Recent interest in maximal proper acceleration as a possible principle generalizing the theory of relativity can draw on the differential geometry of tangent bundles, pioneered by K. Yano, E. T. Davies, and S. Ishihara. The differential equations of geodesics of the spacetime tangent bundle are reduced and investigated in the special case of a Riemannian spacetime base manifold. Simple relations are described between the natural lift of ordinary spacetime geodesics and geodesics in the spacetime tangent (...) class='Hi'>bundle. (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)

Conformal group of Minkowski space-time M is considered as a group of bundle automorphisms of a vector bundle U over M. 4-component spin-vectors (4-spinors) are sections of a subbundle of the tangent bundle over U. Isotropic 4-vectors are images of 4-spinors under projection. This leads to a particularly clear interpretation of the spin properties of Nature.

Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of “gauge” transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.

The standard view is that the Lagrangian and Hamiltonian formulations of classical mechanics are theoretically equivalent. Jill North, however, argues that they are not. In particular, she argues that the state-space of Hamiltonian mechanics has less structure than the state-space of Lagrangian mechanics. I will isolate two arguments that North puts forward for this conclusion and argue that neither yet succeeds. 1 Introduction2 Hamiltonian State-space Has less Structure than Lagrangian State-space2.1 Lagrangian state-space is metrical2.2 Hamiltonian state-space is symplectic2.3 Metric > (...) symplectic3 Hamiltonian State-space Does Not Have Less Structure than Lagrangian State-space3.1 Lagrangian state-space has less than metric structure3.1.1 A potential worry3.1.2 General Lagrangians3.2 Hamiltonian state-space has more than symplectic structure3.2.1 A dual structure on the Hamiltonian state-space3.2.2 Simple Hamiltonians3.3 Comparing Lagrangian and Hamiltonian structures3.3.1 Counting mathematical structure3.3.2 Symplectic and metric structure are incomparable4 An Alternative Argument for LS4.1 The argument for P3*4.2 Symplectic manifold vs. tangent bundle structure4.3 Trying to patch up the argument for P3*5 Interpreting Mathematical Structure5.1 State-space realism5.2 Model isomorphism and theoretical equivalence6 Conclusion. (shrink)

For a standard Finsler F on a manifold M, the domain is the whole tangent bundle T M and the fundamental tensor g is positive-definite. However, in many cases, these two conditions hold in a relaxed form only, namely one has either a psuedo-Finsler metric or a conic Finsler metric. Our aim is twofold. First, we want to give an account of quite a few subtleties that appear under such generalizations, say, for conic pseudo-finsler metrics. Second, we aim (...) to provide some criteria that determine when a pseudo-Finsler metric F obtained as a general homogeneous combination of Finsler metrics and one-forms is again a Finsler-metric -- or, more precisely, that the conic domain on which g remains positive-definite. Such a combination generalizes the known -metrics in different directions. Remarkably, classical examples of Finsler metrics are reobtained and extended, with explicit computations of their fundamental tensors. (shrink)

A geometric formulation of the gravitation theory in the spacetime R × S 3 is given. A linear connection is introduced on the tangent bundle T(R × S 3 ) and then the connection coefficients and the Riemann curvature tensor are calculated. It is shown that their expressions differ from those of Carmeli and Malin [Found. Phys.17, 407 (1987)] by supplementary terms due to the noncommutativity of derivatives used on the spacetime R × S 3 . The Einstein (...) field equations are written as usually and a comparison with other results is given. Finally, some observations about a possible gauge theory of gravitation in the spacetime R × S 3 are made. (shrink)

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R) and complexified Clifford Cl C (4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale $$(\hbar \lambda / R)$$. Previous work led us to show from (...) first principles why the observed value of the vacuum energy density (cosmological constant) is given by a geometric mean relationship $$\rho \sim L_{\rm Planck}^{-2}R^{-2} = L_{P}^{-4} (L_{\rm Planck} / R)^{2} \sim 10^{-122}M_{\rm Planck}^4$$, and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. We proceed with an extensive review of Smith’s 8D model based on the Clifford algebra Cl (1, 7) that reproduces at low energies the physics of the Standard Model and Gravity, including the derivation of all the coupling constants, particle masses, mixing angles,....with high precision. Geometric actions are presented like the Clifford-Space extension of Maxwell’s Electrodynamics, and Brandt’s action related to the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries). Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit. (shrink)

Using Finsler brane solutions [see details and methods in: S. Vacaru, Class. Quant. Grav. 28:215001, 2011], we show that neutrinos may surpass the speed of light in vacuum which can be explained by trapping effects from gravity theories on eight dimensional (co) tangent bundles on Lorentzian manifolds to spacetimes in general and special relativity. In nonholonomic variables, the bulk gravity is described by Finsler modifications depending on velocity/momentum coordinates. Possible super-luminal phenomena are determined by the width of locally anisotropic (...) brane (spacetime) and induced by generating functions and integration functions and constants in coefficients of metrics and nonlinear connections. We conclude that Finsler brane gravity trapping mechanism may explain neutrino super-luminal effects and almost preserve the paradigm of Einstein relativity as the standard one for particle physics and gravity. (shrink)

