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  1.  99
    The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics.Bob Hale (ed.) - 2001 - Oxford University Press.
    Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized as the (...)
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  2.  79
    Abstract Objects.Bob Hale - 1988 - Blackwell.
  3.  36
    Essence and Definition by Abstraction.Bob Hale - forthcoming - Synthese:1-17.
    We may define words or concepts, and we may also, as Aristotle and others have thought, define the things for which words stand and of which concepts are concepts. Definitions of words or concepts may be explicit or implicit, and may seek to report preexisting synonymies, as Quine put it, but they may instead be wholly or partly stipulative. Definition by abstraction, of which Hume’s principle is a much discussed example, seek to define a term-forming operator, such as the number (...)
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  4. Necessity, Caution and Scepticism.Bob Hale & Crispin Wright - 1989 - Aristotelian Society Supplementary Volume 63 (1):175 - 238.
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  5. Necessary Beings: An Essay on Ontology, Modality, and the Relations Between Them.Bob Hale - 2013 - Oxford University Press.
    Bob Hale presents a broadly Fregean approach to metaphysics, according to which ontology and modality are mutually dependent upon one another. He argues that facts about what kinds of things exist depend on facts about what is possible. Modal facts are fundamental, and have their basis in the essences of things--not in meanings or concepts.
     
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  6. Horse Sense.Bob Hale & Crispin Wright - 2012 - Journal of Philosophy 109 (1-2):85-131.
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  7. The Source Of Necessity.Bob Hale - 2002 - Noûs 36 (s16):299-319.
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  8. A Companion to the Philosophy of Language.Bob Hale & Crispin Wright (eds.) - 1997 - Wiley-Blackwell.
  9.  92
    Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.
    On the neo-Fregean approach to the foundations of mathematics, elementary arithmetic is analytic in the sense that the addition of a principle wliich may be held to IMJ explanatory of the concept of cardinal number to a suitable second-order logical basis suffices for the derivation of its basic laws. This principle, now commonly called Hume's principle, is an example of a Fregean abstraction principle. In this paper, I assume the correctness of the neo-Fregean position on elementary aritlunetic and seek to (...)
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  10. Absolute Necessities.Bob Hale - 1996 - Philosophical Perspectives 10:93 - 117.
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  11.  20
    Paolo Mancosu: Abstraction and Infinity.Bob Hale - 2018 - Journal of Philosophy 115 (3):158-166.
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  12. The Bearable Lightness of Being (Vol 20, Pg 399, 2010).Bob Hale - 2011 - Axiomathes 21 (4):597 - 597.
    How are philosophical questions about what kinds of things there are to be understood and how are they to be answered? This paper defends broadly Fregean answers to these questions. Ontological categories—such as object , property , and relation —are explained in terms of a prior logical categorization of expressions, as singular terms, predicates of varying degree and level, etc. Questions about what kinds of object, property, etc., there are are, on this approach, reduce to questions about truth and logical (...)
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  13. On Some Arguments for the Necessity of Necessity.Bob Hale - 1999 - Mind 108 (429):23-52.
    Must we believe in logical necessity? I examine an argument for an affirmative answer given by Ian McFetridge in his posthumously published paper 'Logical Necessity: Some Issues', and explain why it fails, as it stands, to establish his conclusion. I contend, however, that McFetridge's argument can be effectively buttressed by drawing upon another argument aimed at establishing that we ought to believe that some propositions are logically necessary, given by Crispin Wright in his paper 'Inventing Logical necessity'. My contention is (...)
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  14.  92
    Second-Order Logic: Properties, Semantics, and Existential Commitments.Bob Hale - forthcoming - Synthese:1-27.
    Quine’s most important charge against second-, and more generally, higher-order logic is that it carries massive existential commitments. The force of this charge does not depend upon Quine’s questionable assimilation of second-order logic to set theory. Even if we take second-order variables to range over properties, rather than sets, the charge remains in force, as long as properties are individuated purely extensionally. I argue that if we interpret them as ranging over properties more reasonably construed, in accordance with an abundant (...)
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  15. Benacerraf's Dilemma Revisited.Bob Hale & Crispin Wright - 2002 - European Journal of Philosophy 10 (1):101–129.
  16.  31
    Implicit Definition and the a Priori.Bob Hale & Crispin Wright - 2000 - In Paul Boghossian & Christopher Peacocke (eds.), New Essays on the a Priori. Oxford University Press. pp. 286--319.
  17. Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics.Bob Hale & Crispin Wright - 2003 - Oxford University Press UK.
    Bob Hale and Crispin Wright draw together here the key writings in which they have worked out their distinctive neo-Fregean approach to the philosophy of mathematics. The two main components in Frege's mathematical philosophy were his platonism and his logicism -- the claims, respectively, that mathematics is a body of knowledge about independently existing objects, and that this knowledge may be acquired on the basis of general logical laws and suitable definitions. The central thesis of this collection is that Frege (...)
     
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  18. The Metaontology of Abstraction.Bob Hale & Crispin Wright - 2009 - In David John Chalmers, David Manley & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 178-212.
