The aim of this article is to shed light on an understudied aspect of Giordano Bruno's intellectual biography, namely, his career as a mathematical practitioner. Early interpreters, especially, have criticized Bruno's mathematics for being “outdated” or too “concrete”. However, thanks to developments in the study of early modern mathematics and the rediscovery of Bruno's first mathematical writings (four dialogues on Fabrizio's Mordente proportional compass), we are in a position to better understand Bruno's mathematics. In particular, this article aims to reopen (...) the question of whether Bruno anticipated the concept of infinitesimal quantity. It does so by providing an analysis of the dialogues on Mordente's compass and of the historical circumstances under which those dialogues were written. (shrink)

At the turn of the seventeenth century, Bruno and Cavalieri independently developed two theories, central to which was the concept of the geometrical indivisible. The introduction of indivisibles had significant implications for geometry – especially in the case of Cavalieri, for whom indivisibles provided a forerunner of the calculus. But how did this event occur? What can we learn from the fact that two theories of indivisibles arose at about the same time? These are the questions addressed in this paper. (...) Relying on the methodology of “historical epistemology”, this paper asserts that the similarities and differences between the theories of Bruno and Cavalieri can be explained in terms of “shared knowledge”. The paper shows that the idea – on which both Bruno and Cavalieri build – that geometrical objects are generated by motion was part of the mathematical culture of the time. Tracing this idea back to its Pythagorean origins thus sheds light on the relationship between motion and continuum in mathematics. (shrink)

Most studies of René Descartes’s legacy have focused on the novelty of his ideas, but little has been done to uncover the conditions that allowed these ideas to spread. Seventeenth-century Europe was already a small world—it presented a high degree of connectedness with a few brokers bridging otherwise disparate regions. A communication network known as the Republic of Letters enabled scholars to trade ideas—including Descartes’s—by means of correspondence. This article offers an analysis—both qualitative and quantitative—of a corpus of letters written (...) during Descartes’s lifetime and mentioning his name. The aim is to unveil the factors that drove the diffusion of Descartes’s ideas. The results are twofold. First, a close reading of the letters reveals that they were not used to create awareness about Descartes and his works but rather to discuss his ideas. Second, a network analysis of the letters shows that ideas do not spread like viruses, thus undermining the ‘social contagion’ model, and that weak ties are not as effective in promoting innovations as they are in circulating information. (shrink)

The purpose of this paper is to show the argument-establishing features of a Renaissance altarpiece. Looking to Panofsky’s seminal studies and to more recent contributions, this essay shows how in a special environment like the Florentine pre-Renaissance, people could easily relate to the evocative and contrastive potential of images. In the Santa Lucia de’ Magnoli Altarpiece painted by Domenico Veneziano we see an interesting dialogue between the main piece and the predella panels. This juxtaposition can be formalized into a basic (...) argumentative text. (shrink)

L’articolo esamina l’episodio della _spogliazione_ di Francesco d’Assisi intersecando la lettura delle prime narrazioni della vita del santo e dei romanzi contemporanei che hanno raccontato la sua vicenda. L’atto di rinuncia ai beni paterni e la rottura che esso determina lungo il corso della vita di Francesco vengono posti in relazione al tema della follia, che costituisce un cambio del paradigma con cui guardare il mondo e la sua logica. La scelta di Francesco di rinunciare al potere e alla proprietà (...) proprie del mondo, oppone ad esse una nuova logica che si traduce non nella rinuncia al mondo, ma nella capacità di trascenderlo rimanendo al suo interno. _The article examines the episode of the _dispossession_ of Francis of Assisi by intersecting the reading of the first narrations of the life of the saint and contemporary novels that have told his story. The act of renouncing his father's goods and the rupture that it determines along the course of Francis' life are placed in relation to the theme of folly, which constitutes a change of paradigm with which to look at the world and its logic. The choice of Francis to renounce the power and the property of the world, opposes to them a new logic that is translated not in the renunciation of the world, but in the capacity to transcend it by remaining within it_. (shrink)

