The Weak Principle of the Identity of Indiscernibles (weak PII), states that numerically distinct items must be discernible by a symmetrical and irreflexive relation. Recently, some authors have proposed that weak PII holds in non relativistic quantum mechanics, contradicting a long tradition claiming PII to be simply false in that theory. The question that arises then is: are relations allowed in the scope of PII? In this paper, we propose that quantum mechanics does not help us in deciding matters concerning (...) that problem, since that is a metaphysical problem rather than a quantum mechanical one. We argue further that weak PII is unmotivated on metaphysical grounds. We examine three metaphysical theses (bundle theory, counting, empiricism) that may provide reasons for one to sustain PII, and we conclude that weak PII gets no independent motivation from them. (shrink)

Arenhart_Krause_Uma-logica-da-indistinguibilidade.

The Received View on quantum non-individuality is, roughly speaking, the view according to which quantum objects are not individuals. It seems clear that the RV finds its standard expression nowadays through the use of the formal apparatuses of non-reflexive logics, mainly quasi-set theory. In such logics, the relation of identity is restricted, so that it does not apply for terms denoting quantum particles; this “lack of identity” formally characterizes their non-individuality. We face then a dilemma: on the one hand, identity (...) seems too important to be given up, on the other hand the RV seems to require that identity be given up. In this paper we shall discuss how the specific characterization of the RV through non-reflexive logics came to be framed. We examine some of the main objections to this version of the RV and argue that they are misguided under this specific “non-reflexive” understanding of the RV. Finally, we shall also argue that this non-reflexive view is not the only option for a metaphysical articulation of the RV: less radical approaches to identity and logic are open. In particular, some of these alternative approaches to the RV we present may be immune to most of the criticisms presented against the non-reflexive approach. (shrink)

Ontic Structural Realism is a version of realism about science according to which by positing the existence of structures, understood as basic components of reality, one can resolve central difficulties faced by standard versions of scientific realism. Structures are invoked to respond to two important challenges: one posed by the pessimist meta-induction and the other by the underdetermination of metaphysics by physics, which arises in non-relativistic quantum mechanics. We argue that difficulties in the proper understanding of what a structure is (...) undermines the realist component of the view. Given the difficulties, either realism should be dropped or additional metaphysical components not fully endorsed by science should be incorporated. (shrink)

In this paper we discuss some questions proposed by Prof. Newton da Costa on the foundations of quasi-set theory. His main doubts concern the possibility of a reasonable semantical understanding of the theory, mainly due to the fact that identity and difference do not apply to some entities of the theory’s intended domain of discourse. According to him, the quantifiers employed in the theory, when understood in the usual way, rely on the assumption that identity applies to all entities in (...) the domain of discourse. Inspired by his provocation, we suggest that, using some ideas presented by da Costa himself in his seminars at UFSC and by one of us in some papers, these difficulties can be overcome both on a formal level and on an informal level, showing how quantification over items for which identity does not make sense can be understood without presupposing a semantics based on a ‘classical’ set theory. (shrink)

A close examination of the literature on ontology may strike one with roughly two distinct senses of this word. According to the first of them, which we shall call traditional ontology , ontology is characterized as the a priori study of various “ontological categories”. In a second sense, which may be called naturalized ontology , ontology relies on our best scientific theories and from them it tries to derive the ultimate furniture of the world. From a methodological point of view (...) these two senses of ontology are very far away. Here, we discuss a possible relationship between these senses and argue that they may be made compatible and complement each other. We also examine how logic, understood as a linguistic device dealing with the conceptual framework of a theory and its basic inference patterns must be taken into account in this kind of study. The idea guiding our proposal may be put as follows: naturalized ontology checks for the applicability of the ontological categories proposed by traditional ontology and give substantial feedback for it. The adequate expression of some of the resulting ontological frameworks may require a different logic. We conclude with a discussion of the case of orthodox quantum mechanics, arguing that this theory exemplifies the kind of relationship between the two senses of ontology. We also argue that the view proposed here may throw some light in ontological questions concerning this theory. (shrink)

