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Switch to: References
Citations of:
Necessitism, Contingentism, and Plural Quantification
Mind 119 (475):657-748 (2010)
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Inspired by Cantor's Theorem (CT), orthodoxy takes infinities to come in different sizes. The orthodox view has had enormous influence in mathematics, philosophy, and science. We will defend the contrary view---Countablism---according to which, necessarily, every infinite collection (set or plurality) is countable. We first argue that the potentialist or modal strategy for treating Russell's Paradox, first proposed by Parsons (2000) and developed by Linnebo (2010, 2013) and Linnebo and Shapiro (2019), should also be applied to CT, in a way that (...) |
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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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Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...) |
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Let us distinguish two kinds of contingentism: entity contingentism and metaphysical contingentism. Here, I use ‘entity’ very broadly to include anything over which we can quantify—objects (abstract and concrete), properties, and relations. Then entity contingentism about some entity, E, is the view that E exists contingently: that is, that E exists in some possible worlds and not in others. By contrast, entity necessitarianism about E is the view that E exists of necessity: that is, that E exists in all possible (...) |
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When the necessity of identity (NI) is combined with composition as identity (CAI), the contingency of composition (CC) is at risk. In the extant literature, either NI is seen as the basis for a refutation of CAI or CAI is associated with a theory of modality, such that: either NI is renounced (if counterpart theory is adopted); or CC is renounced (if the theory of modal parts is adopted). In this paper, we investigate the prospects of a new variety of (...) |
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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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This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory. |
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We consider a natural-language sentence that cannot be formally represented in a first-order language for epistemic two-dimensional semantics. We also prove this claim in the “Appendix” section. It turns out, however, that the most natural ways to repair the expressive inadequacy of the first-order language render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal. |
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Attributions of omnipresence, most familiar within the philosophy of religion, typically take the omnipresence of an entity to either consist in that entity's occupation of certain regions or be dependent upon other of that entity's attributes, such as omnipotence or omniscience. This paper defends an alternative conception of omnipresence that is independent of other purported divine attributes and dispenses with occupation. The resulting view repurposes the metaphysics of necessitism and permanentism, taking omnipresent entities to be those entities that exist at (...) |
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Different versions of the A-theory of time are traditionally defined in terms of whether everything is present, or whether there are also past and future things. In this paper I argue that the traditional way of defining A-theories should be abandoned. I focus on the traditional definition of presentism, according to which always, everything is present. First, I argue that there are good reasons to reject all the most plausible interpretations of the predicate ‘is present’ as it appears in the (...) |
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The actually-operator, understood as a rigidifier, has been employed for a range of purposes in natural language semantics. In this article I argue that the properties of the operator do not correspond to any feature of natural language or feature natural language users have access to. Nor is it needed to provide a formal representation of natural language sentences—the examples usually provided to illustrate the indispensability of the operator are much more plausibly interpreted using plural quantifiers. This lack of connection (...) |
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Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal scope. I (...) |
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There has been very little discussion of the appropriate principles to govern a modal logic of plurals. What debate there has been has accepted a principle I call (Necinc); informally if this is one of those then, necessarily: this is one of those. On this basis Williamson has criticised the Boolosian plural interpretation of monadic second-order logic. I argue against (Necinc), noting that it isn't a theorem of any logic resulting from adding modal axioms to the plural logic PFO+, and (...) |
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Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relative expressivity of quantified modal logics with so-called inner and outer (...) |
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According to Essentialism, an object’s properties divide into those that are essential and those that are accidental. While being human is commonly thought to be essential to Socrates, being a philosopher plausibly is not. We can motivate the distinction by appealing—as we just did—to examples. However, it is not obvious how best to characterize the notion of essential property, nor is it easy to give conclusive arguments for the essentiality of a given property. In this paper, I elaborate on these (...) |
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Pace Necessitism – roughly, the view that existence is not contingent – essential properties provide necessary conditions for the existence of objects. Sufficiency properties, by contrast, provide sufficient conditions, and individual essences provide necessary and sufficient conditions. This paper explains how these kinds of properties can be used to illuminate the ontological status of merely possible objects and to construct a respectable possibilist ontology. The paper also reviews two points of interaction between essentialism and modal logic. First, we will briefly (...) |
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Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it has been argued (...) |
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One important challenge for contingentists is that they seem to be unable to account for the meaning of some apparently meaningful modal discourse that is perfectly intelligible for necessitists. This worry is particularly pressing for higher-order contingentists, contingentists who hold that it is not only contingent which objects there are, but also contingent which semantic values there are for higher-order variables to quantify over. Objections against higher-order contingentism along these lines have been presented in Williamson (Mind 119(475):657–748, 2010; Modal logic (...) |
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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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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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Modal potentialism as proposed by Barbara Vetter (2015) is the view that every possibility is grounded in something having a potentiality. Drawing from work by Jessica Leech (2017), Samuel Kimpton-Nye (2021) argues that potentialists can have an S5 modal logic. I present a novel argument to the conclusion that the most straightforward way of spelling out modal potentialism cannot validate an S5 modal logic. Then I will propose a slightly tweaked version of modal potentialism that can validate an S5 modal (...) |