  19. Introduction.Bob Hale & Crispin Wright - 2001 - In Bob Hale & Crispin Wrigth (eds.), The Reason's Proper Study. Essays Towards a Neo-Fregean Philosophy of Mathematics. Oxford University Press. pp. 1-27.
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  20.  5
    The Basis of Necessity and Possibility.Bob Hale - 2018 - Royal Institute of Philosophy Supplement 82:109-138.
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  21. A Desperate Fix.Bob Hale - 1995 - Analysis 55 (2):74-81.
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  22.  63
    Relative Necessity Reformulated.Bob Hale & Jessica Leech - 2017 - Journal of Philosophical Logic 46 (1):1-26.
    This paper discusses some serious difficulties for what we shall call the standard account of various kinds of relative necessity, according to which any given kind of relative necessity may be defined by a strict conditional - necessarily, if C then p - where C is a suitable constant proposition, such as a conjunction of physical laws. We argue, with the help of Humberstone, that the standard account has several unpalatable consequences. We argue that Humberstone’s alternative account has certain disadvantages, (...)
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  23.  34
    Abstraction and Set Theory.Bob Hale - 2000 - Notre Dame Journal of Formal Logic 41 (4):379--398.
    The neo-Fregean program in the philosophy of mathematics seeks a foundation for a substantial part of mathematics in abstraction principles—for example, Hume’s Principle: The number of Fs D the number of Gs iff the Fs and Gs correspond one-one—which can be regarded as implicitly definitional of fundamental mathematical concepts—for example, cardinal number. This paper considers what kind of abstraction principle might serve as the basis for a neo- Fregean set theory. Following a brief review of the main difficulties confronting the (...)
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  24.  64
    Can Arboreal Knotwork Help Blackburn Out of Frege's Abyss? [REVIEW]Bob Hale - 2002 - Philosophy and Phenomenological Research 65 (1):144–149.
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  25.  91
    Focus Restored: Comments on John MacFarlane.Bob Hale & Crispin Wright - 2009 - Synthese 170 (3):457 - 482.
    In “Double Vision Two Questions about the Neo-Fregean Programme”, John MacFarlane’s raises two main questions: (1) Why is it so important to neo-Fregeans to treat expressions of the form ‘the number of Fs’ as a species of singular term? What would be lost, if anything, if they were analysed instead as a type of quantifier-phrase, as on Russell’s Theory of Definite Descriptions? and (2) Granting—at least for the sake of argument—that Hume’s Principle may be used as a means of implicitly (...)
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  26.  9
    Abstract Objects.John P. Burgess & Bob Hale - 1992 - Philosophical Review 101 (2):414.
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  27. Can There Be a Logic of Attitudes?Bob Hale - 1993 - In John Haldane & Crispin Wright (eds.), Reality, Representation, and Projection. Oxford University Press. pp. 337--63.
  28.  26
    Review: The Compleat Projectivist. [REVIEW]Bob Hale - 1986 - Philosophical Quarterly 36 (142):65 - 84.
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  29.  94
    Abstraction and Additional Nature.Bob Hale & Crispin Wright - 2008 - Philosophia Mathematica 16 (2):182-208.
    What is wrong with abstraction’, Michael Potter and Peter Sullivan explain a further objection to the abstractionist programme in the foundations of mathematics which they first presented in their ‘Hale on Caesar’ and which they believe our discussion in The Reason's Proper Study misunderstood. The aims of the present note are: To get the character of this objection into sharper focus; To explore further certain of the assumptions—primarily, about reference-fixing in mathematics, about certain putative limitations of abstractionist set theory, and (...)
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  30. Nominalism and the Contingency of Abstract Objects.Crispin Wright & Bob Hale - 1992 - Journal of Philosophy 89 (3):111-135.
  31. Knowledge of Possibility and of Necessity.Bob Hale - 2002 - Proceedings of the Aristotelian Society 103 (1):1–20.
    I investigate two asymmetrical approaches to knowledge of absolute possibility and of necessity--one which treats knowledge of possibility as more fundamental, the other according epistemological priority to necessity. Two necessary conditions for the success of an asymmetrical approach are proposed. I argue that a possibility-based approach seems unable to meet my second condition, but that on certain assumptions--including, pivotally, the assumption that logical and conceptual necessities, while absolute, do not exhaust the class of absolute necessities--a necessity-based approach may be able (...)
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  32.  31
    Is Platonism Epistemologically Bankrupt?Bob Hale - 1994 - Philosophical Review 103 (2):299-325.
  33.  96
    A Reductio Ad Surdum? Field on the Contingency of Mathematical Objects.Bob Hale & Crispin Wright - 1994 - Mind 103 (410):169-184.
  34.  56
    Real Numbers and Set Theory – Extending the Neo-Fregean Programme Beyond Arithmetic.Bob Hale - 2005 - Synthese 147 (1):21-41.
