Este artigo propõe a discussão da educação escolar tomando como ponto de partida a burocracia, a racionalidade e o conceito de desencantamento do mundo proposto por Max Weber. Por fim, discutimos os impactos para a subjetividade dos principais envolvidos no processo educacional – professor e aluno – para sinalizar possíveis movimentos que tornem mais dinâmica as relações humanas na educação institucionalizada.

Founding our analysis on the Geneva-Brussels approach to quantum mechanics, we use conventional macroscopic objects as guiding examples to clarify the content of two important results of the beginning of twentieth century: Einstein–Podolsky–Rosen’s reality criterion and Heisenberg’s uncertainty principle. We then use them in combination to show that our widespread belief in the existence of microscopic particles is only the result of a cognitive illusion, as microscopic particles are not particles, but are instead the ephemeral spatial and local manifestations of (...) non-spatial and non-local entities. (shrink)

This paper focuses on Kant's account of physical geography and his theory of the Earth. In spelling out the epistemological foundations of Kant's physical geography, the paper examines 1) their connection to the mode of holding-to-be-true, mathematical construction and empirical certainty and 2) their implications for Kant's view of cosmopolitan right. Moreover, by showing the role played by the mathematical model of the Earth for the foundations of Kant's Doctrine of Right, the exact relationship between the latter and physical geography (...) is highlighted. Finally, this paper shows how, in Kant's view, the progress of physical geography can be assured if and only if the free circulation of human beings is established and regulated by law. Therefore, examining the mutual relationship between the theory of Earth and the foundations of right opens new perspectives on the relationship between epistemology and practical philosophy within Kant's system. (shrink)

We consider the classical concept of time of permanence and observe that its quantum equivalent is described by a bona fide self-adjoint operator. Its interpretation, by means of the spectral theorem, reveals that we have to abandon not only the idea that quantum entities would be characterizable in terms of spatial trajectories but, more generally, that they would possess the very attribute of spatiality. Consequently, a permanence time shouldn’t be interpreted as a “time” in quantum mechanics, but as a measure (...) of the total availability of a quantum entity in participating to a process of creation of a spatial localization. (shrink)

In The Explanatory Dispensability of Idealizations, Sam Baron suggests a possible strategy enabling the indispensability argument to break the symmetry between mathematical claims and idealization assumptions in scientific models. Baron’s distinction between mathematical and non-mathematical idealization, I claim, is in need of a more compelling criterion, because in scientific models idealization assumptions are expressed through mathematical claims. In this paper I argue that this mutual dependence of idealization and mathematics cannot be read in terms of symmetry and that Baron’s non-causal (...) notion of mathematical difference-making is not effective in justifying any symmetry-breaking between mathematics and idealization. The function of making a difference that Baron attributes to mathematics cannot be referred to physical facts, but to the features of quantities, such as step lengths or time intervals taken into account in the models. It appears, indeed, that it does not follow from Baron’s argument that idealizations do not help to carry the explanatory load at least for two reasons: mathematics is not independent of idealizations in modelling and idealizations help mathematics to carry the explanatory load of a model in different degrees. (shrink)

In the section of the Antinomy of pure Reason Kant presents three notions of infinity. By investigating these concepts of infinity, this paper highlights important ‘building blocks’ of the structure of the mathematical antinomies, such as the ability of reason of producing ascending and descending series, as well as the notions of given and givable series. These structural features are discussed in order to clarify Ernst Zermelo’s reading of Kant’s antinomy, according to which the latter is deeply rooted in the (...) tendency of the mind of producing “creative progress” and “inclusive closure”. The aim of this paper is to explain in which sense and why Kant’s treatment of the antinomies attracts the attention of Zermelo in the early 1900s and which aspects of his second axiomatic system have been inspired by Kant’s philosophy. Thus, by reading Kant’s antinomy ‘through Zermelo’s eyes’—with emphasis on the concept of regressive series in indefinitum and on that of regressive series ad infinitum – this paper identifies the echoes of Kant’s work in the making of the ZFC set theory. (shrink)

