Una raccolta di riflessioni originali sul rapporto tra la scienza e la nostra società, a partire dal pensiero del grande fisico e intellettuale Carlo Bernardini.

Modern color science finds its birth in the middle of the nineteenth century. Among the chief architects of the new color theory, the name of the polymath Hermann von Helmholtz stands out. A keen experimenter and profound expert of the latest developments of the fields of physiological optics, psychophysics, and geometry, he exploited his transdisciplinary knowledge to define the first non-Euclidean line element in color space, i.e., a three-dimensional mathematical model used to describe color differences in terms of color distances. (...) Considered as the first step toward a metrically significant model of color space, his work inaugurated researches on higher color metrics, which describes how distance in the color space translates into perceptual difference. This paper focuses on the development of Helmholtz’s mathematical derivation of the line element. Starting from the first experimental evidence which opened the door to his reflections about the geometry of color space, it will be highlighted the pivotal role played by the studies conducted by his assistants in Berlin, which provided precious material for the elaboration of the final model proposed by Helmholtz in three papers published between 1891 and 1892. Although fallen into oblivion for about three decades, Helmholtz’s masterful work was rediscovered by Schrödinger and, since the 1920s, it has provided the basis for all subsequent studies on the geometry of color spaces up to the present time. (shrink)

The issue as to whether an atomistic or holistic viewof knowledge and meaning is correct relies on the way part/whole relationships is analysed,exactly as the issue as to whether a constructive or realistic view of knowledge and meaningis correct relies on the way internal/external relationships is analysed. Both theprinciple of compositionality and the context principle depend on how finely the constituents,the nature and the size of the context are identified; both the notion of meaning andthe notion of truth depend on (...) the resources of internalisation/externalisation. Thus thespectrum of semantic and epistemological theories varies from (global) atomismto (global) holism, and from minimal to maximal internalisation. Are compositionaltheories necessarily extensional? Does formal semantics necessarily rely on set theory?Does the domain-specific character of the notions of element, part and whole prevent anygeneral, non-trivial account? The aim of the present paper is to provide a negative answerto these questions by exploring some of the features a theory covering the phenomenologyof part and whole should have. This phenomenology will only be sketched through a fewparadigmatic examples, showing how the reference of notions of part and wholevaries and which are the constraints inherentin such variation. Categorytheory provides the tools for fashioning this framework, since it allows describing any coherentcollection of objects (with actions defined over them) and (action preserving) maps betweenthe objects, as well as the variation of such collections in terms of suitablefunctors, coding the ways parts and wholes undergo co-variation. The main thesis is thatthere are interference patterns between the two pairs Local/Global and Internal/External,only in terms of which the above phenomenology can be properly described.Se mai tu diventeraimetá di te stesso, e te l''auguro, ragazzo, capirai cose al di lá della comune intelligenza dei cervelli interi.Avrai perso metá di te e del mondo, ma la realtá rimasta sará mille volte piú profonda e preziosa. E tupure vorrai che tutto sia dimezzato e straziato a tua immagine, perchè bellezza e sapienza e giustizia ci sono soloin ció che é fatto a brani. (shrink)

Among the main concerns of 20th century philosophy was that of the foundations of mathematics. But usually not recognized is the relevance of the choice of a foundational approach to the other main problems of 20th century philosophy, i.e., the logical structure of language, the nature of scientific theories, and the architecture of the mind. The tools used to deal with the difficulties inherent in such problems have largely relied on set theory and its “received view”. There are specific issues, (...) in philosophy of language, epistemology and philosophy of mind, where this dependence turns out to be misleading. The same issues suggest the gain in understanding coming from category theory, which is, therefore, more than just the source of a “non-standard” approach to the foundations of mathematics. But, even so conceived, it is the very notion of what a foundation has to be that is called into question. The philosophical meaning of mathematics is no longer confined to which first principles are assumed and which “ontological” interpretation is given to them in terms of some possibly updated version of logicism, formalism or intuitionism. What is central to any foundational project proper is the role of universal constructions that serve to unify the different branches of mathematics, as already made clear in 1969 by Lawvere. Such universal constructions are best expressed by means of adjoint functors and representability up to isomorphism. In this lies the relevance of a category-theoretic perspective, which leads to wide-ranging consequences. One such is the presence of functorial constraints on the syntax–semantics relationships; another is an intrinsic view of (constructive) logic, as arises in topoi and, subsequently, in more general fibrations. But as soon as theories and their models are described accordingly, a new look at the main problems of 20th century’s philosophy becomes possible. The lack of any satisfactory solution to these problems in a purely logical and set-theoretic setting is the result of too circumscribed an approach, such as a static and punctiform view of objects and their elements, and a misconception of geometry and its historical changes before, during, and after the foundational “crisis”, as if algebraic geometry and synthetic differential geometry – not to mention algebraic topology – were secondary sources for what concerns foundational issues. The objectivity of basic geometrical intuitions also acts against the recent version of structuralism proposed as ‘the’ philosophy of category theory. On the other hand, the need for a consistent and adequate conceptual framework in facing the difficulties met by pre-categorical theories of language and scientific knowledge not only provides the basic concepts of category theory with specific applications but also suggests further directions for their development (e.g., in approaching the foundations of physics or the mathematical models in the cognitive sciences). This ‘virtuous’ circle is by now largely admitted in theoretical computer science; the time is ripe to realise that the same holds for classical topics of philosophy. (shrink)

