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  1. Composition and Relative Counting.Massimiliano Carrara & Giorgio Lando - 2017 - Dialectica 71 (4):489-529.
    According to the so-called strong variant of Composition as Identity (CAI), the Principle of Indiscernibility of Identicals can be extended to composition, by resorting to broadly Fregean relativizations of cardinality ascriptions. In this paper we analyze various ways in which this relativization could be achieved. According to one broad variety of relativization, cardinality ascriptions are about objects, while concepts occupy an additional argument place. It should be possible to paraphrase the cardinality ascriptions in plural logic and, as a consequence, relative (...)
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  • Composition as Identity: A Study in Ontology and Philosophical Logic.Einar Bohn - unknown
    In this work I first develop, motivate, and defend the view that mereological composition, the relation between an object and all its parts collectively, is a relation of identity. I argue that this view implies and hence can explain the logical necessity of classical mereology, the formal study of the part-whole relation. I then critically discuss four contemporary views of the same kind. Finally, I employ my thesis in a recent discussion of whether the world is fundamentally one in number.
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  • Reference to Numbers in Natural Language.Friederike Moltmann - 2013 - Philosophical Studies 162 (3):499 - 536.
    A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract objects, (...)
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  • Two Syllogisms in the Mozi: Chinese Logic and Language.Byeong-uk Yi - 2019 - Review of Symbolic Logic 12 (3):589-606.
    This article examines two syllogistic arguments contrasted in an ancient Chinese book, the Mozi, which expounds doctrines of the Mohist school of philosophers. While the arguments seem to have the same form, one of them is valid but the other is not. To explain this difference, the article uses English plural constructions to formulate the arguments. Then it shows that the one-horse argument is valid because it has a valid argument form, the plural cousin of a standard form of valid (...)
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  • Metalogic and the Overgeneration Argument.Salvatore Florio & Luca Incurvati - 2019 - Mind 128 (511):761-793.
    A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely, the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. (...)
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  • Untyped Pluralism.Salvatore Florio - 2014 - Mind 123 (490):317-337.
    In the semantic debate about plurals, pluralism is the view that a plural term denotes some things in the domain of quantification and a plural predicate denotes a plural property, i.e. a property that can be instantiated by many things jointly. According to a particular version of this view, untyped pluralism, there is no type distinction between objects and properties. In this article, I argue against untyped pluralism by showing that it is subject to a variant of a Russell-style argument (...)
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  • Plural Identity.Joongol Kim - forthcoming - Philosophy and Phenomenological Research.
    Philosophy and Phenomenological Research, EarlyView.
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  • Higher‐Level Plurals Versus Articulated Reference, and an Elaboration of Salva Veritate.Hanoch Ben-Yami - 2013 - Dialectica 67 (1):81-102.
    In recent literature on plurals the claim has often been made that the move from singular to plural expressions can be iterated, generating what are occasionally called higher-level plurals or superplurals, often correlated with superplural predicates. I argue that the idea that the singular-to-plural move can be iterated is questionable. I then show that the examples and arguments intended to establish that some expressions of natural language are in some sense higher-level plurals fail. Next, I argue that these and some (...)
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  • Two Views of the Logic of Plurals and a Reduction of One to the Other.Nino B. Cocchiarella - 2015 - Studia Logica 103 (4):757-780.
    There are different views of the logic of plurals that are now in circulation, two of which we will compare in this paper. One of these is based on a two-place relation of being among, as in ‘Peter is among the juveniles arrested’. This approach seems to be the one that is discussed the most in philosophical journals today. The other is based on Bertrand Russell’s early notion of a class as many, by which is meant not a class as (...)
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  • Is There a Plural Object?Byeong-Uk Yi - forthcoming - In Donal Baxter & Aaron Cotnoir (eds.), Composition as Identity. Oxford University Press.
    A plurality or plural object is a single object that is also many, and pluralitism is the thesis that there is such an object. This paper argues that pluralitism and closely related theses (e.g., the many-one identity thesis and the composition as identity thesis) violate logic. To do so, it formulates an approach to the logic and semantics of plural constructions that results in plural logic and relates treatments of plural constructions to accounts of natural number. And it gives a (...)
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  • ‘Identity’ as a Mereological Term.Jeroen Smid - 2017 - Synthese 194 (7):2367-2385.
    The mereological predicate ‘is part of’ can be used to define the predicate ‘is identical with’. I argue that this entails that mereological theories can be ideologically simpler than nihilistic theories that do not use the notion of parthood—contrary to what has been argued by Ted Sider. Moreover, if one accepts an extensional mereology, there are good philosophical reasons apart from ideological simplicity to give a mereological definition of identity.
