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)

In a long-term transformation, that begins in Antiquity but takes a crucial turn in the Renaissance anatomies, the “fibre” becomes from around 1750 the operative building block and at the same time the first unifying principle of function-structure-complexes of organic bodies. It occupies the role that the cell takes up in the cell œconomies of the second third of the nineteenth century. In this paper, I will first discuss some key notions, technical analogies, and images that are related to (...) “fibre”-concepts from Andreas Vesalius to Albrecht von Haller and then focus on Charles Bonnet's and Denis Diderot's fibre œconomies. In Bonnet's and Diderot's fibre œconomies, the self-active, regulating properties of fibre-agents and their material structures, that reach from fibre bundles, tissues and membranes to apparati of organs, are united within the concrete whole of individual organized “systems” or “networks.”. (shrink)

This paper sets out a moderate version of metaphysical structural realism that stands in contrast to both the epistemic structural realism of Worrall and the—radical—ontic structural realism of French and Ladyman. According to moderate structural realism, objects and relations (structure) are on the same ontological footing, with the objects being characterized only by the relations in which they stand. We show how this position fares well as regards philosophical arguments, avoiding the objections against the other two versions of structural realism. (...) In particular, we set out how this position can be applied to space-time, providing for a convincing understanding of space-time points in the standard tensor formulation of general relativity as well as in the fibre bundle formulation. (shrink)

Στις κβαντικές θεωρίες πεδίου, οι οποίες στην πιο ολοκληρωμένη τους μορφή εκφράζονται μέσω του μαθηματικού φορμαλισμού που ονομάζεται δεσμίδες ινών (fibre bundles), χρησιμοποιούνται εκτενώς η έννοια της συμμετρίας και η αλληλένδετη με αυτήν έννοια της διατήρησης. Ο στόχος του παρόντος άρθρου είναι η αποσαφήνιση του όρου συμμετρία, όπως αυτός εμφανίζεται στο εν λόγω πλαίσιο, καθώς και η εξέταση του ρόλου κάποιων συγκεκριμένων μαθηματικών δομών , οι οποίες εμφανίζονται ως αποτέλεσμα της χρήσης των συμμετριών, στην επιστημονική εξήγηση των φαινομένων (...) που περιγράφονται από τις κβαντικές θεωρίες πεδίου. (shrink)

Like moths attracted to a bright light, philosophers are drawn to glitz. So in discussing the notions of ‘gauge’, ‘gauge freedom’, and ‘gauge theories’, they have tended to focus on examples such as Yang–Mills theories and on the mathematical apparatus of fibre bundles. But while Yang–Mills theories are crucial to modern elementary particle physics, they are only a special case of a much broader class of gauge theories. And while the fibre bundle apparatus turned out, in retrospect, (...) to be the right formalism to illuminate the structure of Yang–Mills theories, the strength of this apparatus is also its weakness: the fibre bundle formalism is very flexible and general, and, as such, fibre bundles can be seen lurking under, over, and around every bush. What is needed is an explanation of what the relevant bundle structure is and how it arises, especially for theories that are not initially formulated in fibre bundle language. Here I will describe an approach that grows out of the conviction that, at least for theories that can be written in Lagrangian/Hamiltonian form, gauge freedom arises precisely when there are Lagrangian/Hamiltonian constraints of an appropriate character. This conviction is shared, if only tacitly, by that segment of the physics community that works on constrained Hamiltonian systems. (shrink)

The constrained Hamiltonian formalism is recommended as a means for getting a grip on the concepts of gauge and gauge transformation. This formalism makes it clear how the gauge concept is relevant to understanding Newtonian and classical relativistic theories as well as the theories of elementary particle physics; it provides an explication of the vague notions of “local” and “global” gauge transformations; it explains how and why a fibre bundle structure emerges for theories which do not wear their bundle (...) structure on their sleeves; it illuminates the connections of the gauge concept to issues of determinism and what counts as a genuine “observable”; and it calls attention to problems which arise in attempting to quantize gauge theories. Some of the limitations and problematic aspects of the formalism are also discussed. (shrink)