The development of Artificial Intelligence has led to many controversies of philosophical interest involving issues of logic, computer science, software engeneering. The paper goes through the main steps of this development, deals with their philosophical relevance and sketches the unsolved problems, with special emphasis on the AI models of semantic competence. Some criticisms raised to such models in AI, either in its “classical” or “neural networks” format, are examined. On the ground of the discussion of these criticisms, a view is (...) proposed which avoids the inherited gap between the project of AI and naturalistic philosophy and suggests that filling the gap also provides a filter in order to select a definite form of naturalism. (shrink)

Can epistemology be naturalized? The question has more than one sense. There are many forms of both the naturalistic stance and its denial in relation to different topics and by means of different strategies. Only some of them are instantiated in the existing literature. After a taxonomy of the range of possible forms of naturalism and anti-naturalism, the paper suggests an emergentist view which shifts the issue from psychology to cosmology.

Born in 1945, John Lane Bell is not only one of the greatest logicians of our time, but he is also one the most gifted in the art of writing, as witnessed by the success of his introductory texts, many of which were originally written as lecture notes: their essential clarity is an exemplar of the Attic style. More generally, Bell’s works are a rare example of how rigour and sophisticated elegance can coexist.

We examine the relationship between scientific knowledge and the legal system with a focus on the exclusion of expert testimony from trial as ruled by the Daubert standard in the US.We introduce a simple framework to understand and assess the role of judges as “gatekeepers”, monitoring the admission of science in the courtroom. We show how judges face a crucial choice, namely, whether to limit Daubert assessment to the abstract reliability of the methods used by the expert witness or also (...) to check whether the application of those methods was correct. Undesirable outcomes result from both choices, thereby giving rise to the “gatekeeper’s dilemma.” We illustrate the dilemma by analyzing in some detail two well-known cases of Daubert challenges to economic experts. Finally, we present reasons for the absence of straightforward solutions to the dilemma and for its likely endurance. (shrink)

This paper discusses the positions of Italian philosopher Giulio Preti in relation to the quarrel between Analytic and Continental philosophy. Preti?s thought appears as a systematic thought permitting to overcome, through his logical, epistemological and linguistic reflection, the divide between these two approaches. The different features of his philosophy are analyzed here in detail and compared to the main theoretical assumptions of Analytic and Continental philosophy.

This paper discusses the positions of Italian philosopher Giulio Preti (1911?1972) in relation to the quarrel between Analytic and Continental philosophy. Preti?s thought appears as a systematic thought permitting to overcome, through his logical, epistemological and linguistic reflection, the divide between these two approaches. The different features of his philosophy are analyzed here in detail and compared to the main theoretical assumptions of Analytic and Continental philosophy.

This paper defends the viability of de-idealization strategies in economic modeling against recent criticism. De-idealization occurs when an idealized assumption of a theoretical model is replaced with a more realistic one. Recently, some scholars have raised objections against the possibility or fruitfulness of de-idealizing economic models, suggesting that economists do not employ this kind of strategy. We present a detailed case study from the theory of industrial organization, discussing three different models, two of which can be construed as de-idealized versions (...) of the first (the so-called Bertrand model of oligopoly). We conclude that recent pessimism about de-idealization in economics is largely unfounded, and that de-idealization strategies are not only possible but also widely employed in economics. (shrink)

We establish a duality between the category of involutive bisemilattices and the category of semilattice inverse systems of Stone spaces, using Stone duality from one side and the representation of involutive bisemilattices as Płonka sum of Boolean algebras, from the other. Furthermore, we show that the dual space of an involutive bisemilattice can be viewed as a GR space with involution, a generalization of the spaces introduced by Gierz and Romanowska equipped with an involution as additional operation.