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In recent years, a variety of philosophers have argued that the fundamental bearers of representational properties like truth are concrete particulars produced by cognitive agents—representational vehicles (“RVs”), as I will call them. This view apparently conflicts with other judgments that are part of our common sense understanding of truth. For instance, it is plausible that there are truths about the Milky Way that have and never will never be articulated by anyone. Whatever these truths are, it looks like they cannot (...) |
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In this paper, we propose a new actualist and contingentist modal metaphysics – fundamental essentialism – according to which individuals just are realized essences. Orthodox possible worlds semantics is incompatible with actualism and contingentism since Kripke models in which paradigmatic contingentists propositions are true require possible worlds whose domain contain merely possible individuals. In light of this problem, Plantinga has developed modal metaphysics based on essences, but it has been claimed by Fine, Williamson, and others, that it cannot be upheld (...) |
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Necessitism is the controversial thesis that necessarily everything is necessarily something, namely that everything, everywhere, necessarily exists. What is controversial about necessitism is that, at its core, it claims that things could not have failed to exist, while we have a pre-theoretical intuition that not everything necessarily exists. Contingentism, in accordance with common sense, denies necessitism: it claims that some things could have failed to exist. Timothy Williamson is a necessitist and claims that David Lewis is a necessitist too. The (...) |
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In this paper, I motivate a modal account of propositions on the basis of an iterative conception of propositions. As an application, I suggest that the account provides a satisfying solution to the Russell-Myhill paradox. The account is in the spirit of recently developed modal accounts of sets motivated on the basis of the iterative conception of sets. |
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This paper presents a new argument for necessitism, the claim that necessarily everything is necessarily something. The argument appeals to principles about the metaphysics of quantification and predication which are best seen as constraints on reality’s fineness of grain. I give this argument in section 4; the impatient reader may skip directly there. Sections 1-3 set the stage by surveying three other arguments for necessitism. I argue that none of them are persuasive, but I think it is illuminating to consider (...) |
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Neo-Fregean approaches to set theory, following Frege, have it that sets are the extensions of concepts, where concepts are the values of second-order variables. The idea is that, given a second-order entity $X$, there may be an object $\varepsilon X$, which is the extension of X. Other writers have also claimed a similar relationship between second-order logic and set theory, where sets arise from pluralities. This paper considers two interpretations of second-order logic—as being either extensional or intensional—and whether either is (...) |
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Identity is a modally inflexible relation: two objects are necessarily identical or necessarily distinct. However, identity is not alone in this respect. We will look at the relation that one object bears to some objects if and only if it is one of them. In particular, we will consider the credentials of the thesis that no matter what some objects are, an object is necessarily one of them or necessarily not one of them. |
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Consider one of several things. Is the one thing necessarily one of the several? This key question in the modal logic of plurals is clarified. Some defenses of an affirmative answer are developed and compared. Various remarks are made about the broader philosophical significance of the question. |
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Timothy Williamson thinks that every object is a necessary, eternal existent. In defense of his view, Williamson appeals primarily to considerations from modal and tense logic. While I am uncertain about his modal claims, I think there are good metaphysical reasons to believe permanentism: the principle that everything always exists. B-theorists of time and change have long denied that objects change with respect to unqualified existence. But aside from Williamson, nearly all A-theorists defend temporaryism: the principle that there are temporary (...) |
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A‐theorists of time postulate a deep distinction between the present, past and future. Settling on an appropriate logic for such a view is no easy matter. This Philosophy Compass article describes one of the most vexing formal problems facing A‐theorists. It is commonly thought that A‐theories can only be formally expressed in a tense logic: a logic with operators like P and F . And it seems natural to think that we live in a world where objects come to exist (...) |
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Resumen En una serie de escritos Timothy Williamson ha argumentado a favor del necesitismo, esto es, la tesis de que es necesario que todo exista necesariamente. Este trabajo discute el necesitismo de segundo orden, esto es, la tesis de que es necesario que toda propiedad exista necesariamente, considerando líneas de argumentación semejantes a las desplegadas en primer orden. Se examinan tres de estos argumentos: el carácter necesario de ser una propiedad, la aparición de las propiedades en proposiciones, y los compromisos (...) |
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This thesis comprises three main chapters—each comprising one relatively standalone paper. The unifying theme is fragmentalism about truth, which is the view that the predicate “true” either expresses distinct concepts or expresses distinct properties. -/- In Chapter 1, I provide a formal development of alethic pluralism. Pluralism is the view that there are distinct truth properties associated with distinct domains of subject matter, where a truth property satisfies certain truth-characterizing principles. On behalf of pluralists, I propose an account of logic (...) |
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I develop a device for simulating quantification over merely possible objects from the perspective of a modal actualist ---someone who thinks that everything that exists actually exists. |
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The combinatorial theory of modality has long been dogged by the supposed problem that it entails that S5 is not the correct logic for metaphysical modality. In this paper, I suggest a modification to combinatorialism, to eliminate this tension with S5. I argue that the resulting view is more in the spirit of combinatorialism than the original position. |
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RESUMEN Se ha destacado que la Fórmula de Barcan -FB- y la Conversa de la Fórmula de Barcan -CFB- para lógica modal cuantificacional de orden superior parecen válidas. Si se interpreta que los cuantificadores tienen como rango propiedades, la validez de FB y CFB parece implicar la existencia de universales trascendentes, que no requieren estar instanciados para existir en un mundo posible. Se discute esta argumentación, porque la semántica, en la que los resultados de validez se siguen, no requiere que (...) |
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