In this paper, we describe an interdisciplinary study between Latin and Mathematics, where Latin serves as a tool for inquiry, facilitating access to and reflection on the new mathematical concepts that emerged during the Scientific Revolution of the 17th and 18th centuries. By examining original texts in Latin, we trace the genesis of these concepts and their development through the creation of a new Latin lexicon tailored to express them. We analyze texts by Galileo and the Bernoulli brothers concerning the (...) brachistochrone problem, which marks the transition from classical mathematics to the new infinitesimal calculus that laid the groundwork for the Scientific Revolution. From an epistemological perspective, solving this problem—which requires the new tools of differential calculus—offers a significant example of the limitations of classical mathematics. The analysis of primary sources allows us to reconstruct the original thinking that led scientists to propose solutions, while also encountering an epistemological obstacle: the concept of the limit. Furthermore, analyzing the Latin texts reveals the construction and evolution of scientific language as it developed alongside the new mathematics. (shrink)

In this study we explore the encounters emerging from the restructured categorizations of subjectivity in the context of an open system that constantly confronts the structures that create it. On the one hand, science formulates valid propositions through the ratio that ensures and confirms the acquisition of knowledge, but on the other hand, the truth of its propositions is related to those mental processes which seek the truth of deeper values than those discovered on the surface of reality. The question (...) arisen in this case is by what criteria we are able to go back to removing those antinomies (objectivism/perspectivism) in order to develop the interdisciplinary terms between the humanitarian field of science and sciences in a spirit of unification. In this way, we approach the potential of scientific reformulation in terms of the above interpretive perspectives in order to project the overcoming of divisions under the principles of diversity and critical thinking both in the field of philosophy and science as well. (shrink)

Sunto Prendendo in esame quanto il celebre maestro di retorica Marco Fabio Quintiliano (35 d.C. ca - 100 d.C. ca) scrive in età flavia nella sua _Institutio oratoria_ a proposito dell’importanza dello studio della Matematica nella formazione di base del futuro perfetto oratore romano, si intende approfondire in particolare una porzione del lungo passo presente nel I libro (I 10, 34-49), nello specifico i §§ 39-45. In essi l’autore latino, partendo dall’affermazione che la geometria, non meno dell’aritmetica, con il suo (...) procedimento razionale smaschera ciò che, pur apparendo verisimile, in realtà è falso, inserisce in funzione esemplificativa una vera e propria lezione di geometria piana sul problema dell’isoperimetria. Lo scopo dell’autore è di fornire una prova dell’utilità della geometria per educare a un uso corretto dell’_ars_ _dicendi_. _Keywords__: _Quintiliano; retorica; isoperimetria. Abstract Examining what the famous rhetoric teacher Marcus Fabius Quintilian (ca. 35 CE – ca. 100 CE) writes during the Flavian period in his Institutio Oratoria about the importance of studying mathematics as part of the foundational education for the future perfect Roman orator, this paper focuses on a specific section of the long passage found in Book I (I 10, 34-49), particularly §§ 39-45. In this section, the Latin author, starting from the assertion that geometry, no less than arithmetic, with its rational method, reveals what may appear plausible but is actually false, includes a true lesson in plane geometry on the problem of isoperimetry. The author's goal is to demonstrate the utility of geometry in educating one to make proper use of the ars dicendi (art of speaking). _Keywords: _ Quintilian; rhetoric; isoperimetry. (shrink)

As part of the laboratory activities designed for the students of the second year of the Mathematical High School by the research group in Mathematics Education of the Department of Mathematics of the University of Salerno, the theme “From Archimedes and the oxen problem to Pell’s equation” has been designed. The course has not yet been delivered to students and in this paper the didactic path to be developed in the classroom will be described. The students initially will retrace the (...) various solution approaches proposed over the centuries. Subsequently, with a heuristic approach, they will tackle the resolution of the proposed problem by exploiting properties related to the theory of numbers. With the help of some schedules, provided by the teachers-tutors, they will conjecture and argue by answering questions aimed at stimulating didactic reflection. This workshop path involves processes such as exploring and conjecturing through the articulation of different ways of working (individual and in groups), manual and digital. (shrink)

