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Counting Incompossibles

Mind 126 (504):1063–1108 (2017)

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  1. Abstracta and Possibilia: Modal Foundations of Mathematical Platonism.Hasen Khudairi - manuscript
    This paper aims to provide modal foundations for mathematical platonism. I examine Hale and Wright’s (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright’s objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...)
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  • Epistemic Modality, Mind, and Mathematics.Hasen Khudairi - 2020 - Dissertation, University of St Andrews
    This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; the types of mathematical modality; to the epistemic status of undecidable propositions and abstraction principles in the philosophy of mathematics; to the apriori-aposteriori distinction; to the modal profile of (...)
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  • Higher-Order Metaphysics and the Tropes Versus Universals Dispute.Lukas Skiba - forthcoming - Philosophical Studies.
    Higher-order realists about properties express their view that there are properties with the help of higher-order rather than first-order quantifiers. They claim two types of advantages for this way of formulating property realism. First, certain gridlocked debates about the nature of properties, such as the immanentism versus transcendentalism dispute, are taken to be dissolved. Second, a further such debate, the tropes versus universals dispute, is taken to be resolved. In this paper I first argue that higher-order realism does not in (...)
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  • Possible Patterns.Jeffrey Sanford Russell & John Hawthorne - 2018 - Oxford Studies in Metaphysics 11.
    “There are no gaps in logical space,” David Lewis writes, giving voice to sentiment shared by many philosophers. But different natural ways of trying to make this sentiment precise turn out to conflict with one another. One is a *pattern* idea: “Any pattern of instantiation is metaphysically possible.” Another is a *cut and paste* idea: “For any objects in any worlds, there exists a world that contains any number of duplicates of all of those objects.” We use resources from model (...)
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  • Relative Necessity and Propositional Quantification.Alexander Roberts - 2020 - Journal of Philosophical Logic 49 (4):703-726.
    Following Smiley’s influential proposal, it has become standard practice to characterise notions of relative necessity in terms of simple strict conditionals. However, Humberstone and others have highlighted various flaws with Smiley’s now standard account of relative necessity. In their recent article, Hale and Leech propose a novel account of relative necessity designed to overcome the problems facing the standard account. Nevertheless, the current article argues that Hale & Leech’s account suffers from its own defects, some of which Hale & Leech (...)
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  • Asymmetries in the Value of Existence.Jacob M. Nebel - 2019 - Philosophical Perspectives 33 (1):126-145.
    According to asymmetric comparativism, it is worse for a person to exist with a miserable life than not to exist, but it is not better for a person to exist with a happy life than not to exist. My aim in this paper is to explain how asymmetric comparativism could possibly be true. My account of asymmetric comparativism begins with a different asymmetry, regarding the (dis)value of early death. I offer an account of this early death asymmetry, appealing to the (...)
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  • Forms of Luminosity.Hasen Khudairi - 2017
    This dissertation concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The dissertation demonstrates how phenomenal consciousness and gradational possible-worlds models in Bayesian perceptual psychology relate to epistemic modal space. The dissertation demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; logical modality; the types of mathematical modality; to the (...)
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  • Higher-Order Contingentism, Part 1: Closure and Generation.Peter Fritz & Jeremy Goodman - 2016 - Journal of Philosophical Logic 45 (6):645-695.
    This paper is a study of higher-order contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to (...)
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  • Williamson on Fine on Prior on the Reduction of Possibilist Discourse.Kit Fine - 2016 - Canadian Journal of Philosophy 46 (4-5):548-570.
    I attempt to meet some criticisms that Williamson makes of my attempt to carry out Prior's project of reducing possibility discourse to actualist discourse.
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  • Reply to Goodman.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):640-653.
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  • Counting Things That Could Exist.Tobias Rosefeld - 2017 - Philosophical Quarterly 67 (266):127-147.
    The paper deals with cases of counting things that could exist but do not actually exist that resist common strategies for actualist paraphrases and that play an important role in motivating Timothy Williamson's ontology of contingently concrete objects. It is argued that these cases should be understood as cases of quantification not over individual possible objects but rather over kinds of objects, some of which do not actually have instances. This claim is motivated by a comparison with other cases of (...)
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  • A Purely Recombinatorial Puzzle.Fritz Peter - 2017 - Noûs 51 (3):547-564.
    A new puzzle of modal recombination is presented which relies purely on resources of first-order modal logic. It shows that naive recombinatorial reasoning, which has previously been shown to be inconsistent with various assumptions concerning propositions, sets and classes, leads to inconsistency by itself. The context sensitivity of modal expressions is suggested as the source of the puzzle, and it is argued that it gives us reason to reconsider the assumption that the notion of metaphysical necessity is in good standing.
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  • Higher-Order Contingentism, Part 3: Expressive Limitations.Peter Fritz - 2018 - Journal of Philosophical Logic 47 (4):649-671.
    Two expressive limitations of an infinitary higher-order modal language interpreted on models for higher-order contingentism – the thesis that it is contingent what propositions, properties and relations there are – are established: First, the inexpressibility of certain relations, which leads to the fact that certain model-theoretic existence conditions for relations cannot equivalently be reformulated in terms of being expressible in such a language. Second, the inexpressibility of certain modalized cardinality claims, which shows that in such a language, higher-order contingentists cannot (...)
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  • Counterfactuals and Propositional Contingentism.Peter Fritz & Jeremy Goodman - 2017 - Review of Symbolic Logic 10 (3):509-529.
    This article explores the connection between two theses: the principle of conditional excluded middle for the counterfactual conditional, and the claim that it is a contingent matter which (coarse grained) propositions there are. Both theses enjoy wide support, and have been defended at length by Robert Stalnaker. We will argue that, given plausible background assumptions, these two principles are incompatible, provided that conditional excluded middle is understood in a certain modalized way. We then show that some (although not all) arguments (...)
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  • Should Metaphysics Care About Linguistics?Tobias Rosefeldt - 2018 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 49 (2):161-178.
    Naturalized metaphysics is based on the idea that philosophy should be guided by the sciences. The paradigmatic science that is relevant for metaphysics is physics because physics tells us what fundamental reality is ultimately like. There are other sciences, however, that de facto play a role in philosophical inquiries about what there is, one of them being the science of language, i.e. linguistics. In this paper I will be concerned with the question what role linguistics should and does play for (...)
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