In 1975, two experimental groups have independently observed the \-symmetry of neutrons’ spin, when passing through a static magnetic field, using a three-blade interferometer made from a single perfect Si-crystal. In this article, we provide a complete analysis of the experiment, both from a theoretical and conceptual point of view. Firstly, we solve the Schrödinger equation in the weak potential approximation, to obtain the amplitude of the refracted and forward refracted beams, produced by the passage of neutrons through one of (...) the three plates of the LLL interferometer. Secondly, we analyze their passage through a static magnetic field region. This allows us to find explicit expressions for the intensities of the four beams exiting the interferometer, two of which will be interfering and show a typical \-symmetry, when the strength of the magnetic field is varied. In the last part of the article, we provide a conceptual analysis of the experiment, showing that a neutron’s phase change, when passing through the magnetic field, is due to a longitudinal Stern–Gerlach effect, and not to a Larmor precession. We also emphasize that these experiments do not prove the observability of the sign change of the wave function, when a neutron is \ rotated, but strongly indicate that the latter, like any other elementary “particle,” would be a genuinely non-spatial entity. (shrink)

The objectives of the Center Leo Apostel for Interdisciplinary Studies were summarized by his creator as: interdisciplinarity, construction of world views and broad dissemination of scientific knowledge. In compliance with the third of these objectives, we provide a rigorous but accessible popular science version of a research article published by Aerts and Sassoli de Bianchi, where an extended version of the quantum formalism was proposed as a possible solution to the measurement problem. We hope that through articles of this (...) kind, written with an educational spirit and addressed to both academic and nonacademic readers, the interdisciplinary dialogue about foundational issues will be stimulated and the gap between the different sciences reduced. (shrink)

SPECIAL SECTION: BUILDING UNIVERSES: THE PHILOSOPHICAL AND MATHEMATICAL UNDERPINNINGS OF COSMOLOGY (EIGHTEENTH–TWENTIETH CENTURIES) .

The purpose of this article is threefold. Firstly, it aims to present, in an educational and non-technical fashion, the main ideas at the basis of Aerts’ creation-discovery view and hidden measurement approach : a fundamental explanatory framework whose importance, in this author’s view, has been seriously underappreciated by the physics community, despite its success in clarifying many conceptual challenges of quantum physics. Secondly, it aims to introduce a new quantum machine—that we call the δ quantum machine —which is able to (...) reproduce the transmission and reflection probabilities of a one-dimensional quantum scattering process by a Dirac delta-function potential. The machine is used not only to demonstrate the pertinence of the above mentioned explanatory framework, in the general description of physical systems, but also to illustrate (in the spirit of Aerts’ ∊-model) the origin of classical and quantum structures, by revealing the existence of processes which are neither classical nor quantum, but irreducibly intermediate. We do this by explicitly introducing what we call the k-model and by proving that its processes cannot be modelized by a classical or quantum scattering system. The third purpose of this work is to exploit the powerful metaphor provided by our quantum machine, to investigate the intimate relation between the concept of potentiality and the notion of non-spatiality , that we characterize in precise terms, introducing for this the new concept of process-actuality. (shrink)

It is generally assumed, and usually taken for granted, that reality is fully contained in space. However, when taking a closer look at the strange behavior of the entities of the micro-world, we are forced to abandon such a prejudice and recognize that space is just a temporary crystallization of a small theatre for reality, where the material entities can take a place and meet with each other. More precisely, phenomena like quantum entanglement, quantum interference effects and quantum indistinguishability, when (...) analyzed attentively, tell us that there is much more in our physical reality than what meets our three-dimensional human eyes. But if the building blocks of our physical reality are non-spatial, what does it mean? Can we understand what the nature of a non-spatial entity is? And if so, what are the consequences for our view of the world in which we live and evolve as a species? This article was written having in mind one of the objectives of the Center Leo Apostel for Interdisciplinary Studies, that of a broad dissemination of scientific knowledge. Hence, it addresses a transversal audience of readers, both academic and nonacademic, hoping to stimulate in this way the interdisciplinary dialogue about foundational issues in science. (shrink)

This contribution sheds light on the role of infinite idealization in structural analysis, by exploring how infinite elements and finite element methods are combined in civil engineering models. This combination, I claim, should be read in terms of a ‘complementarity function’ through which the representational ideal of completeness is reached in engineering model-building. Taking a cue from Weisberg’s definition of multiple-model idealization, I highlight how infinite idealizations are primarily meant to contribute to the prediction of structural behavior in Multiphysics approaches.