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  • The Number of Planets, a Number-Referring Term?Friederike Moltmann - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism: Essays in Philosophy of Mathematics. Oxford University Press. pp. 113-129.
    The question whether numbers are objects is a central question in the philosophy of mathematics. Frege made use of a syntactic criterion for objethood: numbers are objects because there are singular terms that stand for them, and not just singular terms in some formal language, but in natural language in particular. In particular, Frege (1884) thought that both noun phrases like the number of planets and simple numerals like eight as in (1) are singular terms referring to numbers as abstract (...)
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  • Natural Language Ontology.Friederike Moltmann - 2017 - Oxford Encyclopedia of Linguistics.
    The aim of natural language ontology is to uncover the ontological categories and structures that are implicit in the use of natural language, that is, that a speaker accepts when using a language. This article aims to clarify what exactly the subject matter of natural language ontology is, what sorts of linguistic data it should take into account, how natural language ontology relates to other branches of metaphysics, in what ways natural language ontology is important, and what may be distinctive (...)
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  • A Plural Reference Interpretation of Three-Dimensional Syntactic Trees.Friederike Moltmann - 2017 - In C. van Urk / H. Kotek / C. Halpert (eds.): A Pesky Set. Papers for David Pesetsky . MIT Working Papers in Linguistics (MITWPL) 80, MIT Cambridge (Mass.). Cambridge, MA:
    Various syntacticians have argued that coordinate structures involve a three-dimensional syntactic structure. This paper proposes an interpretation of three-dimensional syntactic structures in terms of plural reference and argues that such structures give further support for plural reference, the view that plural terms refer to several entities at once, rather than referring to a single plural individual.
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  • Mass Nouns and Plural Logic.David Nicolas - 2008 - Linguistics and Philosophy 31 (2):211-244.
    A dilemma put forward by Schein (1993) and Rayo (2002) suggests that, in order to characterize the semantics of plurals, we should not use predicate logic, but non-singular logic, a formal language whose terms may refer to several things at once. We show that a similar dilemma applies to mass nouns. If we use predicate logic and sets, we arrive at a Russellian paradox when characterizing the semantics of mass nouns. Likewise, a semantics of mass nouns based upon predicate logic (...)
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  • Self-Consciousness in Animals: Advantages and Problems of a Multipronged Approach.Florian Leonhard Wüstholz - 2015 - Kriterion - Journal of Philosophy 29 (1):1-18.
    Self-consciousness in non-human animals is a complex phenomenon which raises both conceptual and methodological problems. First, what do we mean by the concept of ‘self-consciousness’? Secondly, what is the best experimental approach to self-consciousness? This paper gives a short overview of the concept of self-consciousness in section 1. We can understand the concept of self-consciousness as capturing the ability of subjects to consciously think about themselves as themselves. If this is accurate, then it is prudent to look at a broad (...)
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  • Semantische Aspekte Pluraler Prädikatenlogischer Sprachen.Jonathan Lukic - 2015 - Kriterion - Journal of Philosophy 29 (1):99-121.
    Plural constructions in mathematical speech are no rarity. E.g., when we want to say that the real numbers are the basis on which we construct Calculus (cf. [16], p. 6), and that the integers are an integral domain (cf. [14], p. 237), we are not talking about one thing, namely the set of the real numbers and the set of the integers, respectively, but we are talking about several things, namely the real numbers and the integers, respectively. In the present (...)
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  • Mass Nouns and Plurals.Peter Lasersohn - 2011 - In Claudia Maienborn, Klaus von Heusinger & Paul Portner (eds.), Semantics: An International Handbook of Natural Language Meaning. De Gruyter Mouton. pp. 2.
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  • Superplurals in English.Øystein Linnebo & David Nicolas - 2008 - Analysis 68 (3):186–197.
    where ‘aa’ is a plural term, and ‘F’ a plural predicate. Following George Boolos (1984) and others, many philosophers and logicians also think that plural expressions should be analysed as not introducing any new ontological commitments to some sort of ‘plural entities’, but rather as involving a new form of reference to objects to which we are already committed (for an overview and further details, see Linnebo 2004). For instance, the plural term ‘aa’ refers to Alice, Bob and Charlie simultaneously, (...)
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  • WHAT More IS.Alexis Wellwood - forthcoming - Philosophical Perspectives.
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  • Plural Logic and Sensitivity to Order.Salvatore Florio & David Nicolas - 2015 - Australasian Journal of Philosophy 93 (3):444-464.
