Background
Field, Hartry Hamlin was born in 1946 in Boston, Massachusetts, United States.
(Science Without Numbers caused a stir in philosophy on it...)
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.
http://www.amazon.com/gp/product/0198777922/?tag=2022091-20
(Saving Truth from Paradox is an ambitious investigation i...)
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 G:odel incompleteness theorems. Hartry Field presents a new approach to the paradoxes and provides a systematic and detailed account of the main competing approaches. Part One examines Tarski's, Kripke's, and Lukasiewicz's theories of truth, and discusses validity and soundness, and vagueness. Part Two considers a wide range of attempts to resolve the paradoxes within classical logic. In Part Three Field turns to non-classical theories of truth that that restrict excluded middle. He shows that there are theories of this sort in which the conditionals obey many of the classical laws, and that all the semantic paradoxes (not just the simplest ones) can be handled consistently with the naive theory of truth. In Part Four, these theories are extended to the property-theoretic paradoxes and to various other paradoxes, and some issues about the understanding of the notion of validity are addressed. Extended paradoxes, involving the notion of determinate truth, are treated very thoroughly, and a number of different arguments that the theories lead to "revenge problems" are addressed. Finally, Part Five deals with dialetheic approaches to the paradoxes: approaches which, instead of restricting excluded middle, accept certain contradictions but alter classical logic so as to keep them confined to a relatively remote part of the language. Advocates of dialetheic theories have argued them to be better than theories that restrict excluded middle, for instance over issues related to the incompleteness theorems and in avoiding revenge problems. Field argues that dialetheists' claims on behalf of their theories are quite unfounded, and indeed that on some of these issues all current versions of dialetheism do substantially worse than the best theories that restrict excluded middle.
http://www.amazon.com/gp/product/0199230749/?tag=2022091-20
(Presenting a selection of thirteen essays on various topi...)
Presenting a selection of thirteen essays on various topics at the foundations of philosophy--one previously unpublished and eight accompanied by substantial new postscripts--this book offers outstanding insight on truth, meaning, and propositional attitudes; semantic indeterminacy and other kinds of "factual defectiveness;" and issues concerning objectivity, especially in mathematics and in epistemology. It will reward the attention of any philosopher interested in language, epistemology, or mathematics.
http://www.amazon.com/gp/product/0199242895/?tag=2022091-20
(This volume presents the work of a philosopher of mathema...)
This volume presents the work of a philosopher of mathematics, and combines central papers in that area with an essay on the philosophy of space and time. The overriding concern of most of the essays is with the development of a satisfactory fictionalist account of mathematics. Hartry Field develops and defends an original anti-Platonist philosophy of mathematics which suggests that mathematics need not be true, but instead must be "conservative" and dispensable in applications. In defending its dispensability, Field is led to reassess prevailing views about modality.
http://www.amazon.com/gp/product/0631163034/?tag=2022091-20
Field, Hartry Hamlin was born in 1946 in Boston, Massachusetts, United States.
University of Wisconsin and Harvard University.
1970-1976, Associate Professor of Philosophy, Princeton University. 1976-1981, Associate Professor of Philosophy, University of Southern California. Since 1981, Professor of Philosophy, University of Southern California.
(Presenting a selection of thirteen essays on various topi...)
(Saving Truth from Paradox is an ambitious investigation i...)
(Science Without Numbers caused a stir in philosophy on it...)
(This volume presents the work of a philosopher of mathema...)
Field argued that Tarski’s theory needed to be supplemented with a causal theory of what he called ‘primitive denotation’. Given his physicalism it was essential that there should be no irreducible semantic concepts any more than there should be any irreducible ‘mentalistic’ ones. Elsewhere he argued for a naturalistic account of intentional notions like ‘belief’, analysing them in terms of relations between the individual and sentences, where these might be concrete expressions of natural language or even expressions in a language of thought encoded in the brain.
Field also espouses what is called the ‘two-factor’ theory of meaning, according to which meaning is determined partly by links between mind and world, and partly by the structure and functioning of that mind, physicalistically construed.
For Field, the problem in mathematics is the prima facie indispensable reference to timeless entities like numbers, which also extends to physical theories. Field’s stategy is to undermine this apparent indispensability and show how mathematics can be applied without being true. Scientific theory itself, therefore, would need to be rewritten in nominalistic terms.
So on this account mathematics is a sort of fiction, justified insofar as it assists inferences from nominalistic premisses to nominalistic conclusions. There is a parallel here with instrumentalism about ‘unobservables’ posited in scientific theories. Fields work has stimulated a wide variety of responses: from John McDowell and Hilary Putnam on his revision of Tarski, to Robert Stalnaker’s criticism of the treatment of the belief relation.
His stance on mathematics has revived the whole Platonistf nominalist debate.