This study is a continuation of the authors’ previous work entitled “Helmholtz and the geometry of color space: gestation and development of Helmholtz’s line element” (Peruzzi and Roberti in Arch Hist Exact Sci. https://doi.org/10.1007/s00407-023-00304-2, 2023), which provides an account of the first metrically significant model of color space proposed by the German polymath Hermann von Helmholtz in 1891–1892. Helmholtz’s Riemannian line element for three-dimensional color space laid the foundation for all subsequent studies in the field of color metrics, although (...) it was largely forgotten for almost three decades from the time of its first publication. The rediscovery of Helmholtz’s masterful work was due to one of the founders of quantum mechanics, Erwin Schrödinger. He established his color metric in three extended papers submitted in 1920 to the Annalen der Physik. Two memoirs were devoted to the so-called lower color metric, which laid the basis for the development of his higher color metric, exposed in the last paper. Schrödinger’s approach to the geometry of color space has been taken as a starting point for future elaborations of color metrics and allows a close examination of the current assumptions about the analysis of color-matching data. This paper presents an overall picture of Schrödinger’s works on color. His color theory developed a tradition first inaugurated by Newton and Young, and which acquired strong scientific ground with Grassmann’s, Maxwell’s, and Helmholtz’s contributions in the 1850s. Special focus will be given to Schrödinger’s account of color metric, which responded directly to Helmholtz’s hypothesis of a Riemannian line element for color space. (shrink)

Before the discovery of the expanding universe, one of the challenges faced in early relativistic cosmology was the determination of the finite and constant curvature radius of space-time by using astronomical observations. Great interest in this specific question was shown by de Sitter, Silberstein, and Lundmark. Their ideas and methods for measuring the cosmic curvature radius, at that time interpreted as equivalent to the size of the universe, contributed to the development of the empirical approach to relativistic cosmology. Their works (...) are a noteworthy example of the efforts made by modern cosmologists toward the understanding of the universe as a whole, its properties, and its content. (shrink)

The changes and general alarm of the current COVID-19 pandemic have amplified the sense of precariousness and vulnerability for family members who, in addition to the emotional trauma of the cancer diagnosis, add the distress and fear of the risks associated with infection. The primary objectives of the present study were to investigate the psychological impact of the COVID-19 pandemic on the parents of pediatric cancer patients, and the level of stress, anxiety, and the child’s quality of life perceived by (...) the parents during the COVID-19 epidemic. The parents of 45 consecutive children with solid and hematological tumors were enrolled. Four questionnaires were administered to the parents at the beginning of the pandemic lockdown. A 75% of parents exhibited remarkable levels of anxiety, with 60 subjects in state scale and 45 subjects in trait scale having scores that reached and exceeded the STAI-Y cut off. The bivariate matrix of correlation found a significant positive correlation between the IES-R and PSS scores. There was a positive correlation between the PSS and PedsQL scale and a negative correlation between IES-R and STAI-Y. The results confirm that parents of pediatric cancer patients have a high psychological risk for post-traumatic symptoms, high stress levels, and the presence of clinically significant levels of anxiety. (shrink)

This book reports on cutting-edge concepts related to Bourbaki’s notion of structures mères. It merges perspectives from logic, philosophy, linguistics and cognitive science, suggesting how they can be combined with Bourbaki’s mathematical structuralism in order to solve foundational, ontological and epistemological problems using a novel category-theoretic approach. By offering a comprehensive account of Bourbaki’s structuralism and answers to several important questions that have arisen in connection with it, the book provides readers with a unique source of information and inspiration for (...) future research on this topic. (shrink)

The property of fundamental mechanical theories which allows to treat compound objects as particles under suitable conditions is considered. It is argued that such a property, called compoundation invariance, is a nonreleasable property of any mechanical theory not declaring to which elementary constituents it applies. Compoundation invariance is discussed in the framework of Bohmian mechanics. It is found that standard Bohmian mechanics satisfies the requirement of compoundation invariance, with some reservation in the case of compound objects with spin. On the (...) contrary that requirement is violated when additional terms are added to the standard velocity. (shrink)