In a recent paper [J. G. Vargas and D. G. Torr, Found. Phys. 27, 599 (1997)], we have shown that a subset of the differential invariants that define teleparallel connections in spacetime generates a teleparallel Kaluza-Klein space (KKS) endowed with a very rich Clifford structure. A canonical Dirac equation hidden in this structure might be uncovered with the help of a teleparallel Kähler calculus in KKS. To bridge the gap to such a calculus from the existing Riemannian Kähler calculus in (...) spacetime, we commence the construction of a teleparallel Kähler calculus in spacetime. In the process, we notice: (a) Unknown to him, one of Einstein's equations in his attempt at unification with teleparallelism states that the interior covariant derivative of the torsion is zero. (b) A mechanism exists in the tangent bundle of teleparallel spaces for producing confinement (in the applicable cases, one would have to show why nonconfinement also occurs, rather than the other way around). (c) When the torsion is not zero, the interior covariant derivative in the sense of Kähler, δF, does not coincide with *d*F. The system (dF = 0, δF = j) rather than (dF = 0, *d*F = j) should then be used for generalizations of Maxwell's electrodynamics. (shrink)

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 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 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)

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 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)

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)

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)

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)

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)

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)

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)

This chapter considers Hume's proposal that we are made up entirely of particular mental states and events: the bundle view. An argument for the bundle view is based on the claim that the traditional idea of substance is dismissed. The bundle view is then shown to follow naturally from widely held claims about diachronic and synchronic personal identity. Reid's objection that bundles of thoughts cannot be thinkers is elaborated and endorsed. It is then argued that the (...) class='Hi'>bundle view cannot easily avoid the thinking‐animal problem. There follows a critical discussion of two related views: that we are bundles of universals and that we are something like computer programs. Both are found to be hopeless. (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)

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)

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)

[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)

1 See for example, E. J. Lowe, The Possibility of Metaphysics, pp. 51-3, 210-220, and David Lewis, The Plurality of Worlds on the notion of concrete object. 2 The properties that are constituents of a particular should be intrinsic properties, though it need not be assumed that all its intrinsic properties are constituents. The notion of intrinsic property is easier if a sparse view (as opposed to an abundant view) of properties is assumed. A sparse view requires a criterion for (...) being a property, such as a causal principle (Shoemaker) or the related Eleatic principle (Armstrong). Intrinsic properties should be real properties. Such a criterion should rule out conjunctive properties, disjunctive properties, and negated properties. On the hand, it could be stipulated that these are not intrinsic properties. Those that believe in abundant properties should use the criterion to divide properties into two classes (natural and non-natural); intrinsic properties would then be located in the first class. Extrinsic properties are properties that an object possesses in virtue of other objects, their properties, and relations that involve them. If these other objects were to disappear all intrinsic properties would be unaffected. Intrinsic properties are non-relational in the sense that an object does not possesses them in virtue of other objects, their properties, and relations between them. However, intrinsic properties can be relational when an object possesses a (monadic) property in virtue of relations between its parts. Paradigmatic intrinsic properties are the mass, charge, magnetic moment, and spin of the electron as normally understood. (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 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 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)

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)

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)

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)

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)

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

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)

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.

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)

Field theories have been central to physics over the last 150 years, and there are several theories in contemporary physics in which physical fields play key causal and explanatory roles. This paper proposes a novel field trope-bundle (FTB) ontology on which fields are composed of bundles of particularized property instances, called tropes and goes on to describe some virtues of this ontology. It begins with a critical examination of the dominant view about the ontology of fields, that fields are (...) properties of a substantial substratum. (shrink)

What is ethnicity and how does it inform the way we understand ethical and political issues involving ethnic change and ethnically conscious public policies? Jorge J. E. Gracia put forth what he calls his ‘Familial-Historical View’ of ethnicity in which Hispanic identity is understood in terms of history and family resemblances. He criticizes what he calls the ‘Common-Bundle View’ of ethnicity which understands ethnic belonging in terms of an essence. I defend two negative theses which lead to the outlines (...) of a positive thesis: (1) Gracia’s arguments against the Common-Bundle View are not effective; (2) the Familial-Historical View is inadequate because it downplays the essential role that cultural phenomena play in making Hispanic history ethnically relevant to Hispanic identity. As a way of building on the Common-Bundle View I sketch a reformulation that avoids Gracia’s criticisms and is more politically and ethically effective than his family resemblance view of ethnicity. (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)

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)

The paper advances the hypothesis that some difficulties in René Descartes reflections on the idea of mind in his ‘Objections and Responses’ would unintentionally lead him to a ‘bundle theory’. In this sense, Descartes would not have been successful in showing that the mind would be something beyond the set of its modes or attributes. This hypothesis is based upon Descartes’ replies to Thomas Hobbes, Antoine Arnauld, Pièrre Gassendi and Marin Mersenne – third, fourth, fifth and sixth sets of (...) objections respectively. (shrink)

We study the impact of a kind of non‐archimedean stratifications (t‐stratifications) on tangent cones of definable sets in real closed fields. We prove that such stratifications induce stratifications of the same nature on the tangent cone of a definable set at a fixed point. As a consequence, the archimedean counterpart of a t‐stratification is shown to induce Whitney stratifications on the tangent cones of a semi‐algebraic set. Extensions of these results are proposed for real closed fields with (...) further structure. (shrink)