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Alan Weir [60]Alan John Weir [1]
  1.  44
    Neo-Fregeanism: An Embarrassment of Riches.Alan Weir - 2003 - Notre Dame Journal of Formal Logic 44 (1):13-48.
    Neo-Fregeans argue that substantial mathematics can be derived from a priori abstraction principles, Hume's Principle connecting numerical identities with one:one correspondences being a prominent example. The embarrassment of riches objection is that there is a plurality of consistent but pairwise inconsistent abstraction principles, thus not all consistent abstractions can be true. This paper considers and criticizes various further criteria on acceptable abstractions proposed by Wright settling on another one—stability—as the best bet for neo-Fregeans. However, an analogue of the embarrassment of (...)
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  2.  73
    ‘Neo-Logicist‘ Logic is Not Epistemically Innocent.Stewart Shapiro & Alan Weir - 2000 - Philosophia Mathematica 8 (2):160--189.
    The neo-logicist argues tliat standard mathematics can be derived by purely logical means from abstraction principles—such as Hume's Principle— which are held to lie 'epistcmically innocent'. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemically innocent. We conclude that the epistemic innocence of mathematics has not been (...)
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  3.  5
    Naive Truth and Sophisticated Logic.Alan Weir - 2005 - In J. C. Beall & Bradley Armour-Garb (eds.), Deflationism and Paradox. Clarendon Press.
  4.  34
    New V, ZF and Abstraction.Stewart Shapiro & Alan Weir - 1999 - Philosophia Mathematica 7 (3):293--321.
    We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to (...)
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  5.  55
    A Robust Non-Transitive Logic.Alan Weir - 2013 - Topoi 34 (1):1-9.
    Logicians interested in naive theories of truth or set have proposed logical frameworks in which classical operational rules are retained but structural rules are restricted. One increasingly popular way to do this is by restricting transitivity of entailment. This paper discusses a series of logics in this tradition, in which the transitivity restrictions are effected by a determinacy constraint on assumptions occurring in both the major and minor premises of certain rules. Semantics and proof theory for 3-valued, continuum-valued and surreal-valued (...)
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  6.  27
    New V, ZF and Abstractiont.Stewart Shapiro & Alan Weir - 1999 - Philosophia Mathematica 7 (3):293-321.
    We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to (...)
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  7.  17
    Truth Through Proof: A Formalist Foundation for Mathematics.Alan Weir - 2010 - Oxford University Press.
    Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance.
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  8. Mary Lengmathematics and Reality.Alan Weir - 2014 - British Journal for the Philosophy of Science 65 (3):657-664.
  9. Kit Fine Precis. Discussion.Stewart Shapiro, Alan Weir & Jamie Tappenden - 2005 - Philosophical Studies 122 (3):305 - 395.
  10.  47
    Token Relativism and the Liar.Alan Weir - 2000 - Analysis 60 (2):156–170.
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  11.  66
    Rejoinder to Tennant.Alan Weir - 1985 - Analysis 45 (2):68 - 72.
  12.  64
    More Trouble for Functionalism.Alan Weir - 2001 - Proceedings of the Aristotelian Society 101 (3):267-293.
    In this paper I highlight certain logical and metaphysical issues which arise in the characterisation of functionalism-in particular its ready coherence with a physicalist ontology, its structuralism and the impredicativity of functionalist specifications. I then utilise these points in an attempt to demonstrate fatal flaws in the functionalist programme. I argue that the brand of functionalism inspired by David Lewis fails to accommodate multiple realisability though such accommodation was vaunted as a key improvement over the identity theory. More standard accounts (...)
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  13.  3
    Is It Too Much to Ask, to Ask for Everything.Alan Weir - 2006 - In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press. pp. 333--68.
    Most of the time our quantifications generalise over a restricted domain. Thus in the last sentence, ‘most of the time’ is arguably not a generalisation over all times in the history of the universe but is restricted to a sub-group of times, those at which humans exist and utter quantified phrases and sentences, say. Indeed the example illustrates the point that quantificational phrases often carry an explicit restriction with them: ‘some people’, ‘all dogs’. Even then, context usually restricts to a (...)
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  14.  83
    An Ultra-Realist Theory of Perception.Alan Weir - 2004 - International Journal of Philosophical Studies 12 (2):105-128.
    In this paper I argue for a theory of perception distinct both from classical sense-datum theories and from intentionalist theories, that is theories according to which one perceives external objects by dint of a relation with a propositional content. The alternative I propose completely rejects any representational element in perception. When one sees that an object has a property, the situation or state of affairs of its having that property is one's perception, so that the object and property are literally (...)
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  15.  23
    Dummett on Impredicativity.Alan Weir - 1998 - Grazer Philosophische Studien 55:65-101.
