Olimpia Lombardi

Standard quantum mechanics poses serious challenges to some principles deeply entrenched in traditional metaphysics. In particular, the theory defies the ontological category of individual object through three of its features: contextuality, non-separability, and indistinguishability. The difficulties have prompted the development of non-traditional ontological frameworks intended to account for the quantum domain. Some approaches advocate replacing the classical conception of a realm of objects endowed with properties by an ontology that either dispenses with the category of object altogether or treats it as a derivative notion. The Modal-Hamiltonian Interpretation (MHI) of quantum mechanics and Ontic Structural Realism (OSR) exemplify this position. MHI proposes an ontology in which quantum systems are non-objectual bundles of properties linked by definite physical relations. The OSR defends the ontological primacy of structures, within which objects are construed as nodes of relations. The aim of this article is to compare these two ontological approaches, highlighting both their points of convergence and their divergences, particularly in light of the ontological challenges posed by quantum mechanics. With this aim, the article is structured as follows. Section 2 outlines the ontology of MHI, introducing the distinction between type-properties and case-properties, characterizing quantum systems as non-objectual bundles, and analyzing the role of symmetry groups in providing physical content to the theory and governing actualization. Section 3 turns to OSR, examining its motivations, its distinction between physical and mathematical structures, and the modal character of structures. Section 4 offers a systematic comparison of the two approaches, considering their respective motivations and scope, their shared commitment to an object-free ontology, the role played by symmetry groups within each framework, and their contrasting interpretations of modality. Finally, Section 5 presents some concluding remarks.

One of the major appeals of Ontic Structural Realism (OSR) is to provide a me-taphysical proposal capable of dealing with the ontological problem of quan-tum indistinguishability. The Modal-Hamiltonian Interpretation of quantum mechanics (MHI), on the other hand, aspires to formulate a “global” solution, in which all the ontological problems of the theory can be adequately addressed in terms of a single ontology. In both proposals, the ontological category of ob-ject is absent. The purpose of the present article is to analyze the MHI ontology by suggesting that it satisfies the central motivations that led to the formulation of OSR but also overcomes the conceptual problems that OSR has faced since its formulation.

Modal Interpretations of quantum mechanics distinguish between the realm of possibility, where the dynamical state determines what may be the case, and the realm of actuality, where the value state represents what actually is the case. In particular, the Modal-Hamiltonian Interpretation proposes an ontology in which there are no individual objects: quantum systems are characterized as non-individual bundles of properties. The aim of the present paper is to propose some first steps towards the development of a new modal logic adapted to describe a possibilist modality in an ontology of properties. The main idea consists in conceiving possibility as fundamental and introducing actuality as an operator acting on possible facts. On this basis, propositions referring to possible facts and propositions referring to actual facts are distinguished, and some relations between the realm of possibility and the realm of actuality are introduced.

When compared with other areas of the philosophy of science, the philosophy of chemistry is a new branch that entered an already highly developed field of research about science. For this reason, in spite of having opened its own agenda, the philosophy of chemistry inherited a style of philosophizing modeled by the post-positivistic analytic tradition. Although one cannot deny the powerful conceptual tools that this tradition offered to the philosophy of science of the twentieth century, one can neither ignore the strong boundaries that it imposed to what can be thought in the field. One of the areas that remained beyond those boundaries was the Kantian philosophy. In fact, the debates about scientific realism were usually confined to the non-observational domain, whereas the existence of a realm of observable entities independent of any knowledge was acritically accepted by the traditional philosophy of science. And although the ?new philosophy of science? began to challenge that strongly entrenched assumption, the analytic tradition rapidly drove the discussions to the domain of language. As a consequence, the problem of realism in science is still analyzed by many authors in terms of the search of a theory of reference for the scientific language, a strategy that confines the debate to a context where the analytic philosophers feel comfortable. The general purpose of this article is to contribute to revert this trend in the contemporary philosophy of science by taking seriously the Copernican revolution proposed by Kant, which places the subject at the center of any research about knowledge. We will argue that Kantian ideas supply a new perspective to face several of the most discussed topics in the philosophy of chemistry, in particular, the relationship between chemistry and physics, as well as the existence of laws in chemistry and the question about chemical kinds.

One of the main ontological challenges posed by quantum mechanics is the problem of the indistinguishability of so-called “identical” particles, that is, particles that share the same state-independent properties. In the framework of this philosophical problem, a quasi-set theory was formulated to provide a proper metalanguage to deal with quantum indistinguishability; this theory included certain Urelemente called m-atoms, representing essentially indistinguishable objects. In turn, over the last two decades, the Modal Hamiltonian Interpretation proposed an ontology of properties, totally devoid of objects, where quantum systems are bundles of instances of universal properties. Therefore, the original quasi-set theory, with its m-atoms, does not adequately reflect the structure of an ontology devoid of objects. The purpose to the present article is to introduce a new quasi-set theory that does not include atoms at all: elementary items correspond to properties and are also represented by quasi-sets, which can be only numerically different. The final aim is to apply this new quasi-set theory to the MHI ontology.

