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Profile: Adam Rieger (Glasgow University)
  1.  16
    Adam Rieger (2011). Paradox, ZF and the Axiom of Foundation. In D. DeVidi, M. Hallet & P. Clark (eds.), Logic, Mathematics, Philosophy, Vintage Enthusiasms: Essays in Honour of John L. Bell. Springer
    This paper seeks to question the position of ZF as the dominant system of set theory, and in particular to examine whether there is any philosophical justification for the axiom of foundation. After some historical observations regarding Poincare and Russell, and the notions of circularity and hierarchy, the iterative conception of set is argued to be a semi-constructvist hybrid without philosophical coherence. ZF cannot be justified as necessary to avoid paradoxes, as axiomatizing a coherent notion of set, nor on pragmatic (...)
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  2. Adam Rieger (2006). A Simple Theory of Conditionals. Analysis 66 (3):233–240.
  3.  16
    Adam Rieger (2015). Moore's Paradox, Introspection and Doxastic Logic. Thought: A Journal of Philosophy 4 (4):215-227.
    An analysis of Moore's paradox is given in doxastic logic. Logics arising from formalizations of various introspective principles are compared; one logic, K5c, emerges as privileged in the sense that it is the weakest to avoid Moorean belief. Moreover it has other attractive properties, one of which is that it can be justified solely in terms of avoiding false belief. Introspection is therefore revealed as less relevant to the Moorean problem than first appears.
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  4.  21
    Adam Rieger (2015). Defending a Simple Theory of Conditionals. American Philosophical Quarterly 52 (3):253-260.
    This paper extends the defense of a simple theory of indicative conditionals previously proposed by the author, in which the truth conditions are material, and Grice-style assertability conditions are given to explain the paradoxes of material implication. The paper discusses various apparent counter-examples to the material account in which conditionals are not asserted, and so the original theory cannot be applied; it is argued that, nevertheless, the material theory can be defended.
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  5. Adam Rieger (2002). Paradox Without Basic Law V: A Problem with Frege’s Ontology. Analysis 62 (276):327–330.
  6.  51
    Adam Rieger (2001). The Liar, the Strengthened Liar, and Bivalence. Erkenntnis 54 (2):195-203.
    A view often expressed is that to classify the liar sentence as neither true nor false is satisfactory for the simple liar but not for the strengthened liar. I argue that in fact it is equally unsatisfactory for both liars. I go on to discuss whether, nevertheless, Kripke''s theory of truth represents an advance on that of Tarski.
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  7.  73
    Adam Rieger (2013). Conditionals Are Material: The Positive Arguments. Synthese 190 (15):3161-3174.
    A number of papers have argued in favour of the material account of indicative conditionals, but typically they either concentrate on defending the account from the charge that it has counterintuitive consequences, or else focus on some particular positive argument in favour of the theory. In this paper, I survey the various positive arguments that can be given, presenting simple versions where possible and showing the connections between them. I conclude with some methodological considerations.
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  8.  70
    Adam Rieger (2011). Voting on Voting Systems, or the Limits of Democracy. Analysis 71 (4):641-642.
    It is natural to think that a society can be organized in a way consistent with the overarching principle that all decisions should be democratic. A regress is constructed to demonstrate that this is, in fact, impossible.
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  9.  40
    Adam Rieger (2000). An Argument for Finsler-Aczel Set Theory. Mind 109 (434):241-253.
    Recent interest in non-well-founded set theories has been concentrated on Aczel's anti-foundation axiom AFA. I compare this axiom with some others considered by Aczel, and argue that another axiom, FAFA, is superior in that it gives the richest possible universe of sets consistent with respecting the spirit of extensionality. I illustrate how using FAFA instead of AFA might result in an improvement to Barwise and Etchemendy's treatment of the liar paradox.
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  10.  51
    Jake Chandler & Adam Rieger (2011). Self-Respect Regained. Proceedings of the Aristotelian Society 111 (2pt2):311-318.
    In a recent article, David Christensen casts aspersions on a restricted version of van Fraassen's Reflection principle, which he dubs ‘Self-Respect’(sr). Rejecting two possible arguments for sr, he concludes that the principle does not constitute a requirement of rationality. In this paper we argue that not only has Christensen failed to make a case against the aforementioned arguments, but that considerations pertaining to Moore's paradox indicate that sr, or at the very least a mild weakening thereof, is indeed a plausible (...)
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  11.  38
    Adam Rieger (2002). Patterns in the Philosophy of Mathematics. [REVIEW] Philosophical Quarterly 52 (207):247–255.
  12.  16
    Adam Rieger (2003). Naturalism in Mathematics. [REVIEW] Philosophical Review 112 (3):425-427.
    Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
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