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Summary Higher-order metaphysics uses the formal languages of higher-order logic to formulate metaphysical views and arguments. Depending on the particular higher-order language used, higher-order quantifiers are often used to express general claims for which one would otherwise have to rely on a plenitudinous ontology of propositions, properties, and relations. For example, saying in English that some relation satisfies the axioms of minimal mereology incurs a commitment to the existence of relations. In contrast, second-order logic allows one conjoin the axioms of minimal mereology, and then generalize with respect to parthood, by replacing the constant for parthood by a binary second-order variable and binding it with an existential quantifier. Some proponents of higher-order metaphysics claim that along these lines, higher-order logic allows one to improve upon ordinary talk of propositions, properties, and relations. Consequently, they adopt a primitivist approach to higher-order languages, on which their intended interpretation is not provided by any translation into informal language or formal model theory.
Key works Williamson 2003 argued for a primitivist interpretation of higher-order logic, and applied a modal higher-order language with such an interpretation to modal metaphysics in Williamson 2013Dorr 2006 made a case for the importance of identifications in higher-order metaphysics. Fritz & Jones 2024 provides an overview of the various debates and positions in the field.
Introductions Skiba 2021, Bacon 2024Goodman 2024
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  1. Could the truths of mathematics have been different?Andrew Bacon - manuscript
    Could the truths of mathematics have been different than they in fact are? If so, which truths could have been different? Do the contingent mathematical facts supervene on physical facts, or are they free floating? I investigate these questions within a framework of higher-order modal logic, drawing sometimes surprising connections between the necessity of arithmetic and analysis and other theses of modal metaphysics: the thesis that possibility in the broadest sense is governed by a logic of S5, that what is (...)
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  2. Special Quantifiers: Higher-Order Quantification and Nominalization.Friederike Moltmann - manuscript
    Special quantifiers are quantifiers like 'something', 'everything', and 'several things'. They are special both semantically and syntactically and play quite an important role in philosophy, in discussions of ontological commitment to abstract objects, of higher-order metaphysics, and of the apparent need for propositions. This paper will review and discuss in detail the syntactic and semantic peculiarities of special quantifiers and show that they are incompatible with substitutional and higher-order analyses that have recently been proposed. It instead defends and develops in (...)
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  3. Mathematical Modality: An Investigation in Higher-order Logic.Andrew Bacon - forthcoming - Journal of Philosophical Logic.
    An increasing amount of contemporary philosophy of mathematics posits, and theorizes in terms of special kinds of mathematical modality. The goal of this paper is to bring recent work on higher-order metaphysics to bear on the investigation of these modalities. The main focus of the paper will be views that posit mathematical contingency or indeterminacy about statements that concern the `width' of the set theoretic universe, such as Cantor's continuum hypothesis. Within a higher-order framework I show that contingency about the (...)
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  4. The Argument from Determinate Vagueness.Jaime Castillo-Gamboa - forthcoming - Oxford Studies in Metaphysics.
    The Lewis-Sider argument from vagueness is one of the most powerful objections against restricted composition. Many have resisted the argument by rejecting its key premise, namely that existence is not vague. In this paper, I argue that this strategy is ineffective as a response to vagueness-based objections against restricted composition. To that end, I formulate a new argument against restricted composition: the argument from determinate vagueness. Unlike the Lewis-Sider argument, my argument doesn’t require accepting that existence is not vague, but (...)
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  5. Monism and the Ontology of Logic.Samuel Elgin - forthcoming - Milton Park, Abingdon, Oxon: Routledge.
    Monism is the claim that only one object exists. While few contemporary philosophers endorse monism, it has an illustrious history – stretching back to Bradley, Spinoza and Parmenides. In this paper, I show that plausible assumptions about the higher-order logic of property identity entail that monism is true. Given the higher-order framework I operate in, this argument generalizes: it is also possible to establish that there is a single property, proposition, relation, etc. I then show why this form of monism (...)