_Sunto_ __L’obiettivo di questo studio è di riflettere su alcune questioni che ruotano intorno alla rappresentazione dell’Intelligenza artificiale, e che riguardano l’impatto della tecnologia sulla sfera esistenziale e sulla condizione umana. In questo quadro mi soffermerò, attraverso un close reading, sul film Her di Spike Jonze, analizzandone in particolare i dialoghi, con l’intento di evidenziare anche la presenza di quei fili che tracciano una continuità con le questioni poste da Alan Turing nel celebre articolo “Computing Machinery and Intelligence” pubblicato sulla (...) rivista Mind nel 1950. Se la domanda al centro dello studio di Turing è Can Machines Think?, e viene ripresa in seguito da Asimov e Dick con la variante Can Machines Lie?, nel film di Spike Jonze la declinazione più stringente dell’interrogativo è Can Machines Feel? Parole chiave: Intelligenza artificiale; solitudine; emozioni; reale/virtuale; modi di amare; trascendenza. _Abstract_ The purpose of this study is to tackle some of the issues that revolve around the representation of Artificial Intelligence and that concern the impact of technology on the existential sphere and the human condition. Within this framework, I will focus on Spike Jonze’s film Her, in particular through a close reading of its dialogues. The aim is also to highlight the presence of threads tracing a continuity with the issues raised by Alan Turing in the famous article “Computing Machinery and Intelligence” published in the journal Mind in 1950. If the question at the heart of Turing’s study is ‘Can Machines Think?’ – later turned into ‘Can Machines Lie?’ in Asimov and Dick’s variant – in Spike Jonze’s film the point at issue becomes ‘Can Machines Feel?’. (shrink)

Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical concepts -- logical constants, logical truths, and logical consequence -- are defined using the internal syntactic and semantic structure of language. For a first-order language, it has been shown that its logical constants are connectives and a certain type of quantifiers for which the universal and existential quantifiers form (...) a functionally complete set of quantifiers. Neither equality nor cardinal quantifiers belong to the logical constants of a first-order language. (shrink)

L’articolo ricostruisce le biografie delle prime donne di cui si hanno notizie nella storia della matematica, filosofia e scienza. Sono descritte le vite e, per quel che permettono le fonti a noi giunte, le opere delle donne pitagoriche (in questo intervento si fa riferimento alle donne vissute dal VI al IV secolo a.C., nelle prime comunità pitagoriche della Magna Grecia), di Maria l’Ebrea alchimista alessandrina, per alcuni storici vissuta tra il I e il III secolo, per altri prima di Cristo, (...) di Ipazia di Alessandria vissuta tra i IV e V secolo, uccisa tragicamente e, martire eroica, divenuta simbolo della libertà di pensiero femminile. (shrink)

The notion of infinity and its atomistic counterpart are discussed in the framework of Giordano Bruno philosophy. The role played by mathematics is considered as well. _Keywords_: mathematics; atomism; philosophy of science; history of science; infinite. [1] Sunto Si discute il ruolo del concetto di infinito e il ruolo della matematica nella _nova filosofia_ di Giordano Bruno, in relazione agli _Infiniti Mondi_ e al problema del _minimo_. _Parole chiave_: matematica; scienza; atomismo; storia della scienza; filosofia della scienza; infinito.

In the literature, the distinction between positivism and interpretivism based on ontological assumptions is somehow clear. Problems in dividing them based on epistemological assumptions continue to exist and appear in several works; for instance, Bhattacherjee’s book (2012) introduced the concept of research design and categorization of methods of data collection based on positivist and interpretivist epistemological assumptions. While acknowledging Bhattacherjee's contribution, nonetheless, the paper argues that since both the quantitative and qualitative research approaches share a few epistemological assumptions, strictly categorizing (...) them into positivism and interpretivism raises some confusion. Consequently, impacting communication among researchers and the implementation of the research projects. Therefore, the paper describes Bhattacherjee's contributions and limitations in understanding the dichotomy existing between positivist and interpretivist methods of data collection. The paper's suggestions aim to resolve such confusion and restore research approaches and their methods of data collection to their original philosophical positions. Thus minimizing the existing confusion on research methodology in the current literature. (shrink)

In the intricate dance between the scientific and the metaphysical, the realms of quantum physics, biocentrism, and Indian philosophy converge, offering profound insights into the nature of reality. This article embarks on a journey to explore the interconnected threads that weave through these seemingly distinct domains, revealing a tapestry that challenges our understanding of existence.

