Is it possible to get by with just one ontological category? We evaluate L.A. Paul's attempt to do so: the mereological bundle theory. The upshot is that Paul's attempt to construct a one category ontology may be challenged with some of her own arguments. In the positive part of the paper we outline a two category ontology with property universals and kind universals. We will also examine Paul's arguments against a version of universal bundle theory that takes spatiotemporal (...) co-location instead of compresence or coinstantiation as the feature by which we can identify genuine bundles. We compare this novel theory, bundle theory with kinds, and Paul's mereological bundle theory and apply them to a case study concerning entangled fermions and co-located bosons. (shrink)

Bundle theory takes objects to be bundles of properties. Some bundle theorists take objects to be bundles of instantiated universals, and some take objects to be bundles of tropes. Tropes are instances of properties: some take instantiated universals to be tropes, while others deny the existence of universals and take tropes to be ontologically fundamental. Historically, the bundling relation has been taken to be a primitive relation, not analyzable in terms of or ontologically reducible to some other relation, (...) and has been variously characterized as, e.g., “compresence,” “concurrence,” or “consubstantiation.” Bertrand Russell (1940) defends compresence of universals, and Hector-Neri Castañeda (1974) defends consubstantiation of universals. John Bacon (1995) defends concurrent tropes and Keith Campbell (1990) defends compresent tropes. Jonathan Schaffer (2001) bucks this trend, endorsing compresence understood as co-location in spacetime, but this brings with it undesireable consequences such as the impossibility of distinguishing between objects (such as electrons or other microentities) with the same location. Mereological bundle theory improves upon traditional bundle theory by taking the primitive relation of bundling to be the more familiar relation of fusing or composing, such that objects are fusions of properties or fusions of property instances. Hence, mereological bundle theorists endorse a property mereology: a mereology where properties or property instances can be parts of objects. An advantage of the approach derives from the fact that standard mereologies take composition to be primitive or define it using a different primitive mereological notion (such as primitive parthood). Thus, taking the basic primitive of bundle theory to be composition can reduce the need for.. (shrink)

The strongest version of the principle of the Identity of Indiscernibles states that of necessity, there are no distinct things with all their universals in common (where such putative haecceities as being Aristotle do not count as universals: I use 'universal' rather than 'property' here and in what follows for the simple reason that 'universal' is the term of art that most safely excludes haecceities from its instances). It is commonly supposed that Max Black's famous paper 'The identity of indiscernibles' (...) (2) refutes this thesis. (Armstong's [1], chapter 9 is representative here.) Black argues ([2], p. 156) that it is perfectly possible that there be a world consisting solely of two indiscernible spheres at some distance to each other and that this world constitutes a counterexample to the principle above. The strongest version of the bundle theory of substance claims that of necessity, the substances that make up the world are bundles of universals.1 It is commonly supposed that a consequence of Black's defeat of the principle of the Identity of Indiscernibles is that this bundle theory of substance is mistaken. (Again, Armstong's [1] is representative.) I shall argue that Black's thought experiment does not defeat the bundle theory and that, as a result, the bundle theory can be used to salvage the principle of the Identity of Indiscernibles. (shrink)

In this paper, I explore several versions of the bundle theory and the substratum theory and compare them, with the surprising result that it seems to be true that they are equivalent (in a sense of 'equivalent' to be specified). In order to see whether this is correct or not, I go through several steps : first, I examine different versions of the bundle theory with tropes and compare them to the substratum theory with tropes by going through (...) various standard objections and arguing for a tu quoque in all cases. Emphasizing the theoretical role of the substratum and of the relation of compresence, I defend the claim that these views are equivalent for all theoretical purposes. I then examine two different versions of the bundle theory with universals, and show that one of them is, here again, equivalent to the substratum theory with universals, by examining how both views face the famous objection from Identity of Indiscernibles in a completely parallel way. It is only the second, quite extreme and puzzling, version of the bundle theory with universals that is not be equivalent to any other view; and the diagnosis of why this is so will show just how unpalatable the view is. Similarly, only a not-so-palatable version of the substratum theory is genuinely different from the other views; and here again it's precisely what makes it different that makes it less appealing. (shrink)

It has been a common assumption that words are substances that instantiate or have properties. In this paper, I question the assumption that our ontology of words requires posting substances by outlining a bundle theory of words, wherein words are bundles of various sorts of properties (such as semantic, phonetic, orthographic, and grammatical properties). I argue that this view can better account for certain phenomena than substance theories, is ontologically more parsimonious, and coheres with claims in linguistics.