Historical work on the emergence of sheaf theory has mainly concentrated on the topological origins of sheaf cohomology in the period from 1945 to 1950 and on subsequent developments. However, a shift of emphasis both in time-scale and disciplinary context can help gain new insight into the emergence of the sheaf concept. This paper concentrates on Henri Cartan’s work in the theory of analytic functions of several complex variables and the strikingly different roles it played at two stages of the (...) emergence of sheaf theory: the definition of a new structure and formulation of a new research programme in 1940–1944; the unexpected integration into sheaf cohomology in 1951–1952. In order to bring this two-stage structural transition into perspective, we will concentrate more specifically on a family of problems, the so-called Cousin problems, from Poincaré (1883) to Cartan. This medium-term narrative provides insight into two more general issues in the history of contemporary mathematics. First, we will focus on the use of problems in theory-making. Second, the history of the design of structures in geometrically flavoured contexts—such as for the sheaf and fibre-bundle structures—which will help provide a more comprehensive view of the structuralist moment, a moment whose algebraic component has so far been the main focus for historical work. (shrink)

An argument of A. Borel [Bor—61, Proposition 3.1] shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for definably compact definably connected groups definable in an o-minimal expansion of a real closed field. As opposed to the Lie case, however, we provide an example showing that the derived subgroup may not have a definable semidirect complement.

Most scientific theories are globally inconsistent. Chunk and Permeate is a method of rational reconstruction that can be used to separate, and identify, locally consistent chunks of reasoning or explanation. This then allows us to justify reasoning in a globally inconsistent theory. We extend chunk and permeate by adding a visually transparent way of guiding the individuation of chunks and deciding on what information permeates from one chunk to the next. The visual representation is in the form of bundle diagrams. (...) We then extend the bundle diagrams to include not only reasoning in the presence of inconsistent information or reasoning in the logical sense of deriving a conclusion from premises, but more generally reasoning in the sense of trying to understand a phenomenon in science. This extends the use of the bundle diagrams in terms of the base space and the fibres. We then apply this to a case in physics, that of understanding binding energies in the nucleus of an atom using together inconsistent models: the liquid drop model and the shell model. We draw some philosophical conclusions concerning scientific reasoning, paraconsistent reasoning, the role of logic in science and the unity of science. (shrink)

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. This completeness transfer (...) result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established. (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)

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.

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)

This article studies preservation of certain algebraic properties of propositional logics when combined by fibring. The logics analyzed here are classified in protoalgebraic, equivalential and algebraizable. By introducing new categories of algebrizable logics and of deductivizable quasi-varieties, it is stated an isomorphism between these categories. This constitutes an alternative to a similar result found in the literature.

A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence and general semantics. (...) An example is provided showing that completeness is not always preserved by fibring ligics endowed with standard (non general) semantics. A categorial characterization of fibring is provided using coproducts and cocartesian liftings. (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)

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)

We study access control policies based on the says operator by introducing a logical framework called Fibred Security Language (FSL) which is able to deal with features like joint responsibility between sets of principals and to identify them by means of first-order formulas. FSL is based on a multimodal logic methodology. We first discuss the main contributions from the expressiveness point of view, we give semantics for the language both for classical and intuitionistic fragment), we then prove that in order (...) to express well-known properties like ‘speaks-for’ or ‘hand-off’, defined in terms of says, we do not need second-order logic (unlike previous approaches) but a decidable fragment of first-order logic suffices. We propose a model-driven study of the says axiomatization by constraining the Kripke models in order to respect desirable security properties, we study how existing access control logics can be translated into FSL and we give completeness for the logic. (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)

The transference of preservation results between importing and unconstrained fibring is investigated. For that purpose, a new formulation of fibring, called biporting, is introduced, and importing is shown to be subsumed by biporting. In consequence, particular cases of importing, like temporalization, modalization and globalization are subsumed by fibring. Capitalizing on these results, the preservation of the finite model property by fibring is transferred to importing and then carried over to globalization.