The aim of this paper is to argue that some objections raised by Jantzen (Synthese, 2010 ) against the separation of the concepts of ‘counting’ and ‘identity’ are misled. We present a definition of counting in the context of quasi-set theory requiring neither the labeling nor the identity and individuality of the counted entities. We argue that, contrary to what Jantzen poses, there are no problems with the technical development of this kind of definition. As a result of being able (...) to keep counting and identity apart for those entities, we briefly suggest that one venerable tradition concerning the nature of quantum particles may be consistently held. According to that tradition, known as the Received View on particles non-individuality, quantum particles may be seen as entities having both features: (i) identity and individuality do not apply to them, (ii) they may be gathered in collections comprising a plurality of them. (shrink)

Two entities are weakly discernible when an irreflexive and symmetric relation holds between them. That weak discernibility holds in quantum mechanics is fairly uncontroversial nowadays. The ontological consequences of weak discernibility, however, are far from clear. Part of the literature seems to imply that weak discernibility points to a definite metaphysics to quantum mechanics. In this paper we shall discuss the metaphysical contribution of weak discernibility to quantum mechanics and argue that, contrary to part of current literature, it does not (...) provide for a fully naturalistic determination of metaphysics. Underdetermination of the metaphysics still plagues the way of the naturalist. (shrink)

Quasi-set theory Q is an alternative set-theory designed to deal mathematically with collections of indistinguishable objects. The intended interpretation for those objects is the indistinguishable particles of non-relativistic quantum mechanics, under one specific interpretation of that theory. The notion of cardinal of a collection in Q is treated by the concept of quasi-cardinal, which in the usual formulations of the theory is introduced as a primitive symbol, since the usual means of cardinal definition fail for collections of indistinguishable objects. In (...) a recent work, Domenech and Holik have proposed a definition of quasi-cardinality in Q. They claimed their definition of quasi-cardinal not only avoids the introduction of that notion as a primitive one, but also that it may be seen as a first step in the search for a version of Q that allows for a greater representative power. According to them, some physical systems can not be represented in the usual formulations of the theory, when the quasi-cardinal is considered as primitive. In this paper, we discuss their proposal and aims, and also, it is presented a modification from their definition we believe is simpler and more general. (shrink)

Celebrando o papel de Newton da Costa na história da paraconsistência, este trabalho examina o uso e abuso da deliberada auto-contradição. Iniciado por Parmênides, desenvolvido por Platão, e continuado por Cícero, uma antiga tradição filosófica usava deliberadamente discursos paraconsistentes para revelar a verdade. Nos tempos modernos, o decisionismo tem usado uma deliberada auto-contradição contra a revelação Judaico-Cristã. DOI:10.5007/1808-1711.2010v14n1p1.

Biological macromolecules, considered as the items of the biochemical domain, are typically conceived under the ontological category of substantial individuals. In this paper, I will argue that the philosophical framework of process ontology, according to which the living world is not populated by individuals but by a dynamic hierarchy of processes, is more adequate to account for the structure and functioning of macromolecules. In particular, I will analyze its application to the phenomenon of cell signaling and to one of its (...) key concepts, cell receptors. Current knowledge in biochemistry allows us to conceive receptors as processual and dynamic entities, relationally stabilized and not separated from the biochemical phenomenon of which they are part. (shrink)

We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum particles interact with ordinary matter, nuclei, atoms, molecules, macroscopic material entities, measuring apparatuses, in a similar way to how human concepts interact with memory structures, human minds or artificial memories. We analyze the most characteristic aspects of quantum theory, i.e. entanglement and non-locality, interference and superposition, identity and (...) individuality in the light of this new interpretation, and we put forward a specific explanation and understanding of these aspects. The basic hypothesis of our framework gives rise in a natural way to a Heisenberg uncertainty principle which introduces an understanding of the general situation of ‘the one and the many’ in quantum physics. A specific view on macro and micro different from the common one follows from the basic hypothesis and leads to an analysis of Schrödinger’s Cat paradox and the measurement problem different from the existing ones. We reflect about the influence of this new quantum interpretation and explanatory framework on the global nature and evolutionary aspects of the world and human worldviews, and point out potential explanations for specific situations, such as the generation problem in particle physics, the confinement of quarks and the existence of dark matter. (shrink)

