Works by Hartry Field
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- Science Without Numbers: A Defence of Nominalism.Hartry H. Field -1980 - Princeton, NJ, USA: Princeton University Press.Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.
- Realism, Mathematics & Modality.Hartry H. Field -1989 - New York, NY, USA: Blackwell.
- Saving truth from paradox.Hartry Field -2008 - New York: Oxford University Press.A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism.
- Realism, Mathematics, and Modality.Hartry Field -1988 -Philosophical Topics 16 (1):57-107.
- Tarski's Theory of Truth.Hartry Field -1972 -Journal of Philosophy 69 (13):347.
- Mental representation.Hartry Field -1978 -Erkenntnis 13 (July):9-61.
- Truth and the absence of fact.Hartry H. Field -2001 - New York: Oxford University Press.Presenting a selection of thirteen essays on various topics at the foundations of philosophy--one previously unpublished and eight accompanied by substantial new postscripts--this book offers outstanding insight on truth, meaning, and propositional attitudes; semantic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.
- (1 other version)Deflationist views of meaning and content.Hartry Field -1994 -Mind 103 (411):249-285.
- Theory change and the indeterminacy of reference.Hartry Field -1973 -Journal of Philosophy 70 (14):462-481.
- Logic, Meaning, and Conceptual Role.Hartry H. Field -1977 -Journal of Philosophy 74 (7):378-409.
- What is the Normative Role of Logic?Hartry Field -2009 -Aristotelian Society Supplementary Volume 83 (1):251-268.The paper tries to spell out a connection between deductive logic and rationality, against Harman's arguments that there is no such connection, and also against the thought that any such connection would preclude rational change in logic. One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form); but the paper points out a serious obstacle to any such (...) view. (shrink)
- What Is Logical Validity.Hartry Field -2015 - In Colin R. Caret & Ole T. Hjortland,Foundations of Logical Consequence. Oxford, England: Oxford University Press.What are people who disagree about logic disagreeing about? The paper argues that (in a wide range of cases) they are primarily disagreeing about how to regulate their degrees of belief. An analogy is drawn between beliefs about validity and beliefs about chance: both sorts of belief serve primarily to regulate degrees of belief about other matters, but in both cases the concepts have a kind of objectivity nonetheless.
- Science without numbers, A Defence of Nominalism.Hartry Field -1980 -Revue Philosophique de la France Et de l'Etranger 171 (4):502-503.
- Epistemology without metaphysics.Hartry Field -2009 -Philosophical Studies 143 (2):249 - 290.The paper outlines a view of normativity that combines elements of relativism and expressivism, and applies it to normative concepts in epistemology. The result is a kind of epistemological anti-realism, which denies that epistemic norms can be (in any straightforward sense) correct or incorrect; it does allow some to be better than others, but takes this to be goal-relative and is skeptical of the existence of best norms. It discusses the circularity that arises from the fact that we need to (...) use epistemic norms to gather the facts with which to evaluate epistemic norms; relatedly, it discusses how epistemic norms can rationally evolve. It concludes with some discussion of the impact of this view on "ground level" epistemology. (shrink)
- Pluralism in logic.Hartry Field -2009 -Review of Symbolic Logic 2 (2):342-359.There are quite a few theses about logic that are in one way or another pluralist: they hold (i) that there is no uniquely correct logic, and (ii) that because of this, some or all debates about logic are illusory, or need to be somehow reconceived as not straightforwardly factual. Pluralist theses differ markedly over the reasons offered for there being no uniquely correct logic. Some such theses are more interesting than others, because they more radically affect how we are (...) initially inclined to understand debates about logic. Can one find a pluralist thesis that is high on the interest scale, and also true? (shrink)
- Truth and the Absence of Fact.Hartry Field -2001 -Tijdschrift Voor Filosofie 64 (4):806-807.No categories
- The Deflationary Conception of Truth.Hartry Field -1986 - In Graham Macdonald & Crispin Wright,Fact, Science and Morality: Essays on A. J. Ayer's Language, Truth and Logic. Blackwell. pp. 55-117.