. The semantic collapse problem is perhaps the main difficulty associated to the very powerful mechanism for combining logics known as fibring. In this paper we propose cryptofibred semantics as a generalization of fibred semantics, and show that it provides a solution to the collapsing problem. In particular, given that the collapsing problem is a special case of failure of conservativeness, we formulate and prove a sufficient condition for cryptofibring to yield a conservative extension of the logics being combined. For (...) illustration, we revisit the example of combining intuitionistic and classical propositional logics. (shrink)

Fibring is recognized as one of the main mechanisms in combining logics, with great signicance in the theory and applications of mathematical logic. However, an open challenge to bring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that bring imposes unwanted interconnections between the given logics. Modulated bring allows a ner control of the combination, solving the collapsing problem both at the semantic and deductive levels. (...) Main properties like soundness and completeness are shown to be preserved, comparison with bring is discussed, and some important classes of examples are analyzed with respect to the collapsing problem. (shrink)

Fibring is a meta-logical constructor that applied to two logics produces a new logic whose formulas allow the mixing of symbols. Homogeneous fibring assumes that the original logics are presented in the same way . Heterogeneous fibring, allowing the original logics to have different presentations , has been an open problem. Herein, consequence systems are shown to be a good solution for heterogeneous fibring when one of the logics is presented in a semantic way and the other by a calculus (...) and also a solution for the heterogeneous fibring of calculi. The new notion of abstract proof system is shown to provide a better solution to heterogeneous fibring of calculi namely because derivations in the fibring keep the constructive nature of derivations in the original logics. Preservation of compactness and semi-decidability is investigated. (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.

Modern applications of logic in mathematics, computer science, and linguistics use combined systems of different types of logic working together. This book develops a method for combining--or fibring--systems by breaking them into simple components which can be manipulated easily and recombined.

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)

This study examines BDI logics in the context of Gabbay's fibring semantics. We show that dovetailing can be adopted as a semantic methodology to combine BDI logics. We develop a set of interaction axioms that can capture static as well as dynamic aspects of the mental states in BDI systems, using Catach's incestual schema G^[a, b, c, d]. Further we exemplify the constraints required on fibring function to capture the semantics of interactions among modalities. The advantages of having a fibred (...) approach is discussed in the final section. (shrink)

:This article examines material economies of carbon fibre as a prosthetic form of masculinity. The paper advances three main arguments. Firstly, carbon fibre can be a site in which disability is overcome, an act of overcoming that is affected through masculinized technology. Secondly, carbon fibre can be a homosocial surface; that is, carbon fibre becomes both a surface extension of the self and a third-party mediator in homosocial relationships, a surface that facilitates intimacy between men in (...) ways that devalue femininity in both male and female bodies. Carbon fibre surfaces are material extensions of subjectivity, and carbon fibre surfaces are vectors of the cultural economies of masculine competition. Thirdly, the article gives an account of Oscar Pistorius as an example of the masculinization of carbon fibre, and the associated binding of a psychic attitude of misogyny and power to a form of violent and competitive masculine subjectivity. The paper unpacks the affects, economies and surfaces of “carbon fibre masculinity” and discusses Pistorius’ use of carbon fibre, homosociality and misogyny as forms of protest masculinity through which he unconsciously attempted to recuperate his gendered identity from emasculating discourses of disability. (shrink)

