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  1. 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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  2. Crispin Wright & Bob Hale, Metaphor.
    Metaphor enters contemporary philosophical discussion from a variety of directions. Aside from its obvious importance in poetics, rhetoric, and aesthetics, it also figures in such fields as philosophy of mind (e.g., the question of the metaphorical status of ordinary mental concepts), philosophy of science (e.g, the comparison of metaphors and explanatory models), in epistemology (e.g., analogical reasoning), and in cognitive studies (in, e.g., the theory of concept-formation). This article will concentrate on issues metaphor raises for the philosophy of language, with (...)
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  3. Bob Hale (2014). Critical Notice of Richard Heck's Frege's Theorem. Mind 123 (490):437-456.
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  4. 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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  5. 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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  6. Bob Hale (2012). What is Absolute Necessity? Philosophia Scientiae 16:117-148.
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  7. Bob Hale & Crispin Wright (2012). Horse Sense. Journal of Philosophy 109 (1-2):85-131.
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  8. 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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  9. 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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  10. Bob Hale (2010). Still Inexplicit? Bob Hale and Crispin Wright. In Bernhard Weiss & Jeremy Wanderer (eds.), Reading Brandom: On Making It Explicit. Routledge. 276.
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  11. Bob Hale & Aviv Hoffmann (eds.) (2010). Modality: Metaphysics, Logic, and Epistemology. Oxford University Press.
    The philosophy of modality investigates necessity and possibility, and related notions--are they objective features of mind-independent reality? If so, are they irreducible, or can modal facts be explained in other terms? This volume presents new work on modality by established leaders in the field and by up-and-coming philosophers. Between them, the papers address fundamental questions concerning realism and anti-realism about modality, the nature and basis of facts about what is possible and what is necessary, the nature of modal knowledge, modal (...)
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  12. 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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  13. 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.
  14. 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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  15. Bob Hale (2007). Into the Abyss: Review of Priest (2005). [REVIEW] Philosophia Mathematica 15:94--110.
     
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  16. Bob Hale (2007). Neo-Fregeanism and Quantifier Variance. Proceedings of the Aristotelian Society 107 (1pt3):375-385.
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  17. Bob Hale (2006). Kit Fine on the Limits of Abstraction. Travaux de Logique 18.
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  18. Bob Hale (2006). The Limits of Abstraction. Philosophy and Phenomenological Research 72 (1):223–232.
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  19. Bob Hale (2005). Mathematical Knowledge. A Defence of Modest and Sober Platonism. In Rene van Woudenberg, Sabine Roeser & Ron Rood (eds.), Basic Belief and Basic Knowledge. Ontos-Verlag. 4--107.
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  20. Bob Hale (2005). Real Numbers and Set Theory – Extending the Neo-Fregean Programme Beyond Arithmetic. 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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  21. 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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  22. Bob Hale (2002). The Source of Necessity. Noûs 36 (s16):299 - 319.
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  23. Bob Hale (2002). Basic Logical Knowledge. Royal Institute of Philosophy Supplement 51:279-304.
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  24. Bob Hale (2002). Books of Essays. Philosophia Mathematica 10 (1):90-93.
  25. 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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  26. Bob Hale (2002). Frege. Review of Metaphysics 56 (1):193-194.
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  27. 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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  28. Bob Hale (2002). * Real Necessity: A Reply to Barnes. Disputatio 13:1 - 7.
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  29. 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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  30. Bob Hale & Crispin Wright (2002). Benacerraf's Dilemma Revisited. European Journal of Philosophy 10 (1):101–129.
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  31. 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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  32. 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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  33. 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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  34. Bob Hale (2000). Transmission and Closure. Noûs 34 (s1):172 - 190.
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  35. 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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  36. Bob Hale (2000). Reals by Abstractiont. 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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  37. Bob Hale (2000). Reply to Ahmed. Mind 109 (433):93-96.
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  38. 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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  39. Bob Hale (1999). Frege's Philosophy of Mathematics. Philosophical Quarterly 49 (194):92–104.
  40. Bob Hale (1999). Intuition and Reflection in Arithmetic: Bob Hale. Aristotelian Society Supplementary Volume 73 (1):75–98.
    [Michael Potter] If arithmetic is not analytic in Kant's sense, what is its subject matter? Answers to this question can be classified into four sorts according as they posit logic, experience, thought or the world as the source, but in each case we need to appeal to some further process if we are to generate a structure rich enough to represent arithmetic as standardly practised. I speculate that this further process is our reflection on the subject matter already obtained. This (...)
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  41. 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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  42. Bob Hale (1999). Review: Penelope Maddy, Naturalism in Mathematics. [REVIEW] Journal of Symbolic Logic 64 (1):394-396.
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  43. Uy Field & Bob Hale (1998). Michael B. Wrigley. Manuscrito 21:269.
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  44. Bob Hale (1998). Review. [REVIEW] British Journal for the Philosophy of Science 49 (1):161-167.
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  45. Bob Hale (1998). Review of J. P. Burgess and G. Rosen, A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics. [REVIEW] British Journal for the Philosophy of Science 49 (1):161-167.
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  46. Bob Hale (1998). Review: W. D. Hart, The Philosophy of Mathematics. [REVIEW] Journal of Symbolic Logic 63 (3):1180-1183.
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  47. Bob Hale (1997). .
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  48. Bob Hale (1997). Grundlagen §64. Proceedings of the Aristotelian Society 97 (3):243–261.
  49. Bob Hale (1997). Realism and its Oppositions. In . 271--308.
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  50. Bob Hale (1997). Rule-Following, Objectivity and Meaning. In Bob Hale & C. Wright (eds.), A Companion to the Philosophy of Language. Blackwell.
     
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