Hofweber (Ontology and the ambitions of metaphysics, Oxford University Press, 2016) argues for a thesis he calls “internalism” with respect to natural number discourse: no expressions purporting to refer to natural numbers in fact refer, and no apparent quantification over natural numbers actually involves quantification over natural numbers as objects. He argues that while internalism leaves open the question of whether other kinds of abstracta exist, it precludes the existence of natural numbers, thus establishing what he calls “restricted nominalism” about (...) natural numbers. We argue that Hofweber’s internalism fails to establish restricted nominalism. Not only is his primary argument for restricted nominalism invalid, the analysis of quantification proposed threatens to collapse internalism into either a traditional form of error theory or realism. (shrink)

This article presents a trope bundle theory of simple substances, the Strong Nuclear Theory[SNT] building on the schematic basis offered by Simons's (1994) Nuclear Theory[NT]. The SNT adopts Ellis's (2001) dispositional essentialist conception of simple substances as powerful particulars: all of their monadic properties are dispositional. Moreover, simple substances necessarily belong to some natural kind with a real essence formed by monadic properties. The SNT develops further the construction of substances the NT proposes to obtain an adequate trope bundle theory (...) of powerful particulars. The SNT allows for co-located powerful particulars. However, every powerful particular is necessarily co-located with its constituent tropes, which determine its causal powers. Every constituent trope of substance i is part of a trope aggregate (the n-bundle or c-bundle) that forms an individual figuring in the basic spatio-temporal relations. The location of these individuals determines the location of individual tropes. Since they are necessarily co-located with substance i when they exist, every trope t of i is necessarily co-located with i when it exits. Every simple substance has nuclear tropes necessary to it. It belongs to certain primary natural kind K because its nuclear tropes belong to certain distinct determinate kinds. (shrink)

This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...) volume includes 35 contributions. It is divided into nine parts: 1. Who Created the Concept of God; 2. Omniscience, Omnipotence, Timelessness and Spacelessness of God; 3. God and Perfect Goodness, Perfect Beauty, Perfect Freedom; 4. God, Fundamentality and Creation of All Else; 5. Simplicity and Ineffability of God; 6. God, Necessity and Abstract Objects; 7. God, Infinity, and Pascal's Wager; 8. God and (Meta-)Mathematics; and 9. God and Mind. (shrink)

The literature on quantum logic emphasizes that the algebraic structures involved with orthodox quantum mechanics are non distributive. In this paper we develop a particular algebraic structure, the quasi-lattice ( $${\mathfrak{I}}$$ -lattice), which can be modeled by an algebraic structure built in quasi-set theory $${\mathfrak{Q}}$$. This structure is non distributive and involve indiscernible elements. Thus we show that in taking into account indiscernibility as a primitive concept, the quasi-lattice that ‘naturally’ arises is non distributive.

Electromagnetism is usually understood as a theory describing how charged particles and eletromagnetic fields interact. In this paper I argue that a double ontology comprising both particles and fields is problematic. Either we should think of electromagnetism as a theory about charged particles directly interacting with each other, or as theory of fields whose local interactions are manifested as field quanta, called "particles." From a purely theoretical point of view the choice between a particle and a field interpretation does not (...) matter much when it concerns classical electromagnetism; both interpretations are possible and, as shown by Quine, there is a general method for translating a theory about one kind of objects into a theory assuming another kind of objects, provided these theories are empirically equivalent. From an empiricist point of view, however, the particle interpretation is the choice, since some particles are directly observable. Testable predictions of electromagnetism are predictions of the motion of charged bodies, in theory represented as particles, so this must be the empiricists' choice of ontology. In quantum electrodynamics one is however forced to chose a field ontology, since a particle ontology for this theory is impossible. So called "quantum particles" are field quanta, which cannot be treated as individuals making up a domain of quantification. There is thus a tension regarding ontology between classical and quantum electrodynamics. But this tension is nothing else than the much debated measurement problem of quantum mechanics. (shrink)

In this work, we focus on a very specific case study: assuming that quantum theories deal with “particles” of some kind, what kind of entity can such particles be? One possible answer, the one we shall examine here, is that they are not the usual kind of object found in daily life: individuals. Rather, we follow a suggestion by Erwin Schrödinger, according to which quantum mechanics poses a revolutionary kind of entity: non-individuals. While physics, as a scientific field, is not (...) concerned with whether entities posited by a specific physical theory are individuals or not, answering this question is part of the quest for a better understanding of physical reality. Here lies, in large measure, the relevance of ontology. (shrink)