    It is known that Hume’s Principle, adjoined to a suitable formulation of second-order logic, gives a theory which is almost certainly consistent4 and suffices for arithmetic in the sense that it yields the Dedekind-Peano axioms as theorems. While Hume’s Principle cannot be taken as a definition in any strict sense requiring that it provide for the eliminative paraphrase of its definiendum in every admissible type of occurrence, we hold that it can be viewed as an implicit definition of a sortal (...)
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  35. Modal Fictionalism: A Simple Dilemma.Bob Hale - 1995 - Analysis 55 (2):63--7.
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  36.  16
    A Response to Potter and Smiley: Abstraction by Recarving.Bob Hale - 2001 - Proceedings of the Aristotelian Society 101 (3):339–358.
  37. The Reason's Proper Study: Essays Toward a Neo-Fregean Philosophy of Mathematics.Bob Hale & Crispin Wright - 2006 - Bulletin of Symbolic Logic 12 (2):291-294.
     
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  38.  55
    Grundlagen §64.Bob Hale - 1997 - Proceedings of the Aristotelian Society 97 (3):243–261.
  39.  14
    What is Absolute Necessity?Bob Hale - 2012 - Philosophia Scientae 16:117-148.
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  40.  7
    Mathematics Without Numbers: Towards a Modal-Structural Interpretation.Bob Hale & Geoffrey Hellman - 1992 - Philosophical Review 101 (4):919.
  41.  70
    What is Absolute Necessity?Bob Hale - 2012 - Philosophia Scientiae 16 (2):117-148.
    On pourrait définir la nécessité absolue comme la vérité dans absolument tous les mondes possibles sans restriction. Mais nous devrions être capables de l’expliquer sans invoquer les mondes possibles. J’envisage trois definitions alternatives de : « Il est absolument nécessaire que p » et défends une définition contrefactuelle généralisée : ∀q.Je montre que la nécessité absolue satisfait le principe S5 et soutiens que la nécessité logique est absolue. Je discute ensuite des relations entre la nécessité logique et la nécessité métaphysique, (...)
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  42.  2
    Knowledge of Possibility and of Necessity.Bob Hale - 2003 - Proceedings of the Aristotelian Society 103 (1):1-20.
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  43. Reply to Ahmed.Bob Hale - 2000 - Mind 109 (433):93-96.
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  44.  17
    Further Into the Abyss: Graham Priest’s Towards Non-Being.Bob Hale - 2017 - Philosophia Mathematica 25 (3):394-406.
    PriestGraham. Towards Non-Being: The Logic and Metaphysics of Intentionality. Oxford University Press, 2016. 2nd ed. ISBN 978-0-19-878359-6 ; 978-0-19-878360-2. Pp. xxxvi + 368.
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  45.  3
    The Bearable Lightness of Being.Bob Hale - 2010 - Axiomathes 20 (4):399-422.
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  46.  39
    Dummett's Critique of Wright's Attempt to Resuscitate Frege.Bob Hale - 1994 - Philosophia Mathematica 2 (2):122-147.
    Michael Dummett mounts, in Frege: Philosophy of Mathematics, a concerted attack on the attempt, led by Crispin Wright, to salvage defensible versions of Frege's platonism and logicism in which Frege's criterion of numerical identity plays a leading role. I discern four main strands in this attack—that Wright's solution to the Caesar problem fails; that explaining number words contextually cannot justify treating them as enjoying robust reference; that Wright has no effective counter to ontological reductionism; and that the attempt is vitiated (...)
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  47.  5
    Singular Terms.Bob Hale - 1994 - In Brian McGuiness & Gianluigi Oliveri (eds.), The Philosophy of Michael Dummett. Kluwer Academic Publishers. pp. 17--44.
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  48.  67
    Erratum To: The Bearable Lightness of Being. [REVIEW]Bob Hale - 2011 - Axiomathes 21 (4):597-597.
    Erratum to: The Bearable Lightness of Being Content Type Journal Article DOI 10.1007/s10516-010-9127-7 Authors Bob Hale, Department of Philosophy, University of Sheffield, 45 Victoria St, Sheffield, S3 7QB UK Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151.
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  49.  47
    Structuralism's Unpaid Epistemological Debts.Bob Hale - 1996 - Philosophia Mathematica 4 (2):124--47.
    One kind of structuralism holds that mathematics is about structures, conceived as a type of abstract entity. Another denies that it is about any distinctively mathematical entities at all—even abstract structures; rather it gives purely general information about what holds of any collection of entities conforming to the axioms of the theory. Of these, pure structuralism is most plausibly taken to enjoy significant advantages over platonism. But in what appears to be its most plausible—modalised—version, even restricted to elementary arithmetic, it (...)
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  50.  58
    Real Numbers, Quantities, and Measurement.Bob Hale - 2002 - Philosophia Mathematica 10 (3):304-323.
    Defining the real numbers by abstraction as ratios of quantities gives prominence to then- applications in just the way that Frege thought we should. But if all the reals are to be obtained in this way, it is necessary to presuppose a rich domain of quantities of a land we cannot reasonably assume to be exemplified by any physical or other empirically measurable quantities. In consequence, an explanation of the applications of the reals, defined in this way, must proceed indirectly. (...)
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