In a recent paper, Sun Demirli (2010) proposes an allegedly new way of conceiving of individuation in the context of the bundle theory of object constitution. He suggests that allowing for distance relations to individuate objects solves the problems with worlds containing indiscernible objects that would otherwise affect the theory. The aim of the present paper is i) To show that Demirli’s proposal falls short of achieving this goal and ii) To carry out a more general critical assessment of (...) the issue by appraising the costs and benefits of Demirli’s view as well as of existing alternatives. (shrink)

1. The Bundle Theory I shall discuss is a theory about the nature of substances or concrete particulars, like apples, chairs, atoms, stars and people. The point of the Bundle Theory is to avoid undesirable entities like substrata that allegedly constitute particulars. The version of the Bundle Theory I shall discuss takes particulars to be entirely constituted by the universals they instantiate.' Thus particulars are said to be just bundles of universals. Together with the claim that it (...) is necessary that particulars have constituents, the fundamental claim of the Bundle Theory is: (BT) Necessarily, for every particular x and every entity y, y constitutes x if and only ify is a universal and x instantiates y. 2 The standard and supposedly devastating objection to the Bundle Theory is that it entails or is committed to a false version of the Principle of Identity of Indiscernibles (Armstrong 1978: 91, Loux 1998: 107), namely: (Pll) Necessarily, for all particulars x and y and every universal z, if z is instantiated by x if and only if z is instantiated byy, then x is numerically identical with y. The most famous counterexample to the Identity of Indiscernibles is that put forward by Max Black, consisting of a world where there are only two iron spheres two miles apart from each other, having the same diameter, temperature, colour, shape, size, etc (Black 1952: 156). Let us from now on think of the properties of the spheres in this world as universals. The possibility of this world, which I shall hereafter refer to as 'Black's world', makes (Pll) false.' And according to common philosophical opinion this means that the Bundle Theory is false.. (shrink)

Bundle theories identify material objects with bundles of properties. On the traditional approach, these are the properties possessed by that material object. That view faces a deep problem: it seems to say that all of an object’s properties are essential to it. Essential bundle theory attempts to overcome this objection, by taking the bundle as a specification of the object’s essential properties only. In this paper, I show that essential bundle theory faces a variant of the (...) objection. To avoid the problem, the theory must accept the contingency of identity. I show how this can be achieved in a coherent and well-motivated way, a way that isn’t available to traditional bundle theories. (shrink)

A and B continue their conversation concerning the Identity of Indiscernibles. Both are aware of recent critiques of the principle that haven’t received replies; B summarizes those critiques, and A offers the replies that are due. B then raises a new worry.

I articulate and discuss a geometrical interpretation of Yang–Mills theory. Analogies and disanalogies between Yang–Mills theory and general relativity are also considered.

Paul (Noûs 36:578–596, 2002; Noûs 40:623–659, 2006, The Handbook of Mereology, forthcoming) has argued for a bundle theory of objects that analyzes the bundling relation between properties and objects in terms of parthood relations. In this paper I argue that any mereological bundle theory with the explanatory power of Paul’s theory will entail the principle of the identity of indiscernibles (PII). This is problematic, since similar bundle theories seem to fall to Max Black’s two sphere counterexample to (...) (PII). I argue, however, that a fully developed mereological bundle theory provides a new way of interpreting Black’s two sphere universe that dispels the counterexample. I argue that this solution to Black’s puzzle is superior to other solutions on offer, and consequently that mereological bundle theory is an attractive ontological strategy for friends of (PII). (shrink)