Can identity itself be vague? Can there be vague objects? Does a positive answer to either question entail a positive answer to the other? In this paper we answer these questions as follows: No, No, and Yes. First, we discuss Evans’s famous 1978 argument and argue that the main lesson that it imparts is that identity itself cannot be vague. We defend the argument from objections and endorse this conclusion. We acknowledge, however, that the argument does not by itself establish (...) either that there cannot be vague objects or that there cannot be identity statements that are indeterminate for ontic reasons. And we further acknowledge that it does not by itself establish that there cannot be identity statements that are indeterminate in virtue of the existence of vague objects. We then go on to argue that, despite this, one who believes in vague objects cannot endorse Evans’s argument. To establish this we offer supplementary arguments that show that if vague objects exist then identity is vague, and that if identity is vague then vague objects exist. Finally we draw attention to an argument parallel to that of Evans’s, but safer, which can be employed against the putative ontic indeterminacy in identity of vague objects which can be differentiated by identity-free properties. (shrink)

This volume, The Brazilian Studies in the Philosophy and History of Science, is the first attempt to present to a general audience, works from Brazil on this subject. The included papers are original, covering a remarkable number of relevant topics of philosophy of science, logic and on the history of science. The Brazilian community has increased in the last years in quantity and in quality of the works, most of them being published in respectable international journals on the subject. The (...) chapters of this volume are forwarded by a general introduction, which aims to sketch not only the contents of the chapters, but it is conceived as a historical and conceptual guide to the development of the field in Brazil. The introduction intends to be useful to the reader, and not only to the specialist, helping them to evaluate the increase in production of this country within the international context. (shrink)

The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical (...) state does it represent? In this book, I aim to make sense of the wave function in quantum mechanics and find the ontological content of the theory. The book can be divided into three parts. The first part addresses the question of the nature of the wave function. After giving a comprehensive and critical review of the competing views of the wave function, I present a new argument for the ontic view in terms of protective measurements. In addition, I also analyze the origin of the wave function by deriving the free Schroedinger equation. The second part analyzes the ontological meaning of the wave function. I propose a new ontological interpretation of the wave function in terms of random discontinuous motion of particles, and give two main arguments supporting this interpretation. The third part investigates whether the suggested quantum ontology is complete in accounting for our definite experience and whether it needs to be revised in the relativistic domain. (shrink)

This paper develops the metaphysical hypothesis that there are irreducibly collective pluralities, pluralities of objects that do not have a singular object among them. A way to formulate this hypothesis using plural quantification will be proposed and the coherence of irreducibly collective existence will be defended. Furthermore, irreducibly collective existence will be shown to allow for bottomless scenarios that do not involve things standing in relations of parthood. This will create logical space for an anti-atomistic form of mereological nihilism.

It can be intuitively understood that sets and their elements in mathematics reflect the atomistic way of thinking in physics: Sets correspond to physical properties, and their elements correspond to particles that have these properties. At the same time, quantum statistics and quantum field theory strongly support the view that quantum particles are not individuals. Some of the problems faced in modern physics may be caused by such discrepancy between set theory and physical theory. The question then arises: Is it (...) possible to reconstruct the concept of set as a collection of objects that model quantum particles rather than as a mere collection of individuals? David Deutsch has argued that identical entities can be diverse in their attributes, and that this nature, what he calls fungibility, must lie at the heart of quantum physics. In line with this idea, a set theory with fungible elements is established, and the collection of such sets is shown to be endowed with an ortholattice structure, which is better known as quantum logic. (shrink)

The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of the (...) so-called “quantum liar paradox,” an experimental set-up alleged to be problematic for a spacetime conception of reality, and conclude by speculating on RBW’s implications for quantum gravity. (shrink)

Este artigo mostra que não há uma tese de subdeterminação de teorias científicas pelos indícios observacionais, mas várias. Identificamos quatro, com significados, plausibilidades e implicações distintos. Mostra-se que as mais fortes não passam de conjeturas, e que as mais fracas são mais plausíveis, mas não possuem implicações filosóficas robustas – em particular, não implicam o antirrealismo científico –, embora forneçam indícios de alternativas teóricas sistematicamente ignoradas na ciência, bem como do emprego de critérios em parte valorativos de escolha de teorias.

