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  1. Alan Weir, Formalism in the Philosophy of Mathematics.
    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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  2. Alan Weir, A Neo-Formalist Approach to Mathematical Truth.
    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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  3. Alan Weir, Naturalism Reconsidered.
    We’re all naturalists now, aren’t we? Well, not quite. It may be said, moreover, that the term ‘naturalism’ means so many different things to different philosophers that calling someone a naturalist has very little substantive content; but this would also be an exaggeration. In what follows I will not spend too much time on terminological matters; in my view, the phrase has a fairly definite content, in the context of discussions in the philosophy of mathematics and science such as this (...)
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  4. Alan Weir (2014). Mary Lengmathematics and Reality. British Journal for the Philosophy of Science 65 (3):657-664.
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  5. Alan Weir (2013). A Robust Non-Transitive Logic. Topoi: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. Alan Weir, Quine's Naturalism.
    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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  7. Alan Weir (2010). Truth Through Proof: A Formalist Foundation for Mathematics. OUP Oxford.
    Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Classic formalists claimed implausibly that mathematical utterances are truth-valueless moves in a game. 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. This framework allows for sentences whose truth-conditions are not representational, which are made true or false by conditions residing (...)
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  8. Alan Weir (2007). Honest Toil or Sheer Magic? Dialectica 61 (1):89–115.
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  9. Alan Weir (2006). Is It Too Much to Ask, to Ask for Everything. In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press. 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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  10. Alan Weir (2006). Indeterminacy of Translation. In Ernest Lepore & Barry C. Smith (eds.), The Oxford Handbook of Philosophy of Language. Oup Oxford.
  11. Alan Weir (2006). ROGER F. GIBSON JR (Ed.), The Cambridge Companion to Quine, Cambridge: Cambridge University Press, 2004 Xx + 323, ISBN 0-521-63056-. [REVIEW] Theoria 72 (3):240-247.
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  12. Stewart Shapiro, Alan Weir & Jamie Tappenden (2005). Kit Fine Precis. Discussion. Philosophical Studies 122 (3):305 - 395.
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  13. Alan Weir (2005). Naive Truth and Sophisticated Logic. In J. C. Beall & Bradley Armour-Garb (eds.), Deflationism and Paradox. Clarendon Press.
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  14. Alan Weir (2005). On Kit Fine's the Limits of Abstraction – Discussion. [REVIEW] Philosophical Studies 122 (3):333 - 348.
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  15. K. Fine & Alan Weir (2004). REVIEWS-The Limits of Abstraction. Bulletin of Symbolic Logic 10 (4):554-557.
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  16. Alan Weir (2004). An Ultra-Realist Theory of Perception. 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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  17. Alan Weir (2004). There Are No True Contradictions. In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction. Clarendon Press.
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  18. Alan Weir (2004). The Limits of Abstraction. Bulletin of Symbolic Logic 10 (4):554-557.
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  19. Alan Weir (2003). Neo-Fregeanism: An Embarrassment of Riches. 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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  20. Alan Weir (2003). Objective Content. 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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  21. Alan Weir (2002). Rejoinder to Laurence Goldstein on the Liar. Analysis 62 (1):26–34.
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  22. Alan Weir (2001). More Trouble for Functionalism. 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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  23. Stewart Shapiro & Alan Weir (2000). ‘Neo-Logicist‘ Logic is Not Epistemically Innocent. 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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  24. Alan Weir (2000). Token Relativism and the Liar. Analysis 60 (2):156–170.
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  25. Stewart Shapiro & Alan Weir (1999). New V, ZF and Abstractiont. 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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  26. Stewart Shapiro & Alan Weir (1999). New V, ZF and Abstraction. 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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  27. Alan Weir (1998). Dummett on Impredicativity. 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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  28. Alan Weir (1998). Naive Set Theory, Paraconsistency and Indeterminacy I. Logique Et Analyse 41:219-66.
     
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  29. Alan Weir (1996). On an Argument for Irrationalism. Philosophical Papers 25 (2):95-114.
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  30. Alan Weir (1996). Lavine, S.-Understanding the Infinite. Philosophical Books 37:136-138.
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  31. Alan Weir (1996). PHILOSOPHY OF MATHEMATICS Understanding the Infinite. Philosophical Books 37 (2):136-139.
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  32. Alan Weir (1996). Ultramaximalist Minimalism! Analysis 56 (1):10–22.
  33. Alan Weir (1995). Gruesome Perceptual Spaces. Analysis 55 (1):27 - 36.
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  34. Alan Weir (1993). Putnam, G Del and Mathematical Realism. International Journal of Philosophical Studies 1 (2):255 – 285.
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  35. Alan Weir (1991). An Instructive Nominalism. Philosophical Books 32 (1):17-26.
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  36. Alan Weir (1990). Relevant Logic: A Philosophical Examination of Inference. Philosophical Books 31 (1):31-33.
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  37. Alan Weir (1989). Neil Tennant, Anti-Realism, and Logic: Truth as Eternal Reviewed By. Philosophy in Review 9 (7):293-296.
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  38. Alan Weir (1988). Rejoinder to George. Mind 97 (385):110-112.
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  39. Alan Weir (1986). Classical Harmony. Notre Dame Journal of Formal Logic 27 (4):459-482.
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  40. Alan Weir (1986). Dummett on Meaning and Classical Logic. Mind 95 (380):465-477.
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  41. Alan Weir (1986). Realism and Behaviourism. Dialectica 40 (3):167-200.
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  42. Alan Weir (1985). Against Holism. Philosophical Quarterly 35 (July):225-244.
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  43. Alan Weir (1985). Rejoinder to Tennant. Analysis 45 (2):68 - 72.
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  44. Alan Weir (1983). Truth Conditions and Truth Values. Analysis 43 (4):176 - 180.
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