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  6. Against Instantiation.Christopher Frugé - forthcoming - Australasian Journal of Philosophy.
    According to traditional universalism, properties are instantiated by objects, where instantiation is a ‘tie’ that binds objects and properties into facts. I offer two arguments against this view. I then develop an alternative higher-order account which holds that properties are primitively predicated of objects yet, unlike traditional nominalism, are nevertheless genuinely real. When it’s a fact that Fo, it’s not because object o instantiates F-ness, but just that Fo – where F still exists. Against orthodox higher-order approaches, however, my arguments (...)
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  7. The Case Against Higher-Order Metaphysics.Thomas Hofweber - forthcoming - Metaphysics 5 (1):29-50.
    Although higher-order metaphysics seems prima facie to be a promising new approach to metaphysics, it is nonetheless based on a mistake. This mistake is tied to a misuse of formal languages in metaphysics in general, not just to the use of higher-order rather than lower-order languages. I hope to highlight the mistake by discussing a popular recent example of higher- order metaphysics: the argument that reality is not structured using reasoning inspired by the Russell-Myhill paradox. A key issue will be (...)
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  8. Review of Properties and Propositions: The Metaphysics of Higher-Order Logic by Robert Trueman. [REVIEW]Nicholas K. Jones - forthcoming - Mind.
    This is a review of "Properties and Propositions: The Metaphysics of Higher-Order Logic" by Robert Trueman. Following an overview of the main themes of the book, I discuss the metaphysical presuppositions of Trueman's Fregean notation for predicate abstraction and evaluate his argument for strict typing.
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  9. Special Quantification: Substitutional, Higher-Order, and Nominalization Approaches.Friederike Moltmann - forthcoming - In Alex Grzankowski & Anthony Savile (eds.), Thought: its Origin and Reach. Essays in Honour of Mark Sainsbury. Routledge.
    Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like 'something' permit a replacement, preserving grammaticality or the same reading of the verb: (1) a. John claims that he won. b. ??? John claims a proposition / some thing. c. John claims something. In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other (...)
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  10. Ordinal Type Theory.Jan Plate - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, understood as (...)
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  11. Engineering Existence?Lukas Skiba - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    This paper investigates the connection between two recent trends in philosophy: higher-orderism and conceptual engineering. Higher-orderists use higher-order quantifiers (in particular quantifiers binding variables that occupy the syntactic positions of predicates) to express certain key metaphysical doctrines, such as the claim that there are properties. I argue that, on a natural construal, the higher-orderist approach involves an engineering project concerning, among others, the concept of existence. I distinguish between a modest construal of this project, on which it aims at engineering (...)
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  12. Mathematical Modality: An Investigation in Higher-order Logic.Andrew Bacon - 2024 - Journal of Philosophical Logic 53 (1):131-179.
    An increasing amount of contemporary philosophy of mathematics posits, and theorizes in terms of special kinds of mathematical modality. The goal of this paper is to bring recent work on higher-order metaphysics to bear on the investigation of these modalities. The main focus of the paper will be views that posit mathematical contingency or indeterminacy about statements that concern the ‘width’ of the set theoretic universe, such as Cantor’s continuum hypothesis. Within a higher-order framework I show that contingency about the (...)
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  13. A Case For Higher-Order Metaphysics.Andrew Bacon - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    Higher-order logic augments first-order logic with devices that let us generalize into grammatical positions other than that of a singular term. Some recent metaphysicians have advocated for using these devices to raise and answer questions that bear on many traditional issues in philosophy. In contrast to these 'higher-order metaphysicians', traditional metaphysics has often focused on parallel, but importantly different, questions concerning special sorts of abstract objects: propositions, properties and relations. The answers to the higher-order and the property-theoretic questions may coincide (...)
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  14. Classicism.Andrew Bacon & Cian Dorr - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press. pp. 109-190.