    Gödel and others held that impredicative specification is illegitimate in a constructivist framework but legitimate elsewhere. Michael Dummett argues to the contrary that impredicativity, though not necessarily illicit, needs justification regardless of whether one assumes the context is realist or constructivist. In this paper I defend the Gödelian position arguing that Dummett seeks a reduction of impredicativity to predicativity which is neither possible nor necessary. The argument is illustrated by considering first highly predicative versions of the equinumerosity axiom for cardinal (...)
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  16.  13
    Indeterminacy of Translation.Alan Weir - 2006 - In Ernest Lepore & Barry C. Smith (eds.), The Oxford Handbook of Philosophy of Language. Oxford University Press.
    W.V. Quine's thesis of the indeterminacy of translation is the theory which launched a thousand doctorates. During the 1970s it sometimes seemed to be as firmly entrenched a dogma among North American philosophers as the existence of God was among medieval theologians. So what is the indeterminacy thesis? It is very tempting, of course, to apply a little reflexivity and deny that there is any determinate thesis of indeterminacy of translation; to charge Quine with championing a doctrine which has no (...)
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  17.  34
    On Kit Fine's the Limits of Abstraction – Discussion. [REVIEW]Alan Weir - 2004 - Philosophical Studies 122 (3):333 - 348.
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  18.  20
    Informal Proof, Formal Proof, Formalism.Alan Weir - forthcoming - Review of Symbolic Logic:1-21.
  19.  80
    Rejoinder to Laurence Goldstein on the Liar.Alan Weir - 2002 - Analysis 62 (1):26–34.
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  20.  4
    Naturalism Reconsidered.Alan Weir - 2005 - In Stewart Shapiro (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press.
    Mathematics poses a difficult problem for methodological naturalists, those who embrace scientific method, and also for ontological naturalists who eschew non-physical entities such as Cartesian souls. Mathematics seems both essential to science but also committed to abstract non-physical entities while methodologically it seems to have no place for experiment or empirical confirmation. The chapter critically reviews a number of responses naturalists have made including logicism, Quinean radical empiricism, and Penelope Maddy’s variant thereof and suggests some further problems both for ontological (...)
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  21.  60
    Formalism in the Philosophy of Mathematics.Alan Weir - unknown
    The guiding idea behind formalism is that mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess. This idea has some intuitive plausibility: consider the tyro toiling at multiplication tables or the student using a standard algorithm for differentiating or integrating a function. It also corresponds to some aspects of the practice of (...)
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  22.  20
    Classical Harmony.Alan Weir - 1986 - Notre Dame Journal of Formal Logic 27 (4):459-482.
  23.  41
    Against Holism.Alan Weir - 1985 - Philosophical Quarterly 35 (July):225-244.
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  24.  61
    A Neo-Formalist Approach to Mathematical Truth.Alan Weir - manuscript
    I outline a variant on the formalist approach to mathematics which rejects textbook formalism's highly counterintuitive denial that mathematical theorems express truths while still avoiding ontological commitment to a realm of abstract objects. The key idea is to distinguish the sense of a sentence from its explanatory truth conditions. I then look at various problems with the neo-formalist approach, in particular at the status of the notion of proof in a formal calculus and at problems which Gödelian results seem to (...)
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  25.  40
    Truth Conditions and Truth Values.Alan Weir - 1983 - Analysis 43 (4):176 - 180.
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  26. There Are No True Contradictions.Alan Weir - 2004 - In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction. Clarendon Press.
     
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  27. Naive Set Theory, Paraconsistency and Indeterminacy I.Alan Weir - 1998 - Logique Et Analyse 41:219-66.
     
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  28.  20
    Quine's Naturalism.Alan Weir - unknown
    Starting with the distinction between epistemological and ontological naturalism, this chapter focuses most on Quine’s epistemological naturalism, not the ontological anti-naturalism he thought it leads to. It is argued that naturalised epistemology is not central to Quine’s epistemology. Quine’s key epistemological principle is:- follow the methods of science, and only those. Can Quine demarcate scientific methods from non-scientific ones? The problems which have been raised here, e.g. in the case of mathematics, are considered. A main theme is the relationship between (...)
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  29.  18
    Dummett on Meaning and Classical Logic.Alan Weir - 1986 - Mind 95 (380):465-477.
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  30.  8
    Putnam, G Del and Mathematical Realism.Alan Weir - 1993 - International Journal of Philosophical Studies 1 (2):255 – 285.
  31.  2
    PHILOSOPHY OF MATHEMATICS Understanding the Infinite.Alan Weir - 1996 - Philosophical Books 37 (2):136-139.
  32.  25
    ROGER F. GIBSON JR (Ed.), The Cambridge Companion to Quine, Cambridge: Cambridge University Press, 2004 Xx + 323, ISBN 0-521-63056-. [REVIEW]Alan Weir - 2006 - Theoria 72 (3):240-247.
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  33.  24
    Gruesome Perceptual Spaces.Alan Weir - 1995 - Analysis 55 (1):27 - 36.