    Sentences that exhibit sensitivity to order (e.g. 'John and Mary arrived at school in that order' and 'Mary and John arrived at school in that order') present a challenge for the standard formulation of plural logic. In response, some authors have advocated new versions of plural logic based on fine-grained notions of plural reference, such as serial reference (Hewitt 2012) and articulated reference (Ben-Yami 2013). The aim of this article is to show that sensitivity to order should be accounted for (...)
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  • Yi on 2.Joongol Kim - 2010 - Philosophia Mathematica 18 (3):329-336.
    Byeong-Uk Yi has argued that number words like ‘two’ primarily function as numerical predicates as in ‘Socrates and Hippias are two ’, and other grammatical uses of number words can be paraphrased in terms of the predicative use. This paper critically examines Yi’s paraphrase scheme and also some other alternative schemes, and argues that the adjectival use of number words as in ‘The Scots and the Irish are two peoples’ cannot be paraphrased in terms of the predicative use.
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  • Abstract Objects and the Core-Periphery Distinction in the Ontological and the Conceptual Domain of Natural Language.Friederike Moltmann - forthcoming - In José Luis Falguera & Concha Martínez-Vida (eds.), Abstract Objects: For and Against. Springer.
    This paper elaborates distinctions between a core and a periphery in the ontological and the conceptual domain associated with natural language. The ontological core-periphery distinction is essential for natural language ontology and is the basis for the central thesis of my 2013 book Abstract Objects and the Semantics of Natural Language, namely that natural language permits reference to abstract objects in its periphery, but not its core.
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  • Predication as Ascription.David Liebesman - 2015 - Mind 124 (494):517-569.
    I articulate and defend a necessary and sufficient condition for predication. The condition is that a term or term-occurrence stands in the relation of ascription to its designatum, ascription being a fundamental semantic relation that differs from reference. This view has dramatically different semantic consequences from its alternatives. After outlining the alternatives, I draw out these consequences and show how they favour the ascription view. I then develop the view and elicit a number of its virtues.
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  • The Logic of the Trinity.Einar Duenger Bohn - 2011 - Sophia 50 (3):363-374.
    Roughly, the problem of the Trinity is the problem of how God can be one and yet be the Father, the Son, and the Holy Spirit, which are three, not one. That one thing is identical with three distinct things seems to violate traditional laws of identity. I propose a solution to this problem according to which it is just an ordinary claim of one-many identity. For example, one pair of shoes is identical with two shoes; and my one body (...)
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  • Can Semantics Guide Ontology?Katherine Ritchie - 2016 - Australasian Journal of Philosophy 94 (1):24-41.
    Since the linguistic turn, many have taken semantics to guide ontology. Here, I argue that semantics can, at best, serve as a partial guide to ontological commitment. If semantics were to be our guide, semantic data and semantic treatments would need to be taken seriously. Through an examination of plurals and their treatments, I argue that there can be multiple, equally semantically adequate, treatments of a natural language theory. Further, such treatments can attribute different ontological commitments to a theory. Given (...)
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  • Leibniz on Infinite Numbers, Infinite Wholes, and Composite Substances.Adam Harmer - 2014 - British Journal for the History of Philosophy 22 (2):236-259.
    Leibniz claims that nature is actually infinite but rejects infinite number. Are his mathematical commitments out of step with his metaphysical ones? It is widely accepted that Leibniz has a viable response to this problem: there can be infinitely many created substances, but no infinite number of them. But there is a second problem that has not been satisfactorily resolved. It has been suggested that Leibniz’s argument against the world soul relies on his rejection of infinite number, and, as such, (...)
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  • Critical Notice.Thomas J. McKay - 2008 - Canadian Journal of Philosophy 38 (2):301-323.
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  • Abstract Objects and the Semantics of Natural Language, by Friederike Moltmann.Byeong-Uk Yi - 2015 - Mind 124 (495):958-964.
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  • Construction Area (No Hard Hat Required).Karen Bennett - 2011 - Philosophical Studies 154 (1):79-104.
    A variety of relations widely invoked by philosophers—composition, constitution, realization, micro-basing, emergence, and many others—are species of what I call ‘building relations’. I argue that they are conceptually intertwined, articulate what it takes for a relation to count as a building relation, and argue that—contra appearances—it is an open possibility that these relations are all determinates of a common determinable, or even that there is really only one building relation.
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  • Composition as Identity: Part 1.Megan B. Wallace - 2011 - Philosophy Compass 6 (11):804-816.
    Many of us think that ordinary objects – such as tables and chairs – exist. We also think that ordinary objects have parts: my chair has a seat and some legs as parts, for example. But once we are committed to the thesis that ordinary objects are composed of parts, we then open ourselves up to a whole host of philosophical problems, most of which center on what exactly the composition relation is. Composition as Identity is the view that the (...)