Modal Interpretations of quantum mechanics distinguish between the realm of possibility, where the dynamical state determines what may be the case, and the realm of actuality, where the value state represents what actually is the case. In particular, the Modal-Hamiltonian Interpretation proposes an ontology in which there are no individual objects: quantum systems are characterized as non-individual bundles of properties. The aim of the present paper is to propose some rst steps towards the development of a new modal logic adapted to describe a possibilist modality in an ontology of properties. The main idea consists in conceiving possibility as fundamental and introducing actuality as an operator acting on possible facts. On this basis, propositions referring to possible facts and propositions referring to actual facts are distinguished, and some relations between the realm of possibility and the realm of actuality are introduced.

One of the main ontological challenges posed by quantum mechanics is the problem of the indistinguishability of so-called “identical” particles, that is, particles that share the same state-independent properties. In the framework of this philosophical problem, a quasi-set theory was formulated to provide a proper metalanguage to deal with quantum indistinguishability; this theory included certain Urelemente called m-atoms, representing essentially indistinguishable objects. In turn, over the last two decades, the Modal Hamiltonian Interpretation proposed an ontology of properties, totally devoid of objects, where quantum systems are bundles of instances of universal properties. Therefore, the original quasi-set theory, with its m-atoms, does not adequately reflect the structure of an ontology devoid of objects. The purpose to the present article is to introduce a new quasi-set theory that does not include atoms at all: elementary items correspond to properties and are also represented by quasi-sets, which can be only numerically different. The final aim is to apply this new quasi-set theory to the MHI ontology.

The concept of molecular structure is one of the most important concepts of chemistry. In fact, molecular structure is closely related to the concept of chemical substance and its set of properties, and it is the main factor in the explanation of reactivity. In fact, much of the behavior of substances is explained in terms of the structure of their component molecules. This may explain why people tend to take the notion of molecular structure for granted. However, the problem begins already when it comes to specifying the concept, since there is no clear definition of ‘molecular structure’ valid for all chemistry. The purpose of the present article is to show that the term ‘molecular structure’ subsumes very different notions, which depend on how the molecule and its components are conceived, and each of which brings its own difficulties. In particular, we will focus on how the molecule and its structure are devised from a classical view and from a quantum–mechanical view, and will discuss the different problems related with molecular structure that arise in each case.

In a series of recent articles, the problem of individuality in quantum theory was addressed from a radical position: there are neither individuals nor quasi-individuals in the quantum ontology; the quantum world is populated by quantum properties that form bundles which, nevertheless, do not acquire the features necessary to be characterized by the ontological category of individual.The aim of the present article is to relate this view with the symmetries of quantum theories. First, we will argue that, although quantum systems are non-individual bundles, the group of symmetry of non-relativistic quantum mechanics, the Galilei group, introduces in the bundle the difference between essential and contingent properties. Under certain conditions, those essential properties generate the illusion of the presence of an individual. Nevertheless, this is not the case when the behavior of the bundle is considered in its relation with other bundles, for instance, when statistical reasoning is involved. Second, we will extrapolate this idea to other quantum theories. For instance, in relativistic quantum mechanics and in quantum field theory, the space-time symmetry represented by the Poincaré group and the gauge symmetries also define the essential properties of the non-individual bundles, which are precisely the properties that define the different kinds of the so-called fundamental “particles”.

The term ‘polymath’ comes from the Greek ‘πολυμαθής’ (‘polimathós’) and means “who knows many things”. It was coined in the Renaissance and was paradigmatically applied to Leonardo Da Vinci for well-known reasons. In today’s world of hyper-specialization, extremely few individuals embody the ideal of the Renaissance man and his polymathy: one such exceptional case is Roberto Torretti. His overwhelming intellectual power allowed him not only to be self-taught in multiple and dissimilar areas, but also to excel in all of them. It is impossible to cover all or even many of the aspects that Torretti developed during his academic life. Therefore, those of us who admire him so much can only take a specific issue and try to contribute to his work with some detail. This is the strategy I will adopt in this article. In particular, I will take as a starting point Torretti’s defense of what he called, following Hilary Putnam, “pragmatic realism”, as well as the particular examples, coming from physics, that he presented to support his position. The aim of the present article is to add a new example, but in this case coming from chemistry: the use of Born-Oppenheimer approximation in the field of quantum chemistry. For this purpose, the paper is organized as follows. In Section 2, I will recall pragmatic realism as conceived by Torretti, and the two examples to which he resorts: Hawking’s explanation for black hole evaporation, and the account of the precession of Mercury’s perihelion. Section 3 will be devoted to introducing an overview of what has been perhaps the central problem of the philosophy of chemistry since its inception: the relationship between chemistry and physics, in particular quantum mechanics. This presentation will allow me, in Section 4, to explain the problem of molecular structure as a particular case of the above problem. On this basis, in Section 5 the role of the Born-Oppenheimer approximation in the account of molecular structure will be discussed, showing how this case points to the same direction as Torretti’s examples. Finally, in Section 6, I will make some closing remarks.