My aim in this article is to contribute to the larger project of assessing the relative merits of different theories of substance. An important preliminary step in this project is assessing the explanatory resources of one main theory of substance, the so-called bundle theory. This article works towards such an assessment. I identify and explain three distinct explanatory challenges an adequate bundle theory must meet. Each points to a putative explanatory gap, so I call them the Gap Challenges. (...) I consider three bundle-theoretic strategies for meeting these challenges. I argue that none of them goes very far. The upshot is that, absent other strategies for meeting the challenges, bundle theory involves a significant amount of stipulation. This black box makes bundle theory relatively weak with respect to its explanatory power—unless, of course, rival theories of substance are unable to do better. (shrink)

In this paper we present a new metaphysical theory of material objects. On our theory, objects are bundles of property instances, where those properties give the nature or essence of that object. We call the theory essential bundle theory. Property possession is not analysed as bundle-membership, as in traditional bundle theories, since accidental properties are not included in the object’s bundle. We have a different story to tell about accidental property possession. This move reaps many benefits. (...) Essential bundle theory delivers a simple theory of the essential properties of material objects; an explanation of how object coincidence can arise; an actual-world ground for modal differences between coincident objects; a simple story about intrinsic properties; and a plausible account of certain ubiquitous cases of causal overdetermination. (shrink)

Bundle theories identify material objects with bundles of properties. On the traditional approach, these are the properties possessed by that material object. That view faces a deep problem: it seems to say that all of an object’s properties are essential to it.Essential bundle theoryattempts to overcome this objection, by taking the bundle as a specification of the object’s essential properties only. In this paper, I show that essential bundle theory faces a variant of the objection. To (...) avoid the problem, the theory must accept the contingency of identity. I show how this can be achieved in a coherent and well-motivated way, a way that isn’t available to traditional bundle theories. (shrink)

The present essay provides a new metaphysical interpretation of Relational Quantum Mechanics (RQM) in terms of mereological bundle theory. The essential idea is to claim that a physical system in RQM can be defined as a mereological fusion of properties whose values may vary for different observers. Abandoning the Aristotelian tradition centered on the notion of substance, I claim that RQM embraces an ontology of properties that finds its roots in the heritage of David Hume. To this regard, defining (...) what kind of concrete physical objects populate the world according to RQM, I argue that this theoretical framework can be made compatible with (i) a property-oriented ontology, in which the notion of object can be easily defined, and (ii) moderate structural realism, a philosophical position where relations and relata are both fundamental. Finally, I conclude that under this reading relational quantum mechanics should be included among the full-fledged realist interpretations of quantum theory. (shrink)

This paper looks at Gregory of Nyssa's so-called "bundle theory" sensible individuals and matter (as recently argued by Gerd Van Riel and Thomas Wauters in a 2020 article) amidst the broader context of Gregory's view of created beings and his reception of Neoplatonist, Stoic, and Aristotelian conceptions of particulars and matter. I argue that Gregory's position is closer to an Aristotelian position, despite the parallels to Plotinus and other contemporaneous bundle theory positions: in arguing against prime matter, and (...) insofar as he emphasizes the identity of each kind of created being with its material substrate—understood as a "bundle" of properties—Gregory inadvertently upholds a reading of Aristotle that refutes an ontological notion of prime matter. (shrink)

Bundle Theory is the view that every concrete particular object is solely constituted by its universals. This theory is often criticized for not accommodating the possibility of symmetrical universes, such as one that contains two indiscernible spheres two meters from each other in otherwise empty space. One bundle theoretic solution to this criticism holds that the fact that the spheres stand in a weakly discerning—i.e., irreflexive and symmetric—relation, such as being two meters from, is sufficient for the numerical (...) diversity of the spheres. For this solution to be effective, however, it should be established that weak discernibility not only necessitates but also explains numerical diversity. In this paper, I argue that the fact that two objects have a certain distance between them does explain why they are non-identical. I also argue that the worry that the weak discernibility approach has some circularity problems is not well-founded. (shrink)