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  • What We Can Do.Katherine Ritchie - forthcoming - Philosophical Studies:1-18.
    Plural first-person pronouns have often been ignored in the literature on indexicals and pronouns. The assumption seems to be that we is just the plural of I. So, we can focus on theorizing about singular indexicals and about non-indexical plurals then combine the results to yield a theory of plural indexicals. Here I argue that the “divide and conquer” strategy fails. By considering data involving plurals, generics, and complex demonstratives, I argue for a referential semantics on which we can refer (...)
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  • On the Innocence and Determinacy of Plural Quantification.Salvatore Florio & Øystein Linnebo - 2016 - Noûs 50 (3):565–583.
    Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics for plural logic (...)
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  • Monism, Emergence, and Plural Logic.Einar Duenger Bohn - 2012 - Erkenntnis 76 (2):211-223.
    In this paper I argue that we need to take irreducibly plural logic more seriously in metaphysical debates due to the fact that the verdict of many metaphysical debates hangs on it. I give two examples. The main example I focus on is the debate recently revived by Jonathan Schaffer over the fundamental cardinality of the world. I show how the three main arguments provided by Schaffer are unsound in virtue of an employment of plural logic. The second example I (...)
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  • Emergence for Nihilists.Richard L. J. Caves - 2018 - Pacific Philosophical Quarterly 99 (1):2-28.
    I defend mereological nihilism, the view that there are no composite objects, against a challenge from ontological emergence, the view that some things have properties that are ‘something over and above’ the properties of their parts. As the nihilist does not believe in composite wholes, there is nothing in the nihilist's ontology to instantiate emergent properties – or so the challenge goes. However, I argue that some simples can collectively instantiate an emergent property, so the nihilist's ontology can in fact (...)
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  • Too Much Reference: Semantics for Multiply Signifying Terms.Greg Frost-Arnold - 2008 - Journal of Philosophical Logic 37 (3):239-257.
    The logic of singular terms that refer to nothing, such as ‘Santa Claus,’ has been studied extensively under the heading of free logic. The present essay examines expressions whose reference is defective in a different way: they signify more than one entity. The bulk of the effort aims to develop an acceptable formal semantics based upon an intuitive idea introduced informally by Hartry Field and discussed by Joseph Camp; the basic strategy is to use supervaluations. This idea, as it stands, (...)
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  • Stuff and Coincidence.Thomas J. McKay - 2015 - Philosophical Studies 172 (11):3081-3100.
    Anyone who admits the existence of composite objects allows a certain kind of coincidence, coincidence of a thing with its parts. I argue here that a similar sort of coincidence, coincidence of a thing with the stuff that constitutes it, should be equally acceptable. Acknowledgement of this is enough to solve the traditional problem of the coincidence of a statue and the clay or bronze it is made of. In support of this, I offer some principles for the persistence of (...)
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  • Tensed Mereology.Paul Hovda - 2013 - Journal of Philosophical Logic 42 (2):241-283.
    Classical mereology (CM) is usually taken to be formulated in a tenseless language, and is therefore associated with a four-dimensionalist metaphysics. This paper presents three ways one might integrate the core idea of flat plenitude, i.e., that every suitable condition or property has exactly one mereological fusion, with a tensed logical setting. All require a revised notion of mereological fusion. The candidates differ over how they conceive parthood to interact with existence in time, which connects to the distinction between endurance (...)
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  • Plural Quantification Logic: A Critical Appraisal.Hanoch Ben-Yami - 2009 - Review of Symbolic Logic 2 (1):208-232.
    I first show that most authors who developed Plural Quantification Logic (PQL) argued it could capture various features of natural language better than can other logic systems. I then show that it fails to do so: it radically departs from natural language in two of its essential features; namely, in distinguishing plural from singular quantification and in its use of an relation. Next, I sketch a different approach that is more adequate than PQL for capturing plural aspects of natural language (...)
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  • Unrestricted Quantification.Salvatore Florio - 2014 - Philosophy Compass 9 (7):441-454.
    Semantic interpretations of both natural and formal languages are usually taken to involve the specification of a domain of entities with respect to which the sentences of the language are to be evaluated. A question that has received much attention of late is whether there is unrestricted quantification, quantification over a domain comprising absolutely everything there is. Is there a discourse or inquiry that has absolute generality? After framing the debate, this article provides an overview of the main arguments for (...)
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  • The Logic and Meaning of Plurals. Part II.Byeong-uk Yi - 2006 - Journal of Philosophical Logic 35 (3):239-288.
    In this sequel to "The logic and meaning of plurals. Part I", I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the (...)
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  • Composition as Identity: Part 1.Meg Wallace - 2011 - Philosophy Compass 6 (11):804-816.
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