- A note on Jeffrey conditionalization.Hartry Field -1978 -Philosophy of Science 45 (3):361-367.Bayesian decision theory can be viewed as the core of psychological theory for idealized agents. To get a complete psychological theory for such agents, you have to supplement it with input and output laws. On a Bayesian theory that employs strict conditionalization, the input laws are easy to give. On a Bayesian theory that employs Jeffrey conditionalization, there appears to be a considerable problem with giving the input laws. However, Jeffrey conditionalization can be reformulated so that the problem disappears, and (...) in fact the reformulated version is more natural and easier to work with on independent grounds. (shrink)
- A priority as an evaluative notion.Hartry Field -2000 - In Paul Artin Boghossian & Christopher Peacocke,New Essays on the A Priori. Oxford, GB: Oxford University Press.
- (1 other version)The power of naive truth.Hartry Field -2022 -Review of Symbolic Logic 15 (1):225-258.Nonclassical theories of truth that take truth to be transparent have some obvious advantages over any classical theory of truth. But several authors have recently argued that there’s also a big disadvantage of nonclassical theories as compared to their “external” classical counterparts: proof-theoretic strength. While conceding the relevance of this, the paper argues that there is a natural way to beef up extant internal theories so as to remove their proof-theoretic disadvantage. It is suggested that the resulting internal theories are (...) preferable to their external counterparts. (shrink)
- Causation in a physical world.Hartry Field -2003 - In Michael J. Loux & Dean W. Zimmerman,The Oxford handbook of metaphysics. New York: Oxford University Press. pp. 435-460.1. Of what use is the concept of causation? Bertrand Russell [1912-13] argued that it is not useful: it is “a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.” His argument for this was that the kind of physical theories that we have come to regard as fundamental leave no place for the notion of causation: not only does the word ‘cause’ not appear in the advanced sciences, but the (...) laws that these sciences state are incompatible with causation as we normally understand it. But Nancy Cartwright has argued [1979] that abandoning the concept of causation would cripple science; her conclusion was based not on fundamental physics, but on more ordinary science such as the search for the causes of cancer. She argues that Russell was right that the fundamental theories of modern physics say nothing, even implicitly, about causation, and concludes on this basis that such theories are incomplete. It is with this cluster of issues that I will begin my discussion. (shrink)
- (1 other version)Recent Debates about the A Priori.Hartry Field -2005 - In Tamar Szabo Gendler & John Hawthorne,Oxford Studies in Epistemology Volume 1. Oxford University Press UK.
- No fact of the matter.Hartry Field -2003 -Australasian Journal of Philosophy 81 (4):457 – 480.Are there questions for which 'there is no determinate fact of the matter' as to which answer is correct? Most of us think so, but there are serious difficulties in maintaining the view, and in explaining the idea of determinateness in a satisfactory manner. The paper argues that to overcome the difficulties, we need to reject the law of excluded middle; and it investigates the sense of 'rejection' that is involved. The paper also explores the logic that is required if (...) we reject excluded middle, with special emphasis on the conditional. There is also discussion of higher order indeterminacy (in several different senses) and of penumbral connections; and there is a suggested definition of determinateness in terms of the conditional and a discussion of the extent to which the notion of determinateness is objective. And there are suggestions about a unified treatment of vagueness and the semantic paradoxes. (shrink)
- Disarming a Paradox of Validity.Hartry Field -2017 -Notre Dame Journal of Formal Logic 58 (1):1-19.Any theory of truth must find a way around Curry’s paradox, and there are well-known ways to do so. This paper concerns an apparently analogous paradox, about validity rather than truth, which JC Beall and Julien Murzi call the v-Curry. They argue that there are reasons to want a common solution to it and the standard Curry paradox, and that this rules out the solutions to the latter offered by most “naive truth theorists.” To this end they recommend a radical (...) solution to both paradoxes, involving a substructural logic, in particular, one without structural contraction. In this paper I argue that substructuralism is unnecessary. Diagnosing the “v-Curry” is complicated because of a multiplicity of readings of the principles it relies on. But these principles are not analogous to the principles of naive truth, and taken together, there is no reading of them that should have much appeal to anyone who has absorbed the morals of both the ordinary Curry paradox and the second incompleteness theorem. (shrink)
- Disquotational truth and factually defective discourse.Hartry Field -1994 -Philosophical Review 103 (3):405-452.