    This three-part chapter explores a higher-order logic we call ‘Classicism’, which extends a minimal classical higher-order logic with further axioms which guarantee that provable coextensiveness is sufficient for identity. The first part presents several different ways of axiomatizing this theory and makes the case for its naturalness. The second part discusses two kinds of extensions of Classicism: some which take the view in the direction of coarseness of grain (whose endpoint is the maximally coarse-grained view that coextensiveness is sufficient for (...)
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  15. A fictionalist theory of universals.Tim Button & Robert Trueman - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.
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  16. Constructive Type Theory, an appetizer.Laura Crosilla - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    Recent debates in metaphysics have highlighted the significance of type theories, such as Simple Type Theory (STT), for our philosophical analysis. In this chapter, I present the salient features of a constructive type theory in the style of Martin-Löf, termed CTT. My principal aim is to convey the flavour of this rich, flexible and sophisticated theory and compare it with STT. I especially focus on the forms of quantification which are available in CTT. A further aim is to argue that (...)
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  17. Symmetry and Hybrid Contingentism.Maegan Fairchild - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    This paper outlines a defense of hybrid contingentism: that it is contingent which individuals there are, but not contingent what properties there are. Critics pursue two main lines of complaint. First, that the hybrid contingentist’s treatment of haecceitistic properties is metaphysically mysterious, and second, that hybrid contingentism involves an unjustified asymmetry in the associated modal logic. I suggest that these complaints may be too quick, at least in the setting of higher-order metaphysics. It is not at all obvious whether and (...)
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  18. Higher-Order Metaphysics.Peter Fritz & Nicholas K. Jones (eds.) - 2024 - Oxford University Press.
    This volume explores the use of higher-order logics in metaphysics. Seventeen original essays trace the development of higher-order metaphysics, discuss different ways in which higher-order languages and logics may be used, and consider their application to various central topics of metaphysics.
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  19. Higher-Order Metaphysics: An Introduction.Peter Fritz & Nicholas K. Jones - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics used in metaphysics, and indicate a (...)
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  20. Higher-order logic as metaphysics.Jeremy Goodman - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, it is then shown how we can use pure higher-order logic to (...)
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  21. Quantification and ontological commitment.Nicholas K. Jones - 2024 - In Anna Sofia Maurin & Anthony Fisher (eds.), Routledge Handbook on Properties.
    This chapter discusses ontological commitment to properties, understood as ontological correlates of predicates. We examine the issue in four metaontological settings, beginning with an influential Quinean paradigm on which ontology concerns what there is. We argue that this naturally but not inevitably avoids ontological commitment to properties. Our remaining three settings correspond to the most prominent departures from the Quinean paradigm. Firstly, we enrich the Quinean paradigm with a primitive, non-quantificational notion of existence. Ontology then concerns what exists. We argue (...)
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  22. Higher-Order Metaphysics in Frege and Russell.Kevin C. Klement - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press. pp. 355-377.
    This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between objects and functions. (...)
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  23. Higher-order metaphysics and propositional attitudes.Harvey Lederman - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    According to relationism, for Alice to believe that some rabbits can speak is for Alice to stand in a relation to a further entity, some rabbits can speak. But what could this further entity possibly be? Higher-order metaphysics seems to offer a simple, natural answer. On this view (roughly put), expressions in different syntactic categories (for instance: names, predicates, sentences) in general denote entities in correspondingly different ontological categories. Alice's belief can thus be understood to relate her to a sui (...)
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  24. 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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  25. Against Second-Order Primitivism.Bryan Pickel - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    In the language of second-order logic, first- and second-order variables are distinguished syntactically and cannot be grammatically substituted. According to a prominent argument for the deployment of these languages, these substitution failures are necessary to block the derivation of paradoxes that result from attempts to generalize over predicate interpretations. I first examine previous approaches which interpret second-order sentences using expressions of natural language and argue that these approaches undermine these syntactic restrictions. I then examine Williamson’s primitivist approach according to which (...)