Projects concerning the participation of citizens to the scientific research have become very popular in recent years. However, the literature seems not offer much foundational investigations into the epistemological conditions that make citizens’ contribution to science a fruitful and rigorous activity. Research institutions and citizens, understood as entities bearing generally distinct requests, practices and goals, knowledge and skills, are totally misaligned. In order to participate to collaborative research, citizens need an epistemic and methodological literacy to overcome common sense ideas, towards (...) an ever adequate vision of phenomena under investigation. Besides understanding the social advantages introduced by the participatory dimension, it is therefore necessary to analyze the related epistemological problems, to understand to what extent and in what respect to the participation of citizens to research processes might be regarded as truly advantageous from an epistemological perspective. (shrink)

The controversy that between 1908 and 1912 saw Benedetto Croce and Giovanni Gentile opposed, on one side, and Federigo Enriques, on the other, did not actually have a conclusive episode, but its end was perceived, for its results on culture, on society and teaching in Italy, as a "defeat" of Enriques. A more careful examination of the events and of the historical context in which it took place seems, however, to clearly demonstrate that we can speak not of a personal (...) defeat of the great mathematician from Livorno, but rather of a defeat of the commendable attempts at cultural and social modernization of Italy in an international perspective, of which Enriques was not the only actor but certainly the most exposed. Such intentions were crushed by the myopic provincial conservatism of the Italian neo-idealism, favored by the fascist regime, concerned only with affirming in the world an alleged autarkic national cultural superiority, based on the traditional literary-humanistic culture, ignoring the progress of the new technical-scientific thought, placed in an international context. Sunto_ La polemica che dal 1908 al 1912 vide contrapposti da una parte Benedetto Croce e Giovanni Gentile e dall’altra Federigo Enriques non ebbe, in realtà, un episodio conclusivo, ma la sua fine è stata percepita, per i suoi esiti sulla cultura, sulla società e sull’insegnamento in Italia, come una “sconfitta” dell’Enriques. Un esame più attento delle vicende e del contesto storico nel quale si svolse sembra, invece, dimostrare chiaramente di poter parlare non di una sconfitta personale del grande matematico livornese, quanto piuttosto di una sconfitta dei lodevoli tentativi di ammodernamento culturale e sociale dell’Italia in una prospettiva internazionale, di cui Enriques non fu l’unico attore ma sicuramente quello più esposto. Tali propositi furono schiacciati dal miope conservatorismo provinciale del neoidealismo italiano, favorito dal regime fascista, preoccupato unicamente di affermare nel mondo una pretesa superiorità culturale nazionale autarchica, basata sulla tradizionale cultura letterario-umanistica, ignorando il progresso del nuovo pensiero tecnico-scientifico, per sua natura, invece, inserito in un contesto internazionale. (shrink)

School inclusion embodies an educational philosophy aimed at ensuring that each and every student, regardless of individual characteristics, abilities, personal circumstances, or social conditions, is fully engaged and actively involved in the educational experience. This approach emphasizes diversity as a value and promotes the acceptance and appreciation of individual differences within the school environment. Despite the desirability of inclusive education systems being enshrined in many international and national Declarations and regulations, practical approaches still often lean towards school “integration”, understood as (...) a paradigm of “assimilation”, which involves adapting disabled students to a school structure primarily designed for typical students. This article underscores the essential functions of assessing inclusion policies within individual educational institutions and, more broadly, evaluating mechanisms within the larger educational system to achieve continuous improvement in the real inclusion of all students, dedicating an in-depth analysis to the Italian context. The effective and adequate assessment in this field is challenging and methodological reflection is absolutely indispensable to define shared frameworks for evaluation policies. Building upon the recent OECD framework proposal (2023), this work suggests expanding the set of indicators to provide a more comprehensive and in-depth evaluation of school inclusion policies. (shrink)

_Sunto_ Nella proposizione 3 della κύκλου μέτρησις Archimede costruisce due numeri razionali che approssimano la misura del rapporto tra la circonferenza e il suo diametro, oggi noto come π. In questo lavoro vogliamo porre l’accento su due aspetti del trattato di Archimede: il primo riguarda le scelte dei valori razionali approssimati per eccesso e per difetto di √3 utilizzati all’inizio della procedura di calcolo, che risultano essere i migliori approssimanti in base alla moderna teoria delle frazioni continue, i cui termini (...) si possono ricavare dall’antico ανθυφαίρεσις euclideo; il secondo riguarda alcune stime utilizzate da Archimede, apparentemente non giustificate e sub-ottime, che invece sono frutto di un preciso procedimento logico da noi ricostruito in termini di un algoritmo. Di tale studio è stata proposta una trasposizione didattica che parte dal testo antico e giunge alla produzione di una traduzione commentata in cui lo studente è protagonista del processo di scoperta. _Abstract_ In proposition 3 of the κύκλου μέτρησις Archimedes constructs two rational numbers that approximate the measure of the ratio between the circumference and its diameter, today known as π. In this work we emphasize two aspects of Archimedes' proof. The first one concerns the choices of the rational values approximated by excess and defect of √3 used at the beginning of the calculation procedure. These values turn out to be the best approximants based on the modern theory of continued fractions, whose terms can be obtained from the ancient Euclidean ανθυφαίρεσις. The second one concerns some estimates used by Archimedes, apparently unjustified and sub-optimal, which instead are the result of a precise logical procedure that we recontruct in terms of an algorithm. We also propose an educational transposition of this study that starts from the ancient text and leads to the production of a commented translation in which the student is the protagonist of the discovery process. (shrink)

