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• Bob Hale & Crispin Wright (2009). Focus Restored: Comments on John MacFarlane. Synthese 170 (3).
  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 (...) defining the number operator, what advantage, if any, does adopting this course possess over a direct stipulation of the Dedekind-Peano axioms? This paper attempts to answer them. In response to the first, we spell out the links between the recognition of numerical terms as vehicles of singular reference and the conception of numbers as possible objects of singular, or object-directed, thought, and the role of the acknowledgement of numbers as objects in the neo-Fregean attempt to justify the basic laws of arithmetic. In response to the second, we argue that the crucial issue concerns the capacity of either stipulation—of Hume’s Principle, or of the Dedekind-Peano axioms—to found knowledge of the principles involved, and that in this regard there are crucial differences which explain why the former stipulation can, but the latter cannot, play the required foundational role. (shrink)

  Mathematical Neo-Fregeanism in Philosophy of Mathematics

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• Bob Hale (2006). The Limits of Abstraction. Philosophy and Phenomenological Research 72 (1):223–232.
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• Bob Hale (2005). Real Numbers and Set Theory – Extending the Neo-Fregean Programme Beyond Arithmetic. Synthese 147 (1).
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• 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.
  Metaphysical Necessity in Metaphysics

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• Bob Hale (2002). Books of Essays. Philosophia Mathematica 10 (1).
  Philosophy of Mathematics

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• Bob Hale (2002). Can Arboreal Knotwork Help Blackburn Out of Frege's Abyss? Philosophy and Phenomenological Research 65 (1):144–149.
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• 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 (...) to do so. (shrink)

  Modal Epistemology, Misc in Metaphysics

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• Bob Hale (2002). Real Numbers, Quantities, and Measurement. Philosophia Mathematica 10 (3).
  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. (...) This paper explains the main complications involved and answers the main objections advanced in Batitsky's paper in this issue. (shrink)

  Philosophy of Mathematics

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• Bob Hale & Crispin Wright (2002). Benacerraf's Dilemma Revisited. European Journal of Philosophy 10 (1):101–129.
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• 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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• 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 (...) most powerful presentation yet of a neo-Fregean program. (shrink)

  Mathematical Neo-Fregeanism in Philosophy of Mathematics

  Analyticity in Mathematics in Philosophy of Mathematics

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• 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 (...) explain one way in which it may be extended to encompass the theory of real numbers, introducing the reals, by means of suitable further abstraction principles, as ratios of quantities. (shrink)

  Philosophy of Mathematics

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• Bob Hale (2000). Reply to Ahmed. Mind 109 (433):93-96.
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• Bob Hale (1999). Frege's Philosophy of Mathematics. Philosophical Quarterly 49 (194):92–104.
  Philosophy of Mathematics

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• Bob Hale (1999). Intuition and Reflection in Arithmetic: Bob Hale. Aristotelian Society Supplementary Volume 73 (1):75–98.
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• 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 (...) that Wright's argument, whilst it likewise fails, as it stands, to establish the necessity of necessity, established enough to close off what appears to me to be the only effective-looking sceptical response to McFetridge's original argument. My paper falls into four principal parts. In the first I expound McFetridge's argument and draw attention to the possibility of a certain type of sceptical counter to it. In the second, I begin a response to this sceptical move, taking it as far as I can without reliance upon argument of the kind given by Wright. Turning, then, to Wright's argument, I explain to what extent I think it is successful and seek to rebut some objections to the argument which, were they well-taken, would show that the argument cannot enjoy even the partial success I which to claim for it. Finally, I return to my main theme and try to show, with the assistance of what I take to be solidly established by Wright's argument, that the sceptical response collapses. (shrink)

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• Bob Hale (1998). Review. British Journal for the Philosophy of Science 49 (1).
  Science, Logic, and Mathematics

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• Bob Hale (1997). Grundlagen §64. Proceedings of the Aristotelian Society 97 (3):243–261.
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• Bob Hale (1996). Absolute Necessities. Philosophical Perspectives 10.
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• Bob Hale (1996). Structuralism's Unpaid Epistemological Debts. Philosophia Mathematica 4 (2).
  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 (...) requires defence of a very strong possibility claim: that there could be a completed w-sequence of concrete objects. There are very serious epistemological difficulties in the way of providing the requisite defence. (shrink)

  Philosophy of Mathematics

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• Bob Hale (1994). Dummett's Critique of Wright's Attempt to Resuscitate Frege. Philosophia Mathematica 2 (2).
  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 (...) by the unavoidable impredicativity of its leading principle—and argue that none of them succeeds. (shrink)

  Gottlob Frege in 20th Century Philosophy

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• Bob Hale (1994). Is Platonism Epistemologically Bankrupt? Philosophical Review 103 (2):299-325.
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• Bob Hale & Crispin Wright (1994). A Reductio Ad Surdum? Field on the Contingency of Mathematical Objects. Mind 103 (410):169-184.
  Mathematical Nominalism in Philosophy of Mathematics

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• Bob Hale (1992). Book Reviews. Mind 101 (403).
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• Crispin Wright & Bob Hale (1992). Nominalism and the Contingency of Abstract Objects. Journal of Philosophy 89 (3):111-135.
  Mathematical Nominalism in Philosophy of Mathematics

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• Bob Hale (1984). Frege's Platonism. Philosophical Quarterly 34 (136):225-241.
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• Bob Hale (1979). Strawson, Geach and Dummett on Singular Terms and Predicates. Synthese 42 (2).
  P. F. Strawson in 20th Century Philosophy

  Singular Terms in Philosophy of Language

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