Bundle Theory is the view that every concrete particular object is solely constituted by its universals. This theory is often criticized for not accommodating the possibility of symmetrical universes, such as one that contains two indiscernible spheres two meters from each other in otherwise empty space. One bundle theoretic solution to this criticism holds that the fact that the spheres stand in a weakly discerning—i.e., irreflexive and symmetric—relation, such as being two meters from, is sufficient for the numerical (...) diversity of the spheres. For this solution to be effective, however, it should be established that weak discernibility not only necessitates but also explains numerical diversity. In this paper, I argue that the fact that two objects have a certain distance between them does explain why they are non-identical. I also argue that the worry that the weak discernibility approach has some circularity problems is not well-founded. (shrink)

ABSTRACT: I argue in this article that, contrary to some recent views, Berkeley’s bundle theory of physical objects is incompatible with the thinking that we immediately perceive such objects. Those who argue the contrary view rightly stress that immediate perception of ideas or objects must be non-conceptual for Berkeley, that is, the concept of the object cannot be made use of in the perception, otherwise it would be mediate perception. After a brief look at the texts, I contrast how (...) a direct realist view of immediate perception differs significantly from a bundle theorist’s view. The difference is so great that one rationale for the alternative view, the claim that Berkeley allies himself with common sense by claiming we immediately perceive physical objects, loses plausibility.RÉSUMÉ: Je soutiens dans cet article que, contrairement à certaines interprétations récentes, la théorie de Berkeley sur la collection d’idées relatives aux objets matériels (bundle theory) est incompatible avec la pensée que nous percevons ces objets defaçon immédiate. Ceux qui ont soutenu le contraire remarquent à juste titre que la perception immédiate des idées ou des objets doit être non conceptuelle pourBerkeley : le concept de l’objet ne peut servir lors de la perception, car il s’agirait alors d’une perception médiate. Suite à un rapide tour d’horizon des textes pertinents, je fais ressortir à quel point une théorie réaliste sur la perception immédiate differe d’une théorie sur la collection d’idées (bundle theory). Ces positions diffèrent tant et si bien que le principe d’exégèse suivant lequel Berkeley se réclamerait du sens commun en défendant que nous percevons les objets materiels de manière immédiate doit être remis en question. (shrink)

In this chapter, we provide an opinionated introduction to contemporary trope bundle theories of substance. We assess different trope bundle theories on the grounds of their two main aims: to provide an adequate account of substances or objects by means of tropes and a reductive analysis of inherence, that is, object's having tropes as their properties. Our discussion begins by a presentation of Donald C. Williams’ and Keith Campbell's paradigmatic trope theories, which maintain that tropes are independent existents. (...) After highlighting the central problems of paradigmatic trope theories, we discuss two more recent developments of trope bundle theory that also take non-relational tropes as independent existents, Anna-Sofia Maurin's and Douglas Ehring's independence theories. Finally, we present two alternative trope bundle theories, according to which tropes are dependent existents, dependence theories, namely, Arda Denkel's Saturation theory and our Strong Nuclear Theory (SNT). Although the latter two theories introduce existential dependencies among tropes, we argue that dependence theories provide a more satisfactory account of substances dividing into natural kinds than independence theories. (shrink)

This paper extends the standard model of bundling to allow products to be substitutes and for products to be supplied by separate sellers. Whether integrated or separate, …rms have an incentive to introduce bundling discounts when demand for the bundle is elastic relative to demand for stand-alone products. Separate …rms often have a unilateral incentive to o¤er inter-…rm bundle discounts, although this depends on the detailed form of substitutability. Bundle discounts mitigate the innate substitutability of products, which (...) can relax competition between …rms and induce an integrated …rm to lower all of its prices when it follows a bundling strategy. (shrink)