The concept of indistinguishable particles in quantum theory is fundamental to questions of ontology. All ordinary matter is made of electrons, protons, neutrons, and photons and they are all indistinguishable particles. Yet the concept itself has proved elusive, in part because of the interpretational difficulties that afflict quantum theory quite generally, and in part because the concept was so central to the discovery of the quantum itself, by Planck in 1900; it came encumbered with revolution. I offer a deflationary reading (...) of the concept ‘indistinguishable’ that is identical to Gibbs’ concept ‘generic phase’, save that it is defined for state spaces with only finitely-many states of bounded volume and energy. That, and that alone, makes for the difference between the quantum and Gibbs concepts of indistinguishability. This claim is heretical on several counts, but here we consider only the content of the claim itself, and its bearing on the early history of quantum theory rather than in relation to contemporary debates about particle indistinguishability and permutation symmetry. It powerfully illuminates that history. (shrink)

This paper aims to cast light on the reasons that explain the shift of opinion—from scepticism to realism—concerning the reality of atoms and molecules in the beginning of the twentieth century, in light of Jean Perrin’s theoretical and experimental work on the Brownian movement. The story told has some rather interesting repercussions for the rationality of accepting the reality of explanatory posits. Section 2 presents the key philosophical debate concerning the role and status of explanatory hypotheses c. 1900, focusing on (...) the work of Duhem, Stallo, Ostwald, Poincaré and Boltzmann. Section 3 examines in detail Perrin’s theoretical account of the molecular origins of Brownian motion, reconstructs the structure and explains the strength of Perrin’s argument for the reality of molecules. Section 4 draws three important lessons for the current debate over scientific realism. (shrink)

We explore a ‘Neo-Cartesian’ account of divine ultimacy that raises the concept of God to its ultimate level of abstraction so that we can do away with even the question of his existence. Our starting point is God’s relation to the logical and metaphysical order of reality and the views of Descartes and Leibniz on this topic. While Descartes held the seemingly bizarre view that the eternal truths are freely created by God, Leibniz stands for the mainstream view that the (...) eternal truths are grounded in God’s nature. We argue that the implausibility of Descartes’ doctrine stems mainly from the assumption that there is a non-epistemic notion of absolute necessity that constitutes the ultimate court of appeal for all modal questions and that this assumption is questionable. We also question the assumption that God’s ultimacy merely requires that all reality be grounded in God in the sense of mere explanation, so that it suffices if the necessary truths are grounded in God’s nature but not in God’s will. This will lead us to a reassessment of Descartes’ position. In the final and main part of the paper, we push Descartes’ doctrine of the creation of the eternal truths to its ‘logical’ conclusion with the aim of getting to a novel conception of ‘God.’. (shrink)

We explore a ‘Neo-Cartesian’ account of divine ultimacy that raises the concept of God to its ultimate level of abstraction so that we can do away with even the question of his existence. Our starting point is God’s relation to the logical and metaphysical order of reality and the views of Descartes and Leibniz on this topic. While Descartes held the seemingly bizarre view that the eternal truths are freely created by God, Leibniz stands for the mainstream view that the (...) eternal truths are grounded in God’s nature. We argue that the implausibility of Descartes’ doctrine stems mainly from the assumption that there is a non-epistemic notion of absolute necessity that constitutes the ultimate court of appeal for all modal questions and that this assumption is questionable. We also question the assumption that God’s ultimacy merely requires that all reality be grounded in God in the sense of mere explanation, so that it suffices if the necessary truths are grounded in God’s nature but not in God’s will. This will lead us to a reassessment of Descartes’ position. In the final and main part of the paper, we push Descartes’ doctrine of the creation of the eternal truths to its ‘logical’ conclusion with the aim of getting to a novel conception of ‘God.’. (shrink)

Philosophers of science have often favoured reductive approaches to how-possibly explanation. This article identifies three alternative conceptions making how-possibly explanation an interesting phenomenon in its own right. The first variety approaches “how possibly X?” by showing that X is not epistemically impossible. This can sometimes be achieved by removing misunderstandings concerning the implications of one’s current belief system but involves characteristically a modification of this belief system so that acceptance of X does not result in contradiction. The second variety offers (...) a potential how-explanation of X. It is usually followed by a range of further potential how-explanations of the same phenomenon. In recent literature the factual claims implied by the second variety have been downplayed whereas the heuristic role of mapping the space of conceptual possibilities has been emphasized. I will focus especially on this truth-bracketing sense of potentiality when looking closer at the second variety in the paper. The third variety has attracted less interest. It presents a partial how-explanation of X. Typically it aims to establish the existence of a mechanism by which X could be and was generated. The third conception stands out as the natural alternative for the advocate of ontic how-possibly explanations. This article transfers Salmon’s view that explanation-concepts can be broadly divided into epistemic, modal, and ontic to the context of how-possibly explanations. Moreover, it is argued that each of the three above-mentioned varieties of how-possibly explanation occurs in science. To recognize this may be especially relevant for philosophers. We are often misled by the promises of various why-explanation accounts, and seem to have forgotten nearly everything about the diversity of how-possibly explanations. (shrink)