The problem of the visio Dei : this refers to understand what God is, not who he is. The key issue is the analogy with the structure of sense knowledge, characterized by the identification between the knowing subject and object known. Love, understood as sensus animae , operates by means of a knowledge identifying through a modification of the feeling, even if with one major difference compared to the other senses, as essentially characterized by freedom. The declination of love and (...) freedom is one of the possible uses of love. Alternate paths can be based on the doctrine of the double image of the man with the result that more is love as sensus animae , another is its rectitudo as identified in the decor . The relationship that develops between the knower and the first term of the cognitive changes, overcoming the opposition of subject and object of his rational knowledge. In the cognitive of ' love , the object is the mirror through which the subject must become transparent to itself. (shrink)

ArgumentThe purpose of this paper is to provide an analysis of Giordano Bruno’s conception of mathematics. Specifically, it intends to highlight two aspects of this conception that have been neglected in previous studies. First, Bruno’s conception of mathematics changed over time and in parallel with another concept that was central to his thought: the concept of infinity. Specifically, Bruno undertook a reform of mathematics in order to accommodate the concept of the infinitely small or “minimum,” which was introduced at a (...) later stage. Second, contrary to what Héléne Védrine claimed, Bruno believed that mathematical objects were mind-dependent. To chart the parallel development of the conceptions of mathematics and infinity, a seven-year time span is considered, from the publication of Bruno’s first Italian dialogue (La cena de le ceneri,1584) to the publication of one of his last Latin works (De minimo, 1591). (shrink)

Hegel’s lectures on fine art, given in the 1820s, were published for the first time in 1835 and continued to influence thinking about aesthetics for the rest of the nineteenth century. After a long period of relative neglect in this century, when idealism in general fell into disfavor, Hegel’s Aesthetics has begun to awaken renewed interest. Appropriately, the larger questions of the relation of art, beauty, and truth have attracted the most attention. His treatment of musical aesthetics, on the other (...) hand, has generally been regarded as much less satisfactory, in spite of his being more qualified than most philosophers of his day to discuss music. It is known that Hegel sang in a choral group at one point, that he had attended operas by Gluck, Mozart, Rossini, and Weber, and that he had heard performances of symphonies and string quartets by Haydn and Mozart. Yet his remarks on music have been dismissed as the product of someone who knew very little about music and who had little sympathy for the newer genres and styles of music that still loom so large in the repertoire today. The important question, however, is whether his aesthetic of music makes sense musically and is philosophically coherent. If so, then his arguments are of more significance than has been recognized. In fact, they reveal the principles and aims of the art of music as it was practiced in his day and as it continued to be understood by many critics in the nineteenth century. They pose a challenge, moreover, to the prevailing ahistorical ways of understanding music in the twentieth century. (shrink)

Questo numero di “Doctor Virtualis” si interroga sul concetto di ordine e sulla sua valenza all’interno della riflessione medievale: siamo di fronte a uno strumento conoscitivo con cui intellettuali di varia formazione e operanti in ambiti diversi cercano di affrontare la complessità del proprio mondo, oppure, come forse è lecito a prima vista attendersi da un’epoca come quella medievale, a una struttura metafisica già data, di tipo _oggettivo_, che rappresenta una garanzia rispetto alla disarmonia del mondo e delle relazioni fra (...) gli uomini? L’ipotesi di ricerca da cui trae origine questo numero è che an­che in epoca medievale l’ordine si presenti come esigenza e dunque come risultato di una costruzione che, attraverso i più svariati stru­menti conoscitivi, punti a rendere conto del disordine, cercando di sciogliere e dipanare l’intreccio di cause ed effetti che caratterizza i vari spazi del mondo abitati dagli uomini. Per questa ragione abbiamo deciso di intitolare il fascicolo _Frammenti di ordine e disordine nel Medioevo_. This issue of "Doctor Virtualis" questions the concept of order and its value within medieval reflection: are we dealing with a cognitive instrument with which intellectuals of various training and operating in different fields try to deal with the complexity of their world, or, as one might at first sight expect from an era such as the Middle Ages, with a metaphysical structure already given, of an _objective_ type, which represents a guarantee against the disharmony of the world and relations between men? The research hypothesis from which this issue originates is that even in the Middle Ages order presents itself as a need and therefore as the result of a construction that, through the most varied cognitive instruments, aims to account for disorder, attempting to unravel and disentangle the interweaving of causes and effects that characterises the various spaces of the world inhabited by men. For this reason, we have decided to title the issue _Fragments of Order and Disorder in the Middle Ages_. (shrink)