[EN] Several conceptions of trope bundles have postulated mutual relations of ontological dependence to explain the unity of the bundle. The idea is that a bundle is a plurality of tropes such that each one of them is dependent on any other. A variant of this idea is that there is a ‘nucleus’ of tropes all of them mutually dependent, and there is also a ‘periphery’ or ‘halo’ of tropes that are dependent on the tropes of the nucleus, (...) but the tropes of the nucleus are not dependent on them. There are several theoretical advantages that trope bundles conceived in this way have. A weakness of the position nevertheless is that it requires an equivalence relation of dependence. But it has been normally supposed that dependence is a strict order, i.e. it is relation irreflexive, asymmetric and transitive. Several recent works have put into question this traditional assumption. Those recent criticisms are discussed and it is argued that they are not convincing. Further arguments are presented for the irreflexivity and transitivity of dependence, from which asymmetry follows. Dependence, then, appears to be in fact a strict order. This implies that most forms of nuclear trope bundles are unintelligible. But not all of them, because nuclear tropes with a unique nuclear trope are coherent. [ES] Varias concepciones de cúmulos de tropos han postulado relaciones de dependencia ontológica mutuas para explicar la unidad del cúmulo. La idea es que un cúmulo es una pluralidad de tropos tal que cada uno de ellos es dependiente de cualquier otro. Una variante de esta idea es que hay un ‘núcleo’ de tropos todos ellos mutuamente dependientes y hay también una ‘periferia’ o ‘halo’ de tropos que son dependientes de los tropos del núcleo, pero los tropos del núcleo no son dependientes de ellos. Hay varias ventajas teóricas que tienen los cúmulos de tropos concebidos de este modo. Una debilidad de esta posición, sin embargo, es que requiere una relación de dependencia que sea una relación de equivalencia. Pero se ha supuesto normalmente que la dependencia es un orden estricto, esto es, una relación irreflexiva, asimétrica y transitiva. Varios trabajos recientes han puesto en cuestión este supuesto tradicional. Estas criticas recientes son aquí discutidas y se argumenta que no son convincentes. Se presentan argumentos adicionales para la irreflexividad y la transitividad de la dependencia, de lo que se sigue la asimetría. Entonces, la dependencia resulta ser un orden estricto. Esto implica que la mayoría de las formas de cúmulos nucleares de tropos son ininteligibles. Pero no todos, porque los cúmulos nucleares con un único tropo nuclear son coherentes. (shrink)

The bundle theory is a theory about the internal constitution of individuals. It asserts that individuals are entirely composed of universals. Typically, bundle theorists augment their theory with a constitutional approach to individuation entailing the thesis ‘identity of constituents is a sufficient ground for numerical identity’ (CIT). But then the bundle theory runs afoul of Black’s duplication case—a world containing two indiscernible spheres. Here I propose and defend a new version of the bundle theory that denies (...) ‘CIT’, and which instead conjoins it with a structural diversity thesis , according to which being separated by distance is a sufficient ground for numerical diversity. This version accommodates Black’s world as well as the three-spheres world —a world containing three indiscernible spheres, arranged as the vertices of an equilateral triangle. In this paper, I also criticize Rodriguez-Pereyra’s alternative attempt to defend the bundle theory against Black’s case and the case of the three-spheres world. (shrink)

The challenge of thick character consists in explaining the apparent fact that one object can be charactered in many ways. If we assume a trope bundle theory, we ought to answer in turn the two following questions: What are the requirements on a trope bundle theory if it is to adequately account for thick-character?; Is a trope bundle theory that meets those requirements preferable to rival theories? In order to address the above questions, the paper proceeds as (...) follows. In the first section I cover two preliminary matters: I introduce the concept of thick-character and distinguish it from other related concepts. Then, I sketch several leading accounts of character and situate bundle theory among them. Also, I pick up and argue that there are three requirements on a trope bundle theory if it is to adequately account for thick-character. Lastly, in the third section I pick up and argue that the requirements spell trouble for trope bundle theory. This trouble, I argue, indicates that trope bundle theory—and hence bundle theory simpliciter—fails to better its chief rival, substance-attribute theory. (shrink)

Shehtman and Skvortsov introduced Kripke bundles as semantics of non-classical first-order predicate logics. We show the structural equivalence between Kripke bundles for intermediate predicate lógics and Kripke-type frames for intuitionistic modal propositional logics. This equivalence enables us to develop the semantical study of relations between intermediate predicate logics and intuitionistic modal propositional logics. New examples of modal counterparts of intermediate predicate logics are given.