In this paper I argue that if the Identity of Indiscernibles is not necessarily true, then Haecceitism ensues—where Haecceitism is the view that there are maximal possibilities that include all the same qualitative possibilities, and yet differ with respect to the non-qualitative possibilities they include. This goes against the common intuition that Anti-Haecceitism is compatible with the Identity of Indiscernibles being only contingently true. My argument is interesting in many respects. First, it shows that in any modal framework there is (...) a connection between the number of worldbound ordinary spatio-temporal objects, and the number of overall possibilities. Second, it has repercussions for the tenability of some philosophical positions, like Generalism, which is usually interpreted as entailing Anti-Haecceitism while at the same time being compatible with the claim that the Identity of Indiscernibles is not necessarily true. If I am correct, Generalism and similar philosophical accounts turn out to be inconsistent. Finally, it provides a strong argument for Haecceitism, given that the majority of authors today find counterexamples to the Identity of Indiscernibles extremely convincing, and many philosophical positions have been and continue being criticised on the basis of their commitment to the Identity of Indiscernibles. The paper is structured as follows: I introduce Haecceitism and the Identity of Indiscernibles in Sects. 1 and 2 respectively. Drawing on a result from the Philosophy of Quantum Mechanics, which I survey in Sect. 3, I give my main argument in Sect. 4. Finally, I discuss some implications in Sect. 5. (shrink)

We discuss the case against Factorism, which is the standard assumption in quantum mechanics that the labels of the $$\otimes$$ ⊗ -factor Hilbert-spaces in direct-product Hilbert-spaces of composite physical systems of similar particles refer to particles, either directly or descriptively. We distinguish different versions of Factorism and argue for their truth or falsehood. In particular, by introducing the concepts of snapshot Hilbert-space and Schrödinger-movie, we demonstrate that there are Hilbert-spaces and $$\otimes$$ ⊗ -factorisations where the labels do refer, even descriptively, (...) to similar particles, which renders them probabilistically absolutely discernible. (shrink)

We maximally extend the quantum‐mechanical results of Muller and Saunders ( 2008 ) establishing the ‘weak discernibility’ of an arbitrary number of similar fermions in finite‐dimensional Hilbert spaces. This confutes the currently dominant view that ( A ) the quantum‐mechanical description of similar particles conflicts with Leibniz’s Principle of the Identity of Indiscernibles (PII); and that ( B ) the only way to save PII is by adopting some heavy metaphysical notion such as Scotusian haecceitas or Adamsian primitive thisness. We (...) take sides with Muller and Saunders ( 2008 ) against this currently dominant view, which has been expounded and defended by many. *Received July 2008; revised May 2009. †To contact the authors, please write to: F. A. Muller, Faculty of Philosophy, Erasmus University Rotterdam, Burg. Oudlaan 50, H5–16, 3062 PA Rotterdam, The Netherlands; e‐mail: [email protected] , and Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected] . M. P. Seevinck, Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected]. (shrink)

This paper puts forward the hypothesis that the distinctive features of quantum statistics are exclusively determined by the nature of the properties it describes. In particular, all statistically relevant properties of identical quantum particles in many-particle systems are conjectured to be irreducible, ‘inherent’ properties only belonging to the whole system. This allows one to explain quantum statistics without endorsing the ‘Received View’ that particles are non-individuals, or postulating that quantum systems obey peculiar probability distributions, or assuming that there are primitive (...) restrictions on the range of states accessible to such systems. With this, the need for an unambiguously metaphysical explanation of certain physical facts is acknowledged and satisfied. (shrink)