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  26. A Theory of Structured Propositions.Andrew Bacon - 2023 - Philosophical Review 132 (2):173-238.
    This paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell-Myhill paradox doesn't arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the $\lambda$-calculus, about what properties and relations can be built. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory is given both a (...)
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  27. Fundamental Things: Theory and Applications of Grounding.Louis deRosset - 2023 - Oxford, GB: Oxford University Press.
    The scientific successes of the last 400 years strongly suggest a view on which things are organized into layers, with phenomena in higher layers dependent on and determined by what goes on below. Philosophers have recently explored the idea that we can make sense of this idea by appeal to a relation called grounding. This book develops the rudiments of a theory of grounding, and applies that theory to questions of independent interest. The theorizing consists in saying in more detail (...)
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  28. Are there iterated essentialist truths?Andreas Ditter - 2023 - Analysis 84 (1):3-12.
    Let an iterated essentialist statement be a statement of the form 'It lies in the nature of x1,x2,... that it lies in the nature of y1,y2,... that φ'. Let Iteration be the thesis that there are true iterated essentialist statements. Iteration has recently been disputed by Dasgupta (2014) and Glazier (2017). Both authors take the falsity of Iteration to be central to the explanatory role of essentialist truths. An important consequence that is not explicitly noted by them is that the (...)
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  29. Two conceptions of absolute generality.Salvatore Florio & Nicholas K. Jones - 2023 - Philosophical Studies 180 (5-6):1601-1621.
    What is absolutely unrestricted quantification? We distinguish two theoretical roles and identify two conceptions of absolute generality: maximally strong generality and maximally inclusive generality. We also distinguish two corresponding kinds of absolute domain. A maximally strong domain contains every potential counterexample to a generalisation. A maximally inclusive domain is such that no domain extends it. We argue that both conceptions of absolute generality are legitimate and investigate the relations between them. Although these conceptions coincide in standard settings, we show how (...)
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  30. The Foundations of Modality: From Propositions to Possible Worlds.Peter Fritz - 2023 - Oxford: Oxford University Press.
    This book develops an argument for a foundational theory of modality using higher-order logic. The use of higher-order logic in metaphysics is motivated, and a particular higher-order logic is introduced. Fine-grained theories of propositional individuation are shown to be problematic, and a course-grained theory of propositional individuation is defended. On the basis of this theory, it is argued that the metaphysical necessities can be delineated using purely logical terms; by adding an actuality operator, it is shown that the logic of (...)
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  31. Operands and Instances.Peter Fritz - 2023 - Review of Symbolic Logic 16 (1):188-209.
    Can conjunctive propositions be identical without their conjuncts being identical? Can universally quantified propositions be identical without their instances being identical? On a common conception of propositions, on which they inherit the logical structure of the sentences which express them, the answer is negative both times. Here, it will be shown that such a negative answer to both questions is inconsistent, assuming a standard type-theoretic formalization of theorizing about propositions. The result is not specific to conjunction and universal quantification, but (...)
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  32. Higher-Order Metaphysics and Small Differences. [REVIEW]Timothy Williamson - 2023 - Analysis 83 (1):213-224.
    Conspicuously missing some planks, a latter-day Ship of Theseus catches the eye when one picks up this Book of Three Authors. Teasingly, differentiated preposit.
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  33. 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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  34. Against Cumulative Type Theory.Tim Button & Robert Trueman - 2022 - Review of Symbolic Logic 15 (4):907-49.
    Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions imposed by (...)
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  35. Modal Pluralism and Higher‐Order Logic.Justin Clarke-Doane & William McCarthy - 2022 - Philosophical Perspectives 36 (1):31-58.
