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  1.  63
    Bob Hale (ed.) (2001). The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. 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. Bob Hale & Crispin Wright (1989). Necessity, Caution and Scepticism. Aristotelian Society Supplementary Volume 63 (1):175 - 238.
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  3.  31
    Bob Hale (1988). Abstract Objects. B. Blackwell.
  4.  21
    Bob Hale & Jessica Leech (forthcoming). Relative Necessity Reformulated. Journal of Philosophical Logic: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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  5. Bob Hale (2013). Necessary Beings: An Essay on Ontology, Modality, and the Relations Between Them. OUP Oxford.
    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. Bob Hale & Crispin Wright (2012). Horse Sense. Journal of Philosophy 109 (1-2):85-131.
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  7.  39
    Bob Hale (forthcoming). Second-Order Logic: Properties, Semantics, and Existential Commitments. 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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  8. C. J. G. Wright & Bob Hale (eds.) (1997). A Companion to the Philosophy of Language. Wiley-Blackwell.
    This volume provides a survey of contemporary philosophy of language. As well as providing a synoptic view of the key issues, figures, concepts and debates, each essay makes new and original contributions to ongoing debate.
     
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  9. Bob Hale (1999). On Some Arguments for the Necessity of Necessity. 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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  10. Bob Hale (1995). A Desperate Fix. Analysis 55 (2):74-81.
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  11.  55
    Bob Hale (2000). Reals by Abstraction. 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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  12. Bob Hale (1996). Absolute Necessities. Philosophical Perspectives 10:93 - 117.
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  13. Bob Hale (2011). The Bearable Lightness of Being (Vol 20, Pg 399, 2010). 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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  14. Bob Hale & Crispin Wright (2002). Benacerraf's Dilemma Revisited. European Journal of Philosophy 10 (1):101–129.
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  15. Bob Hale (2002). The Source of Necessity. Noûs 36 (s16):299 - 319.
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  16. Bob Hale (2000). Reply to Ahmed. Mind 109 (433):93-96.
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  17.  15
    Bob Hale & Crispin Wright (2000). Implicit Definition and the a Priori. In Paul Boghossian & Christopher Peacocke (eds.), New Essays on the a Priori. Oxford University Press 286--319.
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  18.  30
    Bob Hale (2015). Philosophy of Mathematics in the Twentieth Century: Selected Essays By Charles Parsons. Analysis 75 (3):532-535.
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  19. Bob Hale (2002). Knowledge of Possibility and of Necessity. 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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  20. Bob Hale (1995). Modal Fictionalism: A Simple Dilemma. Analysis 55 (2):63--7.
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  21. Bob Hale & Crispin Wright (2003). Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. 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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  22.  51
    Bob Hale (2002). Can Arboreal Knotwork Help Blackburn Out of Frege's Abyss? [REVIEW] Philosophy and Phenomenological Research 65 (1):144–149.
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  23. Crispin Wright & Bob Hale (1992). Nominalism and the Contingency of Abstract Objects. Journal of Philosophy 89 (3):111-135.
  24.  78
    Bob Hale & Crispin Wright (2008). Abstraction and Additional Nature. 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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  25.  67
    Bob Hale & Crispin Wright (2009). Focus Restored: Comments on John MacFarlane. 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.  24
    Bob Hale (2000). Abstraction and Set Theory. 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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  27.  21
    Bob Hale (1986). Review: The Compleat Projectivist. [REVIEW] Philosophical Quarterly 36 (142):65 - 84.
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  28. Bob Hale (1993). Can There Be a Logic of Attitudes? In John Haldane & Crispin Wright (eds.), Reality, Representation, and Projection. Oxford University Press 337--63.
     
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  29.  95
    Bob Hale & Crispin Wright, Focus Restored Comment on John MacFarlane's “Double Vision: Two Questions About the Neo-Fregean Programme”.
    Anything worth regarding as logicism about number theory holds that its fundamental laws – in effect, the Dedekind-Peano axioms – may be known on the basis of logic and definitions alone. For Frege, the logic in question was that of the Begriffschrift – effectively, full impredicative second order logic - together with the resources for dealing with the putatively “logical objects” provided by Basic Law V of Grundgesetze. With this machinery in place, and with the course-of-values operator governed by Basic (...)