In this paper, I consider the philosophical consequences of one tradition in Trinitarian theology, which emphasizes that each of the persons of the Trinity is wholly God. I pay special attention to Leftow’s claim that the persons of the Godhead must be divine in the same sense of the word ‘divine’ as the Godhead itself. I argue that the existing philosophical account of the Trinity which best captures this view is what I have termed the ‘Strong Theory of Relative Identity,’ (...) first proposed Peter Geach. I then develop what I take to be the most pressing objection to this account of the Trinity, namely that it cannot be supplemented with a coherent model-theoretic semantics. I end with a suggestion for responding to this objection. (shrink)

Although the present paper looks upon the formal apparatus of quantum mechanics as a calculus of correlations, it goes beyond a purely operationalist interpretation. Having established the consistency of the correlations with the existence of their correlata, and having justified the distinction between a domain in which outcome-indicating events occur and a domain whose properties only exist if their existence is indicated by such events, it explains the difference between the two domains as essentially the difference between the manifested world (...) and its manifestation. A single, intrinsically undifferentiated Being manifests the macroworld by entering into reflexive spatial relations. This atemporal process implies a new kind of causality and sheds new light on the mysterious nonlocality of quantum mechanics. Unlike other realist interpretations, which proceed from an evolving-states formulation, the present interpretation proceeds from Feynman’s formulation of the theory, and it introduces a new interpretive principle, replacing the collapse postulate and the eigenvalue–eigenstate link of evolving-states formulations. Applied to alternatives involving distinctions between regions of space, this principle implies that the spatiotemporal differentiation of the physical world is incomplete. Applied to alternatives involving distinctions between things, it warrants the claim that, intrinsically, all fundamental particles are identical in the strong sense of numerical identical. They are the aforementioned intrinsically undifferentiated Being, which manifests the macroworld by entering into reflexive spatial relations. (shrink)

In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. Being part of the Scientific Image of the world, the theory concerns the process by which (the physical aspect of) what Sellars called the Manifest Image of the world comes into being. This process consists in the progressive differentiation of an intrinsically undifferentiated entity. By entering (...) into reflexive spatial relations, this entity gives rise to (i) what looks like a multiplicity of relata if the reflexive quality of the relations is not taken into account, and (ii) what looks like a substantial expanse if the spatial quality of the relations is reified. If there is a distinctly quantum domain, it is a non-spatial and non-temporal dimension across which the transition from the unity of this entity to the multiplicity of the world takes place. Instead of being constituents of the physical world, subatomic particles, atoms, and molecules are instrumental in its manifestation. These conclusions are based on the following interpretive principle and its more direct consequences: whenever the calculation of probabilities calls for the addition of amplitudes, the distinctions we make between the alternatives lack objective reality. Applied to alternatives involving distinctions between regions of space, this principle implies that, owing to the indefiniteness of positions, the spatiotemporal differentiation of the physical world is incomplete: the existence of a real-valued spatiotemporal background is an unrealistic idealization. This guarantees the existence of observables whose values are real per se, as against “real by virtue of being indicated by the values of observables that are real per se.” Applied to alternatives involving distinctions between things, it implies that, intrinsically, all fundamental particles are numerically identical and thus identifiable with the aforementioned undifferentiated entity. (shrink)

In this article, I address concerns that the ontological priority claims definitive of ontic structural realism are as they stand unclear, and I do so by placing these claims on a more rigorous formal footing than they typically have been hitherto. I first of all argue that Kit Fine’s analysis of ontological dependence furnishes us with an ontological priority relation that is particularly apt for structuralism. With that in place, and with reference to two case studies prominent within the structuralist (...) literature, I consider whether any of structuralism’s distinctive priority claims may be regarded as warranted. The discussion as a whole has largely negative implications for the radical structuralism of French and Ladyman (including their ‘eliminativist’ interpretation of it), largely positive implications for the moderate structuralism primarily advocated by Esfeld and Lam, and some broad lessons for contemporary fundamentalist metaphysics as a whole. 1 Introduction2 The Right Priority Relation for Structuralism: Supervenience or Dependence?3 Introducing Ontological Dependence4 Fine’s System5 The Priority of Structure 1: Entangled Quantum Particles6 The Priority of Structure 2: The Group-Theoretic Conception of Elementary Particles7 Concluding Remarks. (shrink)