The question of the dimensionality of space has informed the development of physics since the beginning of the twentieth century in the quest for a unified picture of quantum processes and gravitation. Scientists have worked within various approaches to explain why the universe appears to have a certain number of spatial dimensions. The question of why space has three dimensions has a genuinely philosophical nature that can be shaped as a problem of justifying a contingent necessity of the world. In (...) contrast to explanations of three-dimensionality based on anthropic arguments, we support the search for a theory that provides a justification for the dimensionality of space based on a combination of deductive and inductive reasoning applied to science. In doing so, we argue that Kant correctly approached the question in “Thoughts on the true estimation of living forces” by connecting space dimensionality and the inverse square law. In expounding the strategy of Kant’s argument, we describe the main features of a general Kantian explanation of the dimensionality of space and discuss them with respect to current accounts of explanation in the philosophy of science, such as inference to the best explanation and the deductive-nomological model. (shrink)

Founding our analysis on the Geneva-Brussels approach to the foundations of physics, we provide a clarification and classification of the key concept of observation. An entity can be observed with or without a scope. In the second case, the observation is a purely non-invasive discovery process; in the first case, it is a purely invasive process, which can involve either creation or destruction aspects. An entity can also be observed with or without a full control over the observational process. In (...) the latter case, the observation can be described by a symmetry breaking mechanism, through which a specific deterministic observational process is selected among a number of potential ones, as explained in Aerts’ hidden measurement approach. This is what is called a product test, or product observation, whose consequences are that outcomes can only be predicted in probabilistic terms, as it is the case in typical quantum measurements. We also show that observations can be about intrinsic (stable) properties of the observed entity, or about relational (ephemeral) properties between the observer and observed entities; also, they can be about intermediate properties, neither purely classical, nor purely quantum. Our analysis allows us to propose a general conceptual characterization of quantum measurements, as observational processes involving three aspects: (1) product observations, (2) pure creation aspects and (3) ephemeral relational properties. We also discuss the important concept of non-spatiality and emphasize some of the differences and similarities between quantum and classical/relativistic observations. (shrink)

How can we explain the strange behavior of quantum and relativistic entities? Why do they behave in ways that defy our intuition about how physical entities should behave, considering our ordinary experience of the world around us? In this article, we address these questions by showing that the comportment of quantum and relativistic entities is not that strange after all, if we only consider what their nature might possibly be: not an objectual one, but a conceptual one. This not in (...) the sense that quantum and relativistic entities would be human concepts, but in the sense that they would share with the latter a same conceptual nature, similarly to how electromagnetic and sound waves, although very different entities, can share a same undulatory nature. When this hypothesis is adopted, i.e., when a conceptuality interpretation about the deep nature of physical entities is taken seriously, many of the interpretational difficulties disappear and our physical world is back making sense, though our view of it becomes radically different from what our classical prejudice made us believe in the first place. (shrink)

a relação entre razão e natureza envolve um dos principais aspectos da crítica da teleologia de Kant. Visando destacar esta relação, investigarei o conceito de técnica da natureza, tal como introduzida na Crítica da faculdade de julgar. De acordo com Kant, a técnica da natureza permite as leis da razão a representarem o acordo dos princípios transcendentais da razão com a natureza. Deste modo, o conceito da técnica da natureza assume um papel prolífico ao expor, através de uma analogia com (...) as faculdades humanas, a atividade produtiva da natureza, como se sua atividade fosse orientada a fins.The relationship between reason and nature embodies one of the main aspects of Kant‟s critique of teleology. In order to highlight this relation, I shall investigate the concept of the technique of nature, as it has been introduced in Critique of the Power of Judgment. According to Kant, the technique of nature allows the laws of reason to represent the agreement of the transcendental principles of reason with nature. Thus, the concept of the technique of nature assumes a fruitful role by exposing, through an analogy with human faculties, the productive activity of nature, as if its activity were oriented towards ends. (shrink)