- Indeterminacy, degree of belief, and excluded middle.Hartry Field -2000 -Noûs 34 (1):1–30.
- Indicative conditionals, restricted quantification, and naive truth.Hartry Field -2016 -Review of Symbolic Logic 9 (1):181-208.This paper extends Kripke’s theory of truth to a language with a variably strict conditional operator, of the kind that Stalnaker and others have used to represent ordinary indicative conditionals of English. It then shows how to combine this with a different and independently motivated conditional operator, to get a substantial logic of restricted quantification within naive truth theory.
- A revenge-immune solution to the semantic paradoxes.Hartry Field -2003 -Journal of Philosophical Logic 32 (2):139-177.The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema “True(A)↔A”, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in “ordinary” contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A (...) within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are “defective”. We can in fact define a hierarchy of “defectiveness” predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (“revenge problems”) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various “levels of defectiveness” can all be made coherent together within a single object language. (shrink)
- Deflating the conservativeness argument.Hartry Field -1999 -Journal of Philosophy 96 (10):533-540.
- Can We Dispense with Space-Time?Hartry Field -1984 -PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:33-90.This paper is concerned with the debate between substantival and relational theories of space-time, and discusses two difficulties that beset the relationalist: a difficulty posed by field theories, and another difficulty called the problem of quantities. A main purpose of the paper is to argue that possibility can not always be used as a surrogate of ontology, and that in particular that there is no hope of using possibility to solve the problem of quantities.
- Epistemology from an Evaluativist Perspective.Hartry Field -2018 -Philosophers' Imprint 18.The paper presents a kind of normative anti-realist view of epistemology, in the same ballpark as recent versions of expressivism. But the primary focus of the paper is less on this meta-epistemological view itself than on how it should affect ground-level issues in epistemology: for instance, how it should deal with certain forms of skepticism, and how it allows for fundamental revision in epistemic practices. It is hoped that these methodological consequences will seem attractive independent of the normative anti-realism. Indeed, (...) some normative realists seem to embrace the view on skepticism, but it is argued that their position is unstable: the realism undermines the methodology. The general theme of the paper is that the issue of normative realism is deeply entwined with issues of methodology, in strong contrast to the common claim that meta-epistemological views in the tradition of expressivism have no first order impact. (shrink)No categories
- Metalogic and modality.Hartry Field -1991 -Philosophical Studies 62 (1):1 - 22.
- Epistemological Nonfactualism and the a Prioricity of Logic.Hartry Field -1998 -Philosophical Studies 92 (1):1-24.
- The conceptual contingency of mathematical objects.Hartry Field -1993 -Mind 102 (406):285-299.
- The Semantic Paradoxes and the Paradoxes of Vagueness.Hartry Field -2003 - In J. C. Beall,Liars and Heaps: New Essays on Paradox. Oxford, England: Oxford University Press UK. pp. 262-311.Both in dealing with the semantic paradoxes and in dealing with vagueness and indeterminacy, there is some temptation to weaken classical logic: in particular, to restrict the law of excluded middle. The reasons for doing this are somewhat different in the two cases. In the case of the semantic paradoxes, a weakening of classical logic (presumably involving a restriction of excluded middle) is required if we are to preserve the naive theory of truth without inconsistency. In the case of vagueness (...) and indeterminacy, there is no worry about inconsistency; but a central intuition is that we must reject the factual status of certain sentences, and it hard to see how we can do that while claiming that the law of excluded middle applies to those sentences. So despite the different routes, we have a similar conclusion in the two cases. (shrink)
- Conventionalism about mathematics and logic.Hartry Field -2022 -Noûs 57 (4):815-831.Conventionalism about mathematics has much in common with two other views: fictionalism and the multiverse view (aka plenitudinous platonism). The three views may differ over the existence of mathematical objects, but they agree in rejecting a certain kind of objectivity claim about mathematics, advocating instead an extreme pluralism. The early parts of the paper will try to elucidate this anti‐objectivist position, and question whether conventionalism really offers a third form of it distinct from fictionalism and the multiverse view. The paper (...) then turns to anti‐objectivism about logic, and suggests that here too conventionalism offers no distinct alternative, and that there are limits on the extent of pluralism/anti‐objectivism. It also argues that these limits can't be used to argue for more extensive objectivity within mathematics, and also that they do allow for more limited pluralism within logic, e.g. as regards resolution of semantic and property‐theoretic paradoxes. (shrink)
- Quine and the correspondence theory.Hartry Field -1974 -Philosophical Review 83 (2):200-228.A correspondence theory of truth explains truth in terms of various correspondence relations (e.G., Reference) between words and the extralinguistic world. What are the consequences of quine's doctrine of indeterminacy for correspondence theories? in "ontological relativity" quine implicitly claims that correspondence theories are impossible; that is what the doctrine of 'relative reference' amounts to. But quine's doctrine of relative reference is incoherent. Those who think the indeterminacy thesis valid should not try to relativize reference, They should abandon the relation and (...) replace it by certain more general correspondence relations between words and extralinguistic objects. Doing so will not interfere with the task of defining truth in terms of correspondence relations. (shrink)
- Is mathematical knowledge just logical knowledge?Hartry Field -1984 -Philosophical Review 93 (4):509-552.