This is Part 1 of a paper on fibred semantics and combination of logics. It aims to present a methodology for combining arbitrary logical systems L i , i ∈ I, to form a new system L I . The methodology `fibres' the semantics K i of L i into a semantics for L I , and `weaves' the proof theory (axiomatics) of L i into a proof system of L I . There are various ways of doing this, we (...) distinguish by different names such as `fibring', `dovetailing' etc, yielding different systems, denoted by L F I , L D I etc. Once the logics are `weaved', further `interaction' axioms can be geometrically motivated and added, and then systematically studied. The methodology is general and is applied to modal and intuitionistic logics as well as to general algebraic logics. We obtain general results on bulk, in the sense that we develop standard combining techniques and refinements which can be applied to any family of initial logics to obtain further combined logics. The main results of this paper is a construction for combining arbitrary, (possibly not normal) modal or intermediate logics, each complete for a class of (not necessarily frame) Kripke models. We show transfer of recursive axiomatisability, decidability and finite model property. Some results on combining logics (normal modal extensions of K) have recently been introduced by Kracht and Wolter, Goranko and Passy and by Fine and Schurz as well as a multitude of special combined systems existing in the literature of the past 20-30 years. We hope our methodology will help organise the field systematically. (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)

We study access control policies based on the says operator by introducing a logical framework called Fibred Security Language (FSL) which is able to deal with features like joint responsibility between sets of principals and to identify them by means of first-order formulas. FSL is based on a multimodal logic methodology. We first discuss the main contributions from the expressiveness point of view, we give semantics for the language (both for classical and intuitionistic fragment), we then prove that in order (...) to express well-known properties like 'speaks-for' or 'hand- off', defined in terms of says, we do not need second-order logic (unlike previous approaches) but a decidable fragment of first-order logic suffices. We propose a model-driven study of the says axiomatization by constraining the Kripke models in order to respect desirable security properties, we study how existing access control logics can be translated into FSL and we give completeness for the logic. (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)

This paper is part of a research program centered around argumentation networks and offering several research directions for argumentation networks, with a view of using such networks for integrating logics and network reasoning. In Section 1 we introduce our program manifesto. In Section 2 we motivate and show how to substitute one argumentation network as a node in another argumentation network. Substitution is a purely logical operation and doing it for networks, besides developing their theory further, also helps us see (...) how to bring logic and networks closer together. Section 3 develops the formal properties of the new kind of network and Section 4 offers general discussion and comparison with the literature. (shrink)

Although Wittgenstein is famously skeptical about the possibility of making substantial philosophical claims, he can be said to offer significant insights into the difference between inner and outer as well as the difference between self and other.1 He consistently reminds us that inner and outer are intimately connected instead of only causally related, as well as that the self—far from being a wholly independent entity—always already finds itself constituted by its relationships with others. In thus contesting the Cartesian view on (...) subjectivity, however, Wittgenstein may appear to simply reduce the inner to the outer and the self to the other.. (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)

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)

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)

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 gives a simple method for providing categorial brands of feature-based unification grammars with a model-theoretic semantics. The key idea is to apply the paradigm of fibred semantics (or layered logics, see Gabbay (1990)) in order to combine the two components of a feature-based grammar logic. We demonstrate the method for the augmentation of Lambek categorial grammar with Kasper/Rounds-style feature logic. These are combined by replacing (or annotating) atomic formulas of the first logic, i.e. the basic syntactic types, by (...) formulas of the second. Modelling such a combined logic is less trivial than one might expect. The direct application of the fibred semantics method where a combined atomic formula like np (num: sg & pers: 3rd) denotes those strings which have the indicated property and the categorial operators denote the usual left- and right-residuals of these string sets, does not match the intuitive, unification-based proof theory. Unification implements a global bookkeeping with respect to a proof whereas the direct fibring method restricts its view to the atoms of the grammar logic. The solution is to interpret the (embedded) feature terms as global feature constraints while maintaining the same kind of fibred structures. For this adjusted semantics, the anticipated proof system is sound and complete. (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)

Fibring is defined as a mechanism for combining logics with a first-order base, at both the semantic and deductive levels. A completeness theorem is established for a wide class of such logics, using a variation of the Henkin method that takes advantage of the presence of equality and inequality in the logic. As a corollary, completeness is shown to be preserved when fibring logics in that class. A modal first-order logic is obtained as a fibring where neither the Barcan formula (...) nor its converse hold. (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)