Il presente lavoro intende ricostruire il percorso storico-epistemologico che ha condotto, nell’antichità, alla scoperta dell’esistenza delle grandezze incommensurabili. Non si sa con esattezza quando e come sia stata fatta tale importante scoperta e anche tra i commentatori antichi la questione sembra che abbia dato origine a discussioni e congetture varie; ancora oggi si può affermare che nell’ambito della storia della matematica il dibattito sia ancora aperto. È comunque fuori di dubbio che la scoperta sia stata fatta in seno agli sviluppi (...) della matematica greca. This paper seeks to reconstruct the historical-epistemological path that led, in antiquity, to the discovery of the existence of incommensurable quantities. It is not known exactly when and how this important discovery was made; however, there is no doubt that the discovery was made within the developments of Greek mathematics. (shrink)

_Sunto_ Questo articolo si prefigge l’obiettivo di definire e inquadrare il processo di formazione, attuazione e valutazione delle politiche sociali e delle politiche pubbliche che contribuiscono alla costruzione del welfare locale. Tale processo di analisi risulta essere fondamentale sia per comprendere il funzionamento del ciclo di programmazione e le dinamiche intrinseche al processo di _decision making_ sia per specificare il ruolo dello Stato e dei vari attori coinvolti nella definizione e risoluzione delle problematiche di forte rilevanza sociale. Dal punto di (...) vista sociologico, il fenomeno della povertà, inteso come un fenomeno sociale complesso e multiparadigmatico, sarà analizzato sia in senso diacronico, attraverso l’analisi dell’evoluzione del concetto di povertà nel corso dei secoli, sia in senso sincronico, concentrandosi sulle diverse sfaccettature che lo caratterizzano ancora oggi e che lo rendono di difficile contrasto. Infine, si procede all’analisi dei dati riguardanti il problema della povertà in Abruzzo e delle proposte avanzate dalle Regione in materia di servizi, interventi e politiche sociali per affrontare tale problematica. _Abstract_ The paper aims to define and frame the process of formation, implementation and evaluation of social policies and public policies that contribute to the construction of local welfare. This analysis process is fundamental both for understanding the functioning of the planning cycle and the dynamics intrinsic to the decision-making process and for specifying the role of the State and the various actors involved in the definition and resolution of problems of strong social relevance. From a sociological point of view, the phenomenon of poverty, understood as a complex and multi-paradigmatic social phenomenon, will be analyzed both in a diachronic sense, through the analysis of the evolution of the concept of poverty over the centuries, and in a synchronic sense, focusing on the different facets that still characterize it today and that make it difficult to contrast. Finally, the paper will investigate the data regarding the problem of poverty in Abruzzo and the proposals put forward by the Region regarding services, interventions and social policies to address this problem. (shrink)

Sunto In questa prima lettura interpretativa, questo lavoro si focalizza, anche attraverso l’uso di numerose fonti reperite, sulla idea-forza della partecipazione attiva dei cittadini nella vita politica della propria comunità quale elemento centrale per la realizzazione compiuta della democrazia e il perseguimento di una politica sostenibile. Esaminando nel dettaglio sia gli strumenti tradizionali sia le metodologie innovative, si tenterà di comprendere come aumentare la partecipazione attiva, in particolare delle nuove generazioni, e, soprattutto spingendola in modo che sia più consapevole, si (...) riuscirà a costruire una società effettivamente democratica, dove le istituzioni politiche sono identificate come attori chiave nel promuovere la partecipazione democratica, malgrado le difficoltà insite nella spigolosità stessa della tematica affrontata. Abstract In this first interpretative reading, this work focuses, also through the use of numerous sources found, on the idea-strength of the active participation of citizens in the political life of their community as a central element for the complete realization of democracy and the pursuit of a sustainable policy. By examining in detail both the traditional tools and the innovative methodologies, we will try to understand how to increase active participation, in particular of the new generations, and, above all by pushing it so that it is more aware, we will be able to build an effectively democratic society, where political institutions are identified as key actors in promoting democratic participation, despite the difficulties inherent in the very angularity of the topic addressed. (shrink)