- Realism and relativism.Hartry Field -1982 -Journal of Philosophy 79 (10):553-567.
- (1 other version)Solving the paradoxes, escaping revenge.Hartry Field -2007 - In J. C. Beall,The Revenge of the Liar: New Essays on the Paradox. Oxford, England: Oxford University Press UK.It is “the received wisdom” that any intuitively natural and consistent resolution of a class of semantic paradoxes immediately leads to other paradoxes just as bad as the first. This is often called the “revenge problem”. Some proponents of the received wisdom draw the conclusion that there is no hope of any natural treatment that puts all the paradoxes to rest: we must either live with the existence of paradoxes that we are unable to treat, or adopt artificial and ad (...) hoc means to avoid them. Others (“dialetheists”) argue that we can put the paradoxes to rest, but only by licensing the acceptance of some contradictions (presumably in a paraconsistent logic that prevents the contradictions from spreading everywhere). (shrink)
- Attributions of meaning and content.Hartry Field -2001 - In Hartry H. Field,Truth and the absence of fact. New York: Oxford University Press.
- Prospects for a Naive Theory of Classes.Hartry Field,Harvey Lederman &Tore Fjetland Øgaard -2017 -Notre Dame Journal of Formal Logic 58 (4):461-506.The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. In (...) this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)
- Naive truth and restricted quantification: Saving truth a whole lot better.Hartry Field -2014 -Review of Symbolic Logic 7 (1):1-45.Restricted quantification poses a serious and under-appreciated challenge for nonclassical approaches to both vagueness and the semantic paradoxes. It is tempting to explain as ; but in the nonclassical logics typically used in dealing with vagueness and the semantic paradoxes (even those where thend expect. If we’re going to use a nonclassical logic, we need one that handles restricted quantification better.
- Egocentric Content.Hartry Field -2017 -Noûs 51 (3):521-546.The paper distinguishes two approaches to understanding the representational content of sentences and intentional states, and its role in describing people, predicting and explaining their behavior, and so forth. It sets forth the case for one of these approaches, the “egocentric” one, initially on the basis of its ability to explain the near‐indefeasibility of ascriptions of content to our own terms (“‘dogs’ as I use it means dogs”), but more generally on the basis of its providing an attractive overall picture (...) of the descriptive and explanatory role of representational content. In doing this, the paper relates the egocentric view to an “immanent” or “deflationary” view of reference and truth conditions, and also to the view of reference‐talk and truth‐talk as anaphoric devices. It discusses the indeterminacy of content ascriptions to those in communities with radically different theories, a phenomenon that is unsurprising on the egocentric approach, and connects this to the thesis of the normativity of meaning. (It does all this in rather broad brush: many strands of the egocentric account will be familiar, and are the subject of familiar controversies; the point of the paper is less to address these controversies individually than to tie the strands together into what is hoped to be an appealing package.). (shrink)
- Causation in a physical world.Hartry Field -2003 - In Michael J. Loux & Dean W. Zimmerman,The Oxford handbook of metaphysics. New York: Oxford University Press. pp. 435-460.1. Of what use is the concept of causation? Bertrand Russell [1912-13] argued that it is not useful: it is “a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.” His argument for this was that the kind of physical theories that we have come to regard as fundamental leave no place for the notion of causation: not only does the word ‘cause’ not appear in the advanced sciences, but the (...) laws that these sciences state are incompatible with causation as we normally understand it. But Nancy Cartwright has argued [1979] that abandoning the concept of causation would cripple science; her conclusion was based not on fundamental physics, but on more ordinary science such as the search for the causes of cancer. She argues that Russell was right that the fundamental theories of modern physics say nothing, even implicitly, about causation, and concludes on this basis that such theories are incomplete. It is with this cluster of issues that I will begin my discussion. (shrink)
- Conventionalism and instrumentalism in semantics.Hartry H. Field -1975 -Noûs 9 (4):375-405.
