxes of truth and related issues, with occasional forays into
notions such as vagueness, the nature of validity, and the Godel
incompleteness theorems. Hartry Field presents a new approach to
the paradoxes and provides a systematic and detailed account of the
main competing approaches.
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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