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Platonism and Quantification

In Arthur Norman Prior (ed.), Objects of thought. Oxford,: Clarendon Press. pp. 31-47 (1971)

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  1. 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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  • What is a second order theory committed to?Charles Sayward - 1983 - Erkenntnis 20 (1):79 - 91.
    The paper argues that no second order theory is ontologically commited to anything beyond what its individual variables range over.
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  • Pure Logic and Higher-order Metaphysics.Christopher Menzel - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...)
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  • Chains of Being: Infinite Regress, Circularity, and Metaphysical Explanation.Ross P. Cameron - 2022 - Oxford: Oxford University Press.
    'Chains of Being' argues that there can be infinite chains of dependence or grounding. Cameron also defends the view that there can be circular relations of ontological dependence or grounding, and uses these claims to explore issues in logic and ontology.
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  • Closed Structure.Peter Fritz, Harvey Lederman & Gabriel Uzquiano - 2021 - Journal of Philosophical Logic 50 (6):1249-1291.
    According to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, which involves restricting the scope of the claim that (...)
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  • A Theory of Necessities.Andrew Bacon & Jin Zeng - 2022 - Journal of Philosophical Logic 51 (1):151-199.
    We develop a theory of necessity operators within a version of higher-order logic that is neutral about how fine-grained reality is. The theory is axiomatized in terms of the primitive of *being a necessity*, and we show how the central notions in the philosophy of modality can be recovered from it. Various questions are formulated and settled within the framework, including questions about the ordering of necessities under strength, the existence of broadest necessities satisfying various logical conditions, and questions about (...)
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  • Classical Opacity.Michael Caie, Jeremy Goodman & Harvey Lederman - 2019 - Philosophy and Phenomenological Research 101 (3):524-566.
    Philosophy and Phenomenological Research, EarlyView.
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  • Counting Incompossibles.Peter Fritz & Jeremy Goodman - 2017 - Mind 126 (504):1063–1108.
    We often speak as if there are merely possible people—for example, when we make such claims as that most possible people are never going to be born. Yet most metaphysicians deny that anything is both possibly a person and never born. Since our unreflective talk of merely possible people serves to draw non-trivial distinctions, these metaphysicians owe us some paraphrase by which we can draw those distinctions without committing ourselves to there being merely possible people. We show that such paraphrases (...)
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  • Reality is not structured.Jeremy Goodman - 2017 - Analysis 77 (1):43–53.
    The identity predicate can be defined using second-order quantification: a=b =df ∀F(Fa↔Fb). Less familiarly, a dyadic sentential operator analogous to the identity predicate can be defined using third-order quantification: ϕ≡ψ =df ∀X(Xϕ↔Xψ), where X is a variable of the same syntactic type as a monadic sentential operator. With this notion in view, it is natural to ask after general principles governing its application. More grandiosely, how fine-grained is reality? -/- I will argue that reality is not structured in anything like (...)
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  • The essence of grounding.Justin Zylstra - 2019 - Synthese 196 (12):5137-5152.
    I develop a reduction of grounding to essence. My approach is to think about the relation between grounding and essence on the model of a certain conceptof existential dependence. I extend this concept of existential dependence in a coupleof ways and argue that these extensions provide a reduction of grounding to essenceif we use sorted variables that range over facts and take it that for a fact to obtain is forit to exist. I then use the account to resolve various (...)
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  • Essence, necessity, and definition.Justin Zylstra - 2019 - Philosophical Studies 176 (2):339-350.
    What is it for something to be essential to an item? For some time, it was standard to think that the concept of necessity alone can provide an answer: for something to be essential to an item is for it to be strictly implied by the existence of that item. We now tend to think that this view fails because its analysans is insufficient for its analysandum. In response, some argue that we can supplement the analysis in terms of necessity (...)
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  • Yablo Without Gödel.Volker Halbach & Shuoying Zhang - 2017 - Analysis 77 (1):53-59.
    We prove Yablo’s paradox without the diagonal lemma or the recursion theorem. Only a disquotation schema and axioms for a serial and transitive ordering are used in the proof. The consequences for the discussion on whether Yablo’s paradox is circular or involves self-reference are evaluated.
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  • Collective Essence and Monotonicity.Justin Zylstra - 2019 - Erkenntnis 84 (5):1087-1101.
    This paper focuses on the concept of collective essence: that some truths are essential to many items taken together. For example, that it is essential to conjunction and negation that they are truth-functionally complete. The concept of collective essence is one of the main innovations of recent work on the theory of essence. In a sense, this innovation is natural, since we make all sorts of plural predications. It stands to reason that there should be a distinction between essential and (...)
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