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Unrestricted Unrestricted Quantification: the cardinal problem of absolute generality

In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press. pp. 305--32 (2006)

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  1. Reflective Mereology.Bokai Yao - 2023 - Journal of Philosophical Logic 52 (4):1171-1196.
    I propose a new theory of mereology based on a mereological reflection principle. Reflective mereology has natural fusion principles but also refutes certain principles of classical mereology such as Universal Fusion and Fusion Uniqueness. Moreover, reflective mereology avoids Uzquiano’s cardinality problem–the problem that classical mereology tends to clash with set theory when they both quantify over everything. In particular, assuming large cardinals, I construct a model of reflective mereology and second-order ZFCU with Limitation of Size. In the model, classical mereology (...)
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  • Ontology, Set Theory, and the Paraphrase Challenge.Jared Warren - 2021 - Journal of Philosophical Logic 50 (6):1231-1248.
    In many ontological debates there is a familiar challenge. Consider a debate over X s. The “small” or anti-X side tries to show that they can paraphrase the pro-X or “big” side’s claims without any loss of expressive power. Typically though, when the big side adds whatever resources the small side used in their paraphrase, the symmetry breaks down. The big side plus small’s resources is a more expressively powerful and thus more theoretically fruitful theory. In this paper, I show (...)
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  • Bad company generalized.Gabriel Uzquiano - 2009 - Synthese 170 (3):331 - 347.
    The paper is concerned with the bad company problem as an instance of a more general difficulty in the philosophy of mathematics. The paper focuses on the prospects of stability as a necessary condition on acceptability. However, the conclusion of the paper is largely negative. As a solution to the bad company problem, stability would undermine the prospects of a neo-Fregean foundation for set theory, and, as a solution to the more general difficulty, it would impose an unreasonable constraint on (...)
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  • Happy Unhappiness (and Other Stratified Contradictions).Franca D’Agostini - 2022 - Philosophia 50 (5):2423-2440.
    Stratified properties such as ‘happy unhappiness’, ‘ungrounded ground’, ‘fortunate misfortune’, and evidently ‘true falsity’ may generate dialetheias (true contradictions). The aim of the article is to show that if this is the case, then we will have a special, conjunctive, kind of dialetheia: a true state description of the form ‘Fa and not Fa’ (for some property F and object a), wherein the two conjuncts, separately taken, are to be held untrue. The particular focus of the article is on happy (...)
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