Shepherd appears to endorse something like the following biconditonal regarding qualities and objects. □(An object, O, exists ↔ Some bundle of qualities, Q1, Q2, … Qn exists). There is a growing consensus in the secondary literature that she also takes the right side of this biconditional to ground the left side. I.e. Shepherd is a bundle theorist who takes an object to be nothing but a mass of qualities, or causal powers. I argue here that despite appearances, this (...) interpretation reverses Shepherd's actual view. I.e. I argue that for Shepherd qualities, or causal powers, are grounded in the intrinsic constitutions of objects. In the case of "external objects", these intrinsic constitutions are unknowable to us; in the case of "internal objects", we have direct knowledge of them. (shrink)

I offer a mereological bundle of universals theory of material objects. The theory says that objects are identical to fusions of immanent universals at regions of space. Immanent universals are in the objects that instantiate them, and they can be wholly located at many regions of space. The version of the bundle theory I offer explains these characteristics of immanent universals, and it captures the instantiation relation in terms of the part-whole relation. The version of the theory I (...) offer is simpler and more unified than other mereological bundle theories. Yet, it is not as encompassing as other versions. For I suppose throughout that space is a particular substance, but not a bundle of properties. (shrink)

Is the self a substance, as Descartes thought, or is it 'only' a bundle of perceptions, as Hume thought ? In this paper I will examine these two views, especially with respect to two central features that have played a central role in the discussion, both of which can be quickly and usefully explained if one puts them as an objection to the bundle view. First, friends of the substance view have insisted that only if one conceives of (...) the self as a substance is it possible to account for genuine particularity of selves and genuine persistence through time of them. I will discuss in detail this claim as well as a special case of persistence - the case of a fission of a self - and I will ask, as Shoemaker (1997) did, how such a case can be handled by the two competing theories. The second central point of traditional disagreement concerns independence : it is often said that only a substance, but not a mere bundle, is independent enough of its properties to play properly the role of a self, and I will have something to say about this. Concerning all these points, my thesis will be a meta-theoretical one : contrary to appearances, both views can accommodate all of them (particularity at a time, persistence, fission, independence) in the same way, and I will examine two possible conclusions to be drawn from this : either that the differences between the two views are no more than terminological and that they turn out to be equivalent views, or that the differences are metaphysical but that it is epistemically under-determined which one of the views we should choose. (shrink)

If ordinary particulars are bundles of properties, and if properties are said to be universals, then three well-known objections arise : no particular can change, all particulars have all of their properties essentially (even the most insignificant ones), and there cannot be two numerically distinct but qualitatively indiscernible particulars. In this paper, I try to make a little headway on these issues and see how the objections can be met, if one accepts a certain view about persistence through time and (...) across possible worlds – namely, four-dimensionalism and its modal analogue. The paper is especially devoted to the second and third of the three objections. (shrink)

The bundle theory, supposed as a theory concerning the internal constitution of individuals, is often conjoined with a constitutional approach to individuation entailing the thesis ‘no two individuals can share all their constituents’ (CIT). But then it runs afoul of Black’s duplication case. Here a new bundle theory, takingdistance relations between bundles to be a sufficient ground for their diversity, will be proposed. This version accommodates Black’s world. Nonetheless, there is a possible objection. Consider the ‘triplication case’—a world (...) containing three indistinguishable spheres, each 5-meters from each other. Since distance relations are dyadic, this version must fail to distinguish the threespheres world from Black’s world. In response to this objection, I maintain that we must construe distance relations as irreducibly multigrade and n-ary. Then these two worlds will be distinguished by appealing to a triadic relation—R3—that three things enter mutually. Aren’t all polyadic relations in principle reducible to dyadic relations? I won’t deny that. But I will aim lower and argue that R3 cannot be reduced to dyadic relations that obliterate the distinction between the three-spheres world and Black’s world. (shrink)

Kripke bundle [3] and C-set semantics [1] [2] are known as semantics which generalize standard Kripke semantics. In [3] and in [1], [2] it is shown that Kripke bundle and C-set semantics are stronger than standard Kripke semantics. Also it is true that C-set semantics for superintuitionistic logics is stronger than Kripke bundle semantics [5].In this paper, we show that Q-S4.1 is not Kripke bundle complete via C-set models. As a corollary we can give a simple (...) proof showing that C-set semantics for modal logics are stronger than Kripke bundle semantics. (shrink)