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  30.  84
    Bob Hale & Crispin Wright (1994). A Reductio Ad Surdum? Field on the Contingency of Mathematical Objects. Mind 103 (410):169-184.
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  31.  39
    Bob Hale (2012). What is Absolute Necessity? 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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  32. Bob Hale & Crispin Wright (2001). Introduction. In Bob Hale & Crispin Wrigth (eds.), The Reason's Proper Study. Essays Towards a Neo-Fregean Philosophy of Mathematics. Oxford University Press 1-27.
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  33.  24
    Bob Hale (1994). Is Platonism Epistemologically Bankrupt? Philosophical Review 103 (2):299-325.
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  34.  32
    Bob Hale (2002). * Real Necessity: A Reply to Barnes. Disputatio 13:1 - 7.
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  35.  13
    Bob Hale (2001). A Response to Potter and Smiley: Abstraction by Recarving. Proceedings of the Aristotelian Society 101 (3):339–358.
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  36.  36
    Bob Hale (1997). Grundlagen §64. Proceedings of the Aristotelian Society 97 (3):243–261.
  37.  23
    Bob Hale (2006). Kit Fine on the Limits of Abstraction. Travaux de Logique 18.
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  38. Bob Hale & Crispin Wright (2009). The Metaontology of Abstraction. In David John Chalmers, David Manley & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press 178-212.
  39.  23
    Bob Hale (2014). Critical Notice of Richard Heck's Frege's Theorem. Mind 123 (490):437-456.
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  40.  77
    Bob Hale (2004). Putnam's Retreat: Some Reflections on Hilary Putnam's Changing Views About Metaphysical Necessity. Midwest Studies in Philosophy 28 (1):351–378.
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  41.  30
    Bob Hale (2013). Review of G. Duke: Dummett on Abstract Objects. [REVIEW] Journal for the History of Analytical Philosophy 2 (2).
    Review of G. Duke: Dummett onObjects References G. Frege. Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik, 100, 25–50, 1892. Translated in G.Frege, Collected Papers on Mathematics, Logic and Philosophy, edited by B. McGuinness. Oxford, Basil Blackwell, 157–77. G. Frege. Die Grundlagen der Arithmetik. Breslau, Verlag von W. Koebner, 1884. Translated by J.L. Austin as The Foundations of Arithmetic, Oxford, Basil Blackwell, second revised edition 1953. M. Dummett. Frege: Philosophy of Language. London, Duckworth, 1973. M. Dummett. Frege: Philosophy (...)
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  42.  68
    Bob Hale (2002). Books of Essays. Philosophia Mathematica 10 (1):90-93.
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  43.  54
    Bob Hale (2011). Erratum To: The Bearable Lightness of Being. [REVIEW] 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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  44.  5
    Bob Hale (1994). Singular Terms. In Brian McGuiness & Gianluigi Oliveri (eds.), The Philosophy of Michael Dummett. Kluwer 17--44.
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  45.  30
    Bob Hale (1994). Dummett's Critique of Wright's Attempt to Resuscitate Frege. 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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  46.  31
    Bob Hale (1996). Structuralism's Unpaid Epistemological Debts. 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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  47.  40
    Bob Hale (2006). The Limits of Abstraction. Philosophy and Phenomenological Research 72 (1):223–232.
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  48.  33
    Bob Hale (1988). Epistemic Universalizability. Analysis 48 (2):78 - 84.
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  49.  39
    Bob Hale (2002). Real Numbers, Quantities, and Measurement. 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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  50.  45
    Bob Hale (1979). Strawson, Geach and Dummett on Singular Terms and Predicates. Synthese 42 (2):275 - 295.
    In the opening chapter of Subject and Predicate in Logic and Grammar, [1] Professor Strawson develops an explanation of the subjectpredicate distinction on the basis of a supposedly more fundamental distinction or contrast between, on the one hand, spatio-temporal particulars and, on the other, general concepts applicable to such particulars. At a basic level, he argues, these contrasted items occupy a central position in our thought about the world. They form the constituents of a fundamental type of judgment about the (...)
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