Although Bohr’s Correspondence Principle (CP) played a central role in the first days of quantum mechanics, its original version seems to have no present-day relevance. The purpose of this article is to show that the CP, with no need of being interpreted in terms of the quantum-to-classical limit, still plays a relevant role in the understanding of the relationships between the classical and the quantum domains. In particular, it will be argued that a generic version of the CP is very helpful in elucidating the physical meaning of the phenomenon of quantum decoherence.

Some authors, inspired by the theoretical requirements for the formulation of a quantum theory of gravity, proposed a relational reconstruction of the quantum parameter-time—the time of the unitary evolution, which would make quantum mechanics compatible with relativity. The aim of the present work is to follow the lead of those relational programs by proposing a relational reconstruction of the event-time—which orders the detection of the definite values of the system’s observables. Such a reconstruction will be based on the modal-Hamiltonian interpretation of quantum mechanics, which provides a clear criterion to select which observables acquire a definite value and to specify in what situation they do so.

Although the electron density can be calculated with the formal resources of quantum mechanics, in physics it does not play the leading role that the quantum state does. In contrast, the concept of electron density is central in quantum chemistry. There is no doubt about how the electron density is computed in terms of the wave function of an atom or molecule. However, when the interpretation of the concept is at stake, there is no general agreement. In this article we will analyze the two main interpretations of the concept of electron density: the Born-style probability density interpretation and the Schrödinger-style charge density interpretation. In particular, we will examine their differences, their relations with quantum mechanics and the consequences that each of them entails from a strictly quantum point of view.

In a recent article entitled “The problem of molecular structure just is the measurement problem”, Alexander Franklin and Vanessa Seifert argue that insofar as the quantum measurement problem is solved, the problems of molecular structure are resolved as well. The purpose of the present article is to show that such a claim is too optimistic. Although the solution of the quantum measurement problem is relevant to how the problem of molecular structure is faced, such a solution is not sufficient to account for the structure of molecules as understood in the field of chemistry.

El objetivo del presente trabajo es contribuir a la discusión epistemológica acerca de la Teoría del Caos. Nos concentramos en el problema de la definición de caos, argumentando que impredictibilidad y aleatoriedad algorítmica no constituyen una base satisfactoria para definir el caos. El análisis de las diferentes manifestaciones del caos nos permite considerar el problema de encontrar una definición de caos única y adecuada -una definición que brinde condiciones necesarias y suficientes válidas para todas los casos. Sostenemos que, dado el carácter matemático de la temía, la definición debe extraerse a partir de las características de las ecuaciones caóticas.

The concept of molecular structure is one of the most important concepts of chemistry. In fact, molecular structure is closely related to the concept of chemical substance and its set of properties, and it is the main factor in the explanation of reactivity. In fact, much of the behavior of substances is explained in terms of the structure of their component molecules. This may explain why people tend to take the notion of molecular structure for granted. However, the problem begins already when it comes to specifying the concept, since there is no clear definition of ‘molecular structure’ valid for all chemistry. The purpose of the present article is to show that the term ‘molecular structure’ subsumes very different notions, which depend on how the molecule and its components are conceived, and each of which brings its own difficulties. In particular, we will focus on how the molecule and its structure are devised from a classical view and from a quantum–mechanical view, and will discuss the different problems related with molecular structure that arise in each case.

To which ontological category do quantum systems belong? Although we usually speak of particles, it is well known that these peculiar items defy several traditional metaphysical principles. In the present chapter these challenges will be discussed in the light of certain distinctions usually not taken into account in the debate about the ontological nature of quantum systems. On this basis, it will be argued that an ontology of properties without individuals, framed in the algebraic formalism of quantum mechanics, provides adequate answers to the ontological challenges raised by the theory.What kind of item is a quantum system? In the practice of physics it is common to speak of quantum particles, as if they were items of a similar nature to classical items, but obeying different laws of motion. However, as is well known, quantum systems have such peculiar features that they challenge certain ontological principles and categories as understood in traditional metaphysics. In general, these features are analyzed in the context of the so-called problem of indistinguishability, which is a consequence of the particular statistical behavior of quantum systems. But the fact that certain items are “indistinguishable” is not the only difficulty to be overcome in order to elucidate the ontological category of quantum systems.

After the preeminence of logical positivism/empiricism during the most part of twentieth century, during the last decades many authors began to recognize the relevance of the Kantian thought for present-day philosophy of science. This chapter follows this general trend, adopting a realist reading of Kantian teachings. On this basis, I will delineate a Kantian-rooted realism according to which the worlds of science are always the result of a synthesis between the conceptual schemes embodied in scientific theories and practices and the independent noumenal reality. However, my position takes distance from the Kantian doctrine by admitting the possibility of different conceptual schemes, both diachronically and synchronically. This view not only leaves room for abrupt and discontinuous changes in the history of science, but also leads to an ontological pluralism that allows for the coexistence of irreducible and different, even incompatible ontological domains at the same historical time. I will focus particularly on the synchronic case to reject both ontological reductionism and emergentism from a perspective that denies any priority or dependence between domains, in resonance with a non-hierarchical articulation between scientific theories and disciplines.