A review of the literature was conducted to better understand the (potential) role of mental health professionals in physician-assisted suicide. Numerous studies indicate that depression is one of the most commonly encountered psychiatric illnesses in primary care settings. Yet, depression consistently goes undetected and undiagnosed by nonpsychiatrically trained primary care physicians. Noting the well-studied link between depression and suicide, it is necessary to question giving sole responsibility of assisting patients in making end-of-life treatment decisions to these physicians. Unfortunately, the use (...) of mental health consultation by these physicians is not a common occurrence. Greater involvement of mental health professionals in this emerging and debated area is advocated. Beyond describing mental health professionals' role in the assessment of patient competency or decision making capacity, other areas of potential involvement are described. A discussion of ethical principles relevant to this area follows, along with comments on the training necessary to adequately serve patient needs. (shrink)

In this paper we consider the prehistory of quantum gravity (1916–1930) from two perspectives. First, we investigate how this research field constituted itself and we propose for the first time a red thread to trace its evolution in this earliest period. Second, we focus on a case study: the earliest work of Léon Rosenfeld. In 1927 he tried to merge wave mechanics with general relativity in the context of a five‐dimensional universe. We describe how Oskar Klein, Louis de Broglie, and (...) Théophile De Donder influenced Rosenfeld's work and analyze how and why Rosenfeld attempted to reconcile Einstein's theory with quantum phenomena. We argue that Rosenfeld investigated for the first time the corrections to a classical space‐time metric generated by a quantum source. As far as we know, Rosenfeld's approach has been largely ignored until today: he himself considered it “an accident.” After having reconsidered its connection with de Broglie's ideas and Rosenfeld's interpretation of the wave function in 1927, we argue that Rosenfeld's work can be interpreted as a first attempt to introduce the pilot‐wave theory in the context of quantum gravity and we infer that this was one of the reasons that ruled it out. (shrink)

Economists are often called upon as expert witnesses by the parties involved in antitrust litigation. One challenge they may face in US federal courts is compliance with the Daubert standard of admissibility of expert testimony. The interplay between model applicability and the Daubert standard is analyzed, suggesting the importance of distinguishing between weak applicability claims, those that state that a model’s critical assumptions are shared by the target, and strong applicability claims, those that connect empirical models and quantitative market features. (...) Recent antitrust cases in which expert testimonies based on economic models have been assessed following the Daubert standard are examined using this framework. Some normative implications are drawn concerning how to improve judges’ assessment of model-based arguments. (shrink)

The paper addresses the main questions to be dealt with by any semantic theory which is committed to provide an explanation of how meaning is possible. On one side the paper argues that the resources provided by the development of mathematical logic, theoretical computer science, cognitive psychology, and general linguistics in the 20th Century, however indispensable to investigate the structure of language, rely on the existence of end products in the morphogenesis of meaning. On the other, the paper argues that (...) philosophy of language, which, either in the analytic or the structuralist or the hermeneutical tradition, made little use of such resources (when they are not simply rejected). Left the main question unanswered. Though phenomenology intended to focus on the constitutive process, it ended up mostly with philology. Cognitive semantics paved the way to focus on patterns of bodily interaction within the natural environment out of which basic schemes emerge and are metaphorically “lifted” to any universe of discourse. The explanatory commitment is thus endorsed through two hypotheses: (1) these schemes, of topological and kinaesthetic structure, determine the range of forms of atomic sentences of any natural language, and (2) the category-theoretic notion of universality allows for a proper analysis of how such schemes are “lifted”. (shrink)

I now intend to return to Husserl’s argument against psychologism in logic, aiming to frame it within the broader antinaturalistic controversy and see how recent proposals of a natural (or naturalized) epistemology could affect it.

This paper defends the viability of de-idealization strategies in economic modeling against recent criticism. De-idealization occurs when an idealized assumption of a theoretical model is replaced with a more realistic one. Recently, some scholars have raised objections against the possibility or fruitfulness of de-idealizing economic models, suggesting that economists do not employ this kind of strategy. We present a detailed case study from the theory of industrial organization, discussing three different models, two of which can be construed as de-idealized versions (...) of the first. We conclude that recent pessimism about de-idealization in economics is largely unfounded, and that de-idealization strategies are not only possible but also widely employed in economics. (shrink)