Philosophical theories of the nature of concrete particulars come in two basic kinds, those according to which a concrete particular consists of properties and a bearer of those properties (a substratum), and those according to which a concrete particular consists only of its properties, in a relation of compresence or concurrence. Substrata are theoretical entities defined by their explanatory functions. As such, there is not much disagreement about their nature: they are propertyless, unobservable constituents of concrete particulars that are the (...) bearers of properties 1 and the individuators of distinct particulars. The situation is different with respect to properties. Among realists, some think properties are universals, either transcendent (Platonists) or immanent (Aristotelians), and some 2 think they are particulars (“tropes” ). Of the resultant possible positions on the nature of concrete particulars, six have been the focus of recent philosophical attention. These theories variously identify concrete particulars with (i) material substrata bearing transcendent universals, (ii) material substrata bearing immanent universals, (iii) material substrata bearing abstract particulars, (iv) bundles of transcendent universals, (v) bundles of immanent universals, and (vi) bundles of abstract particulars. (shrink)

According to the realist rendering of mathematical structuralism, mathematical structures are ontologically prior to individual mathematical objects such as numbers and sets. Mathematical objects are merely positions in structures: their nature entirely consists in having the properties arising from the structure to which they belong. In this paper, I offer a bundle-theoretic account of this structuralist conception of mathematical objects: what we normally describe as an individual mathematical object is the mereological bundle of its structural properties. An emerging (...) picture is a version of mereological essentialism: the structural properties of a mathematical object, as a bundle, are the mereological parts of the bundle, which are possessed by it essentially. (shrink)

Bundle theory reduces particulars to bundles of properties. Bundle theorists have been working to explain individuation within an ontology of repeatable properties, but the outcomes are not satisfactory. Even the trope approach toward properties is not capable of establishing individuation. This article argues that bundle theorists are wrong in searching for individuators within the bundles of properties. Rather, indi­viduation should be established within ontologically more fundamental level of events. Events, with their spatial and temporal character, enable us (...) to individuate the bundles of properties involved and this is one of the reasons for the superiority of bundle theory to other competitive theories of substance. (shrink)

This paper provides a rational reconstruction of a Platonic trope bundle theory that is a live alternative to contemporary bundle theories. According to the theory, Platonic particulars are composed of what Plato calls images of Forms; contemporary metaphysicians call these tropes. Tropes are dependent on Forms and the Receptacle, while trope bundles are structured by natural kinds using the Phaedo's principles of inclusion and exclusion and the Timaeus’ geometrised elements, as well as by co-location in the Receptacle. Key (...) elements of discussion include persistence and abundance of Plato's tropes. The resulting theory is compared with contemporary trope bundle theories. (shrink)

In this article i defend the claim that an individual is no more and no less than a bundle of instances of properties against the following objections: (1) the concept of an instance of a property presupposes the concept of an individual. i argue that it presupposes only that no instance of a property exists independently of other instances. (2) if a thing were only a bundle of instances of properties, then properties would qualify properties. this objection commits (...) the fallacy of composition. (3) a bundle constituting an individual needs a component which is not a property to individuate it. i argue that such a bundle individuates itself. (4) the bundle theory makes change impossible. i argue against this claim by distinguishing a thing's numerical identity from its "complete" identity. (5) the bundle theory makes all true statements about individuals analytically true. i show that, at least for one interpretation of 'analytically true', this is not so. (shrink)

In this article, I review A Theory of Legal Personhood, explaining what I see as its key contributions to animal law scholarship, while situating it against wider jurisprudential contributions that may be of interest to philosophers and legal scholars grappling with the oft-thorny idea of legal personhood, not just for nonhuman animals but for corporations, artificially intelligent machines, and late-term fetuses. The article will explain Kurki's “bundle” theory of legal personhood as a “cluster” concept and analyze the extremely helpful (...) parsing his theory provides in terms of the active and passive “incidents” of legal personhood. I focus much of the piece on Kurki's view of legal “nonpersons” who nonetheless have some rights or incidents of personhood in order to help clarify the challenge Kurki's theory raises for Steven M. Wise and the Nonhuman Rights Project, as the issues surrounding those litigation efforts will likely be familiar to readers here, who will be wondering how this theory interacts with what Wise seeks to achieve. (shrink)