    In this article, we discuss a simple argument that modal metaphysics is misconceived, and responses to it. Unlike Quine's, this argument begins with the simple observation that there are different candidate interpretations of the predicate ‘could have been the case’. This is analogous to the observation that there are different candidate interpretations of the predicate ‘is a member of’. The argument then infers that the search for metaphysical necessities is misguided in much the way the ‘set-theoretic pluralist’ claims that the (...)
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  36. Essence and Necessity.Andreas Ditter - 2022 - Journal of Philosophical Logic 51 (3):653-690.
    What is the relation between metaphysical necessity and essence? This paper defends the view that the relation is one of identity: metaphysical necessity is a special case of essence. My argument consists in showing that the best joint theory of essence and metaphysical necessity is one in which metaphysical necessity is just a special case of essence. The argument is made against the backdrop of a novel, higher-order logic of essence, whose core features are introduced in the first part of (...)
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  37. The case against higher-order metaphysics.Thomas Hofweber - 2022 - Metaphysics 1 (5):29-50.
    Although higher-order metaphysics seems prima facie to be a promising new approach to metaphysics, it is nonetheless based on a mistake. This mistake is tied to a misuse of formal languages in metaphysics in general, not just to the use of higher-order rather than lower-order languages. I hope to highlight the mistake by discussing a popular recent example of higher- order metaphysics: the argument that reality is not structured using reasoning inspired by the Russell-Myhill paradox. A key issue will be (...)
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  38. In Defence of Hybrid Contingentism.Lukas Skiba - 2022 - Philosophers' Imprint 22 (4):1-30.
    Hybrid contingentism combines first-order contingentism, the view that it is contingent what individuals there are, with higher-order necessitism, the view that it is non-contingent what properties and propositions there are (where these are conceived as entities in the range of appropriate higher-order quantifiers). This combination of views avoids the most delicate problems afflicting alternative contingentist positions while preserving the central contingentist claim that ordinary, concrete entities exist contingently. Despite these attractive features, hybrid contingentism is usually faced with rejection. The main (...)
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  39. Book Review - Trueman, Robert. Properties and Propositions: The Metaphysics of Higher-Order Logic. Cambridge: Cambridge University Press, 2021. [REVIEW]Ricardo Barroso Batista - 2021 - Revista Portuguesa de Filosofia 77 (4):1549-1554.
    A comunidade de filósofos da Metafísica Analítica Contemporânea não consegue entender-se com respeito ao estatuto ontológico das “Propriedades”. Uma parte defende que as propriedades existem, mas, têm grandes dificuldades em explicar a sua existência. Outra parte acredita que as propriedades não existem, mas, não conseguem justificar o problema ontológico da sua predicação. Esta divisão é o tema central deste livro que vos apresentamos, intitulado, “Properties and Propositions: The Metaphysics of Higher-Order Logic” da autoria de Robert Trueman e publicado pela Cambridge (...)
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  40. The Bounds of Possibility: Puzzles of Modal Variation.Cian Dorr, John Hawthorne & Juhani Yli-Vakkuri - 2021 - Oxford: Oxford University Press. Edited by John Hawthorne & Juhani Yli-Vakkuri.
    In general, a given object could have been different in certain respects. For example, the Great Pyramid could have been somewhat shorter or taller; the Mona Lisa could have had a somewhat different pattern of colours; an ordinary table could have been made of a somewhat different quantity of wood. But there seem to be limits. It would be odd to suppose that the Great Pyramid could have been thimble-sized; that the Mona Lisa could have had the pattern of colours (...)
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  41. Unrestricted Quantification and the Structure of Type Theory.Salvatore Florio & Nicholas K. Jones - 2021 - Philosophy and Phenomenological Research 102 (1):44-64.
    Semantic theories based on a hierarchy of types have prominently been used to defend the possibility of unrestricted quantification. However, they also pose a prima facie problem for it: each quantifier ranges over at most one level of the hierarchy and is therefore not unrestricted. It is difficult to evaluate this problem without a principled account of what it is for a quantifier to be unrestricted. Drawing on an insight of Russell’s about the relationship between quantification and the structure of (...)