By exploring the nature of scientific representative practices, I shall define a methodology that relates the use of symmetry to specific practical functions. In order to expound this approach, I shall investigate the role played by the conception of symmetry in representative practices from a philosophical and epistemological perspective. The paper proceeds as follows. In the first part, I introduce the reasons why our conception of representative practices should consider the aims and the objectives towards which they direct their interest. (...) Secondly, by using symmetry as a case study, I try to show that philosophy can find fruitful pathways of interaction with sciences, as it is the case when it deals with the practical implications of the employment of symmetry in modeling. In the third section of the paper I shall refer to other examples that highlight the use of symmetry in scientific representative practices. I shall conclude with some remarks on the implications that this approach involves in epistemology, especially on our conception of objectivity and symmetry. (shrink)

We investigate indeterminism in physical observations. For this, we introduce a distinction between genuinely indeterministic observational processes, and fully deterministic observational processes, which we analyze by drawing a parallel between the localization properties of microscopic entities, like electrons, and the lateralization properties of macroscopic entities, like simple elastic bands. We show that by removing the randomness incorporated in certain of our observational processes, acquiring over them a better control, we also alter these processes in such a radical way that in (...) the end they do not correspond anymore to the observation of the same property. We thus conclude that a certain amount of indeterminism must be accepted and welcomed in our physical observations, as we cannot get rid of it without also diminishing our discriminative power. We also provide in our analysis some elements of clarification regarding the non-spatial nature of microscopic entities, which we illustrate by using an analogy with the process of objectification of human concepts. Finally, the important notion of relational properties is properly defined, and the role played by indeterminism in their characterization clarified. (shrink)

Many advocates of the Everettian interpretation consider that theirs is the only approach to take quantum mechanics really seriously, and that this approach allows to deduce a fantastic scenario for our reality, one that consists of an infinite number of parallel worlds that branch out continuously. In this article, written in dialogue form, we suggest that quantum mechanics can be taken even more seriously, if the many-worlds view is replaced by a many-measurements view. This allows not only to derive the (...) Born rule, thus solving the measurement problem, but also to deduce a one-world non-spatial reality, providing an even more fantastic scenario than that of the multiverse. (shrink)

In the 1780s Kant’s critique of rational cosmology clearly identified the limits of theoretical cosmology in agreement with the doctrine of transcendental idealism of space and time. However, what seems to be less explored, and remains still a desideratum for the literature, is a thorough investigation of the implications of transcendental philosophy for Kant’s view of cosmology in the 1790s. This contribution fills this gap by investigating Kant’s view of teleology and measurement in the Critique of Judgment, exploring their implications (...) for Kant’s late view of cosmology. Considering the historical and scientific context in which Kant developed his reflections motivates my proposal to read Kant’s late view of the universe in terms of “functional cosmology.” -/- . (shrink)

A correction to this paper has been published: https://doi.org/10.1007/s10699-021-09793-2.

We present the fundamentals of the quantum theoretical approach we have developed in the last decade to model cognitive phenomena that resisted modeling by means of classical logical and probabilistic structures, like Boolean, Kolmogorovian and, more generally, set theoretical structures. We firstly sketch the operational-realistic foundations of conceptual entities, i.e. concepts, conceptual combinations, propositions, decision-making entities, etc. Then, we briefly illustrate the application of the quantum formalism in Hilbert space to represent combinations of natural concepts, discussing its success in modeling (...) a wide range of empirical data on concepts and their conjunction, disjunction and negation. Next, we naturally extend the quantum theoretical approach to model some long-standing ‘fallacies of human reasoning’, namely, the ‘conjunction fallacy’ and the ‘disjunction effect’. Finally, we put forward an explanatory hypothesis according to which human reasoning is a defined superposition of ‘emergent reasoning’ and ‘logical reasoning’, where the former generally prevails over the latter. The quantum theoretical approach explains human fallacies as the consequence of genuine quantum structures in human reasoning, i.e. ‘contextuality’, ‘emergence’, ‘entanglement’, ‘interference’ and ‘superposition’. As such, it is alternative to the Kahneman–Tversky research programme, which instead aims to explain human fallacies in terms of ‘individual heuristics and biases’. (shrink)