The feasibility of establishing a proper notion of a distinguishable object in the context of the de Broglie–Bohm approach to quantum mechanics seems, at first sight, uncontroversial by virtue of the fact that this theory can supposedly be interpreted in terms of a system of objective particles distinguished by individuating properties. However, after conducting a critical revision and evaluation of this trivial interpretation, and having assessed different alternatives that have been proposed in recent literature, I argue that within this theory (...) an appropriate notion of a distinguishable object can only be articulated by means of the following theoretical and metaphysical strategies: firstly, by appealing to a pre-existing, symmetrized Bohmian framework that is empirically indistinguishable but physically distinguishable from the standard Bohmian formulation; and secondly, by suggesting a different interpretation of this symmetrized formulation based upon a relational notion of the distinguishable object that can only be appropriately conceived from a structuralist point of view. (shrink)

The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription rule by (...) applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties. (shrink)

In this article I deal with the notion of observation, from a phenomenologically motivated point of view, and its representation mainly by means of the formal language of quantum mechanics. In doing so, I have taken the notion of observation in two diverse contexts. In one context as a notion related with objects of a logical-mathematical theory taken as registered facts of phenomenological perception ( Wahrnehmung ) inasmuch as this phenomenological idea can also be linked with a process of measurement (...) on the quantum-mechanical level. In another context I have taken it as connected with a notion of temporal constitution basically as it is described in E. Husserl’s texts on the phenomenology of temporal consciousness. Given that mathematical objects as formal-ontological objects can be thought of as abstractions of perceptual objects by means of categorial intuition, the question is whether and under what theoretical assumptions we can, in principle, include quantum objects in abstraction in the class of formal-ontological objects and thus inquire on the limits of their description within a formal-axiomatical theory. On the one hand, I derive an irreducibility on the level of individuals taken in formal representation as syntactical atoms-substrates without any further content and on the other hand a transcendental subjectivity of consciousness objectified as a self-constituted temporal unity upon which it is ultimately grounded the possibility of generation of an abstract predicative universe of discourse. (shrink)

In the context of discussions about the nature of ‘identical particles’ and the status of Leibniz’s Principle of the Identity of Indiscernibles in Quantum Mechanics, a novel kind of physical discernibility has recently been proposed, which we call witness-discernibility. We inquire into how witness-discernibility relates to known kinds of discernibility. Our conclusion will be that for a wide variety of cases, including the intended quantum-mechanical ones, witness-discernibility collapses extensionally to absolute discernibility, that is, to discernibility by properties.

The general question to be considered in this paper points to the nature of the world described by chemistry: what is macro-chemical ontology like? In particular, we want to identify the ontological categories that underlie chemical discourse and chemical practice. This is not an easy task, because modern Western metaphysics was strongly modeled by theoretical physics. For this reason, we attempt to answer our question by contrasting macro-chemical ontology with the mainstream ontology of physics and of traditional metaphysics. In particular, (...) we introduce the distinction between stuff-ontology, proper of chemistry, and individual-ontology, proper of physics. These two ontologies differ from each other in the basic categories of their own structures. On this basis, we characterize individual-ontology in such a way that the features of stuff-ontology will arise by contrast with it. (shrink)

The apparent chasm between two camps in metaphysics, analytic metaphysics and scientific metaphysics, is well recognized. I argue that the relationship between them is not necessarily a rivalry; a division of labour that resembles the relationship between pure mathematics and science is possible. As a case study, I look into the metaphysical underdetermination argument for ontic structural realism, a well‐known position in scientific metaphysics, together with an argument for the position in analytic metaphysics known as ontological nihilism. I argue that (...) we can ascribe the same schema to both arguments, which indicates that analytic metaphysics can offer an abstract model that scientific metaphysics may find useful. (shrink)

We discuss the case against Factorism, which is the standard assumption in quantum mechanics that the labels of the ⊗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\otimes$$\end{document}-factor Hilbert-spaces in direct-product Hilbert-spaces of composite physical systems of similar particles refer to particles, either directly or descriptively. We distinguish different versions of Factorism and argue for their truth or falsehood. In particular, by introducing the concepts of snapshot Hilbert-space and Schrödinger-movie, we demonstrate that there are Hilbert-spaces and ⊗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\otimes$$\end{document}-factorisations where the labels do refer, even descriptively, to similar particles, which renders them probabilistically absolutely discernible. (shrink)