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  42. Ground and Grain.Peter Fritz - 2021 - Philosophy and Phenomenological Research 105 (2):299-330.
    Current views of metaphysical ground suggest that a true conjunction is immediately grounded in its conjuncts, and only its conjuncts. Similar principles are suggested for disjunction and universal quantification. Here, it is shown that these principles are jointly inconsistent: They require that there is a distinct truth for any plurality of truths. By a variant of Cantor’s Theorem, such a fine-grained individuation of truths is inconsistent. This shows that the notion of grounding is either not in good standing, or that (...)
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  43. 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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  44. Necessitism, Contingentism, and Theory Equivalence.Bruno Jacinto - 2021 - Bulletin of Symbolic Logic 27 (2):217-218.
    Necessitism, Contingentism, and Theory Equivalence is a dissertation on issues in higher-order modal metaphysics. Consider a modal higher-order language with identity in which the universal quantifier is interpreted as expressing universal quantification and the necessity operator is interpreted as expressing metaphysical necessity. The main question addressed in the dissertation concerns the correct theory formulated in this language. A different question that also takes centre stage in the dissertation is what it takes for theories to be equivalent.The whole dissertation consists of (...)
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  45. Should a higher-order metaphysician believe in properties?David Liggins - 2021 - Synthese 199 (3-4):10017-10037.
    In this paper I take second order-quantification to be a sui generis form of quantification, irreducible to first-order quantification, and I examine the implications of doing so for the debate over the existence of properties. Nicholas K. Jones has argued that adding sui generis second-order quantification to our ideology is enough to establish that properties exist. I argue that Jones does not settle the question of whether there are properties because—like other ontological questions—it is first-order. Then I examine three of (...)
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  46. From Physical to Metaphysical Necessity.Alexander Roberts - 2021 - Mind 131 (524):1216-1246.
    Let Nomological Bound be the thesis that there is nothing objectively possible beyond what is physically possible. Nomological Bound has struck many as a live hypothesis. Nevertheless, in this article I provide a novel argument against it. Yet even though I claim that Nomological Bound is false, I argue that the boundaries of objective possibility can still be characterized intimately in terms of physical necessity. This is philosophically significant, for on a natural understanding it constitutes the powerful anti-sceptical result that (...)
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  47. Is identity non‐contingent?Alexander Roberts - 2021 - Philosophy and Phenomenological Research 106 (1):3-34.
    I present a novel argument against the non-contingency of identity. I first argue that the necessity of distinctness is intimately connected with numerous paradoxes of recombination. In particular, I argue that those who reject the necessity of distinctness have natural solutions to various paradoxes of recombination which have plagued the metaphysics of modality. Moreover, I argue that adding the necessity of distinctness to modest, paradox-free assumptions is sufficient to reinstate the paradoxes. Given that identity is non-contingent only if distinctness is (...)
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  48. Higher‐order metaphysics.Lukas Skiba - 2021 - Philosophy Compass 16 (10):1-11.
    Subverting a once widely held Quinean paradigm, there is a growing consensus among philosophers of logic that higher-order quantifiers (which bind variables in the syntactic position of predicates and sentences) are a perfectly legitimate and useful instrument in the logico-philosophical toolbox, while neither being reducible to nor fully explicable in terms of first-order quantifiers (which bind variables in singular term position). This article discusses the impact of this quantificational paradigm shift on metaphysics, focussing on theories of properties, propositions, and identity, (...)
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  49. Higher-order metaphysics and the tropes versus universals dispute.Lukas Skiba - 2021 - Philosophical Studies 178 (9):2805-2827.
    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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  50. Logical Combinatorialism.Andrew Bacon - 2020 - Philosophical Review 129 (4):537-589.
    In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the “book of the world.” This paper attempts to make good on this metaphor. To that end, a modality is introduced that, put informally, stands to propositions as logical truth stands to sentences. (...)
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