We present the fundamentals of the quantum theoretical approach we have developed in the last decade to model cognitive phenomena that resisted modeling by means of classical logical and probabilistic structures, like Boolean, Kolmogorovian and, more generally, set theoretical structures. We firstly sketch the operational-realistic foundations of conceptual entities, i.e. concepts, conceptual combinations, propositions, decision-making entities, etc. Then, we briefly illustrate the application of the quantum formalism in Hilbert space to represent combinations of natural concepts, discussing its success in modeling (...) a wide range of empirical data on concepts and their conjunction, disjunction and negation. Next, we naturally extend the quantum theoretical approach to model some long-standing ‘fallacies of human reasoning’, namely, the ‘conjunction fallacy’ and the ‘disjunction effect’. Finally, we put forward an explanatory hypothesis according to which human reasoning is a defined superposition of ‘emergent reasoning’ and ‘logical reasoning’, where the former generally prevails over the latter. The quantum theoretical approach explains human fallacies as the consequence of genuine quantum structures in human reasoning, i.e. ‘contextuality’, ‘emergence’, ‘entanglement’, ‘interference’ and ‘superposition’. As such, it is alternative to the Kahneman–Tversky research programme, which instead aims to explain human fallacies in terms of ‘individual heuristics and biases’. (shrink)

This book focuses on two central topics that could help us answer how Plato conceives of the physical world and its relationship to Forms. The first one is the Platonic concept of time. What is it, how is it defined, what is it not, and how does it help us describe the changing realities surrounding us? The second one is Plato’s understanding of the perceptible world. How is it related to Forms, and how exactly does it work? These are central, (...) wide-ranging, and highly contested questions garnering attention in recent Platonic scholarship. We have ensembled an international team that aims to offer bold, innovative, and thought-provoking answers to these questions. The nine contributions in this book represent a diverse range of starting points, methodologies, and interpretative traditions whose collective aim is to challenge your assumptions about Plato’s philosophy and help you rethink and revisit the Platonic corpus with fresh eyes. (shrink)

The passage of a spin-1/2neutral particle through a region of uniform magnetic field and the corresponding precession mechanism is analyzed from the viewpoint of scattering theory, with particular consideration of the role of the field boundaries.

In the first half of this two-part article, we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of Two Different Wind Directions, and showed that the data violate the CHSH version of Bell’s inequality, with same magnitude as in typical Bell-test experiments in physics. In this second part, we complete our analysis by presenting a symmetrized version of the experiment, still violating the CHSH inequality but now (...) also obeying the marginal law, for which we provide a full quantum modeling in Hilbert space, using a singlet state and suitably chosen product measurements. We also address some of the criticisms that have been recently directed at experiments of this kind, according to which they would not highlight the presence of genuine forms of entanglement. We explain that these criticisms are based on a view of entanglement that is too restrictive, thus unable to capture all possible ways physical and conceptual entities can connect and form systems behaving as a whole. We also provide an example of a mechanical model showing that the violations of the marginal law and Bell inequalities are generally to be associated with different mechanisms. (shrink)

We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of Two different wind directions. Data are shown to violate the CHSH version of Bell’s inequality with the same magnitude as in typical Bell-test experiments with entangled spins. Wind directions thus appear to be conceptual entities connected through meaning, in human cognition, in a similar way as spins appear to be entangled in experiments conducted in physics (...) laboratories. This is the first part of a two-part article. In the second part we present a symmetrized version of the same experiment for which we provide a quantum modeling of the collected data in Hilbert space. (shrink)

How can we explain the strange behavior of quantum and relativistic entities? Why do they behave in ways that defy our intuition about how physical entities should behave, considering our ordinary experience of the world around us? In this article, we address these questions by showing that the comportment of quantum and relativistic entities is not that strange after all, if we only consider what their nature might possibly be: not an objectual one, but a conceptual one. This not in (...) the sense that quantum and relativistic entities would be human concepts, but in the sense that they would share with the latter a same conceptual nature, similarly to how electromagnetic and sound waves, although very different entities, can share a same undulatory nature. When this hypothesis is adopted, i.e., when a conceptuality interpretation about the deep nature of physical entities is taken seriously, many of the interpretational difficulties disappear and our physical world is back making sense, though our view of it becomes radically different from what our classical prejudice made us believe in the first place. (shrink)