- Properties, Propositions and Conditionals.Hartry Field -2020 -Australasian Philosophical Review 4 (2):112-146.ABSTRACT Section 1 discusses properties and propositions, and some of the motivation for an account in which property instantiation and propositional truth behave ‘naively’. Section 2 generalizes a standard Kripke construction for naive properties and propositions, in a language with modal operators but no conditionals. Whereas Kripke uses a 3-valued value space, the generalized account allows for a broad array of value spaces, including the unit interval [0,1]. This is put to use in Section 3, where I add to the (...) language a conditional suitable for restricting quantification. The shift from a value space based on the ‘mini-space’ {0,, 1} to one based on the ‘mini-space’ [0,1] leads to more satisfactory results than I was able to achieve in previous work: a vast variety of paradoxical sentences can now be treated very simply. In Section 4 I make a further addition to the language, a conditional modeled on the ordinary English conditional, paying particular attention to how it interacts with the restricted quantifier conditional. This is all done in the [0,1] framework, and two alternatives are considered for how the ordinary conditional is to be handled; one of them results from adding a tweak to a construction by Ross Brady. Section 5 discusses a further alternative, a standard relevance conditional (for the ordinary conditional, perhaps for use with a different quantifier-restricting conditional), but argues that it is not promising. Section 6 discusses the identity conditions of properties and propositions (again in the setting of a value space based on [0,1]); the issue of achieving naivety for coarse-grained properties is seen to be more complicated than some brief remarks in Field [2010] suggested, but a way to get a fair degree of coarse-grainedness is shown. (shrink)
- 1. the concept of apriority.Hartry Field -2000 - In Paul Artin Boghossian & Christopher Peacocke,New Essays on the A Priori. Oxford, GB: Oxford University Press. pp. 117.
- Critical notice.Hartry Field -1984 -Canadian Journal of Philosophy 14 (4):637-662.
- The Consistency of The Naive Theory of Properties.Hartry Field -2004 -Philosophical Quarterly 54 (214):78-104.If properties are to play a useful role in semantics, it is hard to avoid assuming the naïve theory of properties: for any predicate Θ(x), there is a property such that an object o has it if and only if Θ(o). Yet this appears to lead to various paradoxes. I show that no paradoxes arise as long as the logic is weakened appropriately; the main difficulty is finding a semantics that can handle a conditional obeying reasonable laws without engendering paradox. (...) I employ a semantics which is infinite-valued, with the values only partially ordered. Can the solution be adapted to naïve set theory? Probably not, but limiting naïve comprehension in set theory is perfectly satisfactory, whereas this is not so in a property theory used for semantics. (shrink)
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David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Area Editors:
David Bourget
Gwen Bradford
Berit Brogaard
Margaret Cameron
David Chalmers
James Chase
Rafael De Clercq
Ezio Di Nucci
Esa Diaz-Leon
Barry Hallen
Hans Halvorson
Jonathan Ichikawa
Monte Johnson
Michelle Kosch
Øystein Linnebo
Paul Livingston
Brandon Look
Manolo Martínez
Matthew McGrath
Michiru Nagatsu
Susana Nuccetelli
Giuseppe Primiero
Jack Alan Reynolds
Darrell P. Rowbottom
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