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  34.  21
    Objective Content.Alan Weir - 2003 - Proceedings of the Aristotelian Society 77 (77):47-72.
    [Alan Weir] This paper addresses the problem of how to account for objective content-for the distinction between how we actually apply terms and the conditions in which we ought to apply them-from within a naturalistic framework. Though behaviourist or dispositionalist approaches are generally held to be unsuccessful in naturalising objective content or 'normativity', I attempt to restore the credibility of such approaches by sketching a behaviouristic programme for explicating objective content. /// [Alexander Miller] Paul Boghossian (1989, 1990) has argued, on (...)
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  35.  1
    It’s Not Just the Economy, Dunderheid.Alan Weir - 2014 - The Philosophers' Magazine 67:22-34.
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  36.  18
    Honest Toil or Sheer Magic?Alan Weir - 2006 - Dialectica 61 (1):89–115.
    In this article I discuss the ‘procedural postulationist’ view of mathematics advanced by Kit Fine in a recent paper. I argue that he has not shown that this view provides an avenue to knowledge of mathematical truths, at least if such truths are objective truths. In particular, more needs to be said about the criteria which constrain which types of entities can be postulated. I also argue that his reliance on second‐order quantification means that his background logic is not free (...)
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  37.  2
    Honest Toil or Sheer Magic?Alan Weir - 2007 - Dialectica 61 (1):89-115.
    In this article I discuss the ‘procedural postulationist’ view of mathematics advanced by Kit Fine in a recent paper. I argue that he has not shown that this view provides an avenue to knowledge of mathematical truths, at least if such truths are objective truths. In particular, more needs to be said about the criteria which constrain which types of entities can be postulated. I also argue that his reliance on second‐order quantification means that his background logic is not free (...)
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  38.  7
    On an Argument for Irrationalism.Alan Weir - 1996 - Philosophical Papers 25 (2):95-114.
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  39.  4
    Realism and Behaviourism.Alan Weir - 1986 - Dialectica 40 (3):167-200.
    SummaryMany contemporary philosophers of language believe that realist metaphysics and a beha‐viouristic approach to language are incompatible, debate centring on which is to be given up. In this paper I argue that no incompatibility has been shown to exist. In the first section I attempt to give both a characterization of, and an argument for, behaviourism. Then I attempt to characterize realism more generally than is often done, evaluating the work of Dummett, Quine, Putnam and Wittgenstein, as recently interpreted, in (...)
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  40.  3
    Relevant Logic: A Philosophical Examination of Inference.Alan Weir - 1990 - Philosophical Books 31 (1):31-33.
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  41.  5
    Rejoinder to George.Alan Weir - 1988 - Mind 97 (385):110-112.
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  42.  1
    On Kit Fine’s The Limits of Abstraction – Discussion.Alan Weir - 2004 - Philosophical Studies 122 (3):333-348.
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  43.  2
    The Limits of Abstraction.Alan Weir - 2004 - Bulletin of Symbolic Logic 10 (4):554-557.
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  44.  1
    XIII*—More Trouble for Functionalism.Alan Weir - 2001 - Proceedings of the Aristotelian Society 101 (3):267-294.
    In this paper I highlight certain logical and metaphysical issues which arise in the characterisation of functionalism-in particular its ready coherence with a physicalist ontology, its structuralism and the impredicativity of functionalist specifications. I then utilise these points in an attempt to demonstrate fatal flaws in the functionalist programme. I argue that the brand of functionalism inspired by David Lewis fails to accommodate multiple realisability though such accommodation was vaunted as a key improvement over the identity theory. More standard accounts (...)
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  45.  1
    An Instructive Nominalism.Alan Weir - 1991 - Philosophical Books 32 (1):17-26.
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  46. REVIEWS-The Limits of Abstraction.K. Fine & Alan Weir - 2004 - Bulletin of Symbolic Logic 10 (4):554-557.
     
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  47. Dummett on Impredicativity.Alan Weir - 1998 - Grazer Philosophische Studien 55:65-101.
    Gödel and others held that impredicative specification is illegitimate in a constructivist framework but legitimate elsewhere. Michael Dummett argues to the contrary that impredicativity, though not necessarily illicit, needs justification regardless of whether one assumes the context is realist or constructivist. In this paper I defend the Gödelian position arguing that Dummett seeks a reduction of impredicativity to predicativity which is neither possible nor necessary. The argument is illustrated by considering first highly predicative versions of the equinumerosity axiom for cardinal (...)
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  48. Gruesome perceptual spaces.Alan Weir - 1995 - Erkenntnis 55:27.
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  49. I—Alan Weir.Alan Weir - 2003 - Aristotelian Society Supplementary Volume 77 (1):47-72.
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  50. Lavine, S.-Understanding the Infinite.Alan Weir - 1996 - Philosophical Books 37:136-138.
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