We consider a uniform r-bundle E on a complex rational homogeneous space X and show that if E is poly-uniform with respect to all the special families of lines and the rank r is less than or equal to some number that depends only on X, then E is either a direct sum of line bundles or unstable with respect to some numerical class of a line. So we partially answer a problem posted by Muñoz et al.. In particular, (...) if X is a generalized Grassmannian \ and the rank r is less than or equal to some number that depends only on X, then E splits as a direct sum of line bundles. So we improve the main theorem of Muñoz et al. 664:141–162, 2012, Theorem 3.1) when X is a generalized Grassmannian. Moreover, by calculating the relative tangent bundles between two rational homogeneous spaces, we give explicit bounds for the generalized Grauert–Mülich–Barth theorem on rational homogeneous spaces. (shrink)

Should Medicaid pay for supportive housing for homeless persons? After describing current limits on how states can use Medicaid funds to support housing, this article considers whether justice requires treating Medicaid recipients residing in nursing homes and Medicaid recipients needing supportive housing similarly.

1 A particular may have other particulars as parts, but according to the bundle theory its ultimate constituents are confined to universals. Parts are different from constituents or components. A part is a type of constituent, but there are constituents that are not parts. Parts belong to the same general category as the whole: if a concrete particular has parts, those parts will themselves be concrete particulars. This is not always the case with constituents: the constituents of a fact (...) do not have to be facts and the constituents (or members) of a set do not have to be sets. The relation of “being a part of” is also transitive, whereas the relation of “being a constituent of” is not always transitive. If a particular has parts, such as atoms, then its constituents include its intrinsic properties, its atoms, and the arrangement relation. If an atom has parts, such as subatomic particles, then the constituents of the atom include its properties, the subatomic particles, and the arrangement universal. If it is like this all the way down without any termination (no bedrock), then the bundle theory says that at each stage there are only universals and ordinary particulars with parts, in other words there are no bare particulars. This approach should also work if there were arbitrary undetached parts that are real entities. The alternative to no bedrock is metaphysical atomism. There are two ways that metaphysical atomism could be true in classical mechanics: (1) if the ultimate constituents of matter are point particles — perhaps electrons are point particles, (2) if matter is continuously divisible and arbitrary undetached parts are not real entities or real parts. But it would be rash to say that these were the only two options for all theories. Point particles are a convenient kind of particular to think about when discussing the bundle theory. There could be just three properties bundled together, a certain mass, a certain charge, and the property of being point like.. (shrink)

People often speak loosely, uttering sentences that are plainly false on their most strict interpretation. In understanding such speakers, we face a problem of underdetermination: there is often no unique interpretation that captures what they meant. Focusing on the case of incomplete definite descriptions, this paper suggests that speakers often mean bundles of propositions. When a speaker means a bundle, their audience can know what they mean by deriving any one of its members. Rather than posing a problem for (...) the interpretation of loose talk, the underdetermination of a uniquely correct interpretation allows for various ways in which the audience can grasp the speaker’s meaning. (shrink)

Recently, Dewar (2019) has suggested that one can apply the strategy of 'sophistication' - as exemplified by sophisticated substantivalism as a response to the diffeomorphism invariance of General Relativity - to gauge theories such as electrodynamics. This requires a shift to the formalism of fibre bundles. In this paper, I develop and defend this suggestion. Where my approach differs from previous discussions is that I focus on the metaphysical picture underlying the fibre bundle formalism. In particular, I aim to (...) affirm the physical reality of gauge properties. I argue that this allows for a local and separable explanation of the Aharonov-Bohm effect. Its puzzling features are explained by a form of holism inherent to fibre bundles. (shrink)