La discussione medievale sul tema dei futuri contingenti pone al centro dell’attenzione, da un lato, il modo di concepire conoscenza e potenza divine e, dall’altro, lo statuto degli eventi futuri. Pier Damiani, monaco dell’XI secolo, distingue fra la possibilità divina di mutare le conseguenze del passato e quella di produrre un passato interamente diverso. Pedro Damian, protagonista del racconto di Borges, riscatta il suo comportamento giovanile producendo poco alla volta un altro, diverso, passato. La potenza della memoria invece della potenza (...) di Dio. (shrink)

Ever since its foundation in 1540, the Society of Jesus had had one mission—to restore order where Luther, Calvin and the other instigators of the Reformation had brought chaos. To stop the hemorrhage of believers, the Jesuits needed to form a united front. No signs of internal disagreement could to be shown to the outside world, lest the congregation lose its credibility. But in 1570s two prominent Jesuits, Cristophorus Clavius and Benito Perera, had engaged in a bitter controversy. The issue (...) at stake had apparently nothing to do with the values on which Ignazio of Loyola had built the Society of Jesus. And yet the dispute between Clavius and Perera was matter of concern for the entire Jesuit community. They were... (shrink)

L’articolo si propone di formulare una prima ipotesi relativa ai rapporti fra i diversi tipi di legge presenti nel pensiero di Bonaventura da Bagnoregio; la ricostruzione avverrà a partire dal basso, prendendo le mosse dalla _ lex politica _, per risalire, solo nelle conclusioni, alla _ lex aeterna _, nella sua doppia funzione di fondamento e ordine. L’articolo non si propone alcun obiettivo di esaustività, si presenta piuttosto come il primo passo di un’indagine che ha bisogno di altri e ben (...) più significativi livelli di approfondimento. _ The article aims to formulate a first hypothesis relating to the relationships between the different types of law present in the thought of Bonaventura da Bagnoregio; the reconstruction will take place starting from the bottom, starting from the _ lex politica _, to go back, only in the conclusions, to the _ lex aeterna _, in its double function of foundation and order. The article does not aim to be exhaustive, rather it presents itself as the first step of an investigation that requires other and much more significant levels of in-depth analysis. _. (shrink)

By foregrounding a first-person perspective, this text enacts and explores self-reflection as a mode of inquiry in educational research and highlights the centrality of the individual researcher in the construction of knowledge. Engaging in particular with the work of Thomas Merton through a dialogical approach to his writings Self and Wisdom in Arts-Based Contemplative Inquiry in Education offers rich examples of personal engagement with text and art to illustrate the pervasive influence of the personal in reflective, narrative, and aesthetic forms (...) of inquiry. Chapters considers methodological and philosophical implications of self-study and contemplative research in educational contexts, and show how dialogic approaches can enrich empirical forms of inquiry, and inform pedagogical practice. In its embrace of a contemplative voice within an academic treatise, the text offers a rich example of arts-based contemplative inquiry. This unique text will be of interest to postgraduate scholars, researchers, and academics working in the fields of educational philosophy, arts-based and qualitative research methodologies, and Merton studies. (shrink)

Teodicea e relazione. La teologia come garanzia di giustizia nella dialettica tra ordine e libero arbitrio. Teodicy and relationship. The theology as guarantee of justice in the dialectics between order and free will.

This article explores an episode in the reception of Hegel's philosophy of history and historiography of philosophy with reference to the question of the possibility of non-Western philosophy, in particular African philosophy. Section I briefly outlines the contents of the Hatäta Zär'a Ya‛ǝqob and the controversy over its authorship, focusing in particular on the argument of the Ethiopianist and scholar of Semitic languages Carlo Conti Rossini that ‘rationalistic’ philosophy was impossible in Ethiopia. In section II I suggest that a (...) major component of the intellectual background to this notion of the impossibility of philosophy in Africa can be traced to Hegel's philosophy of history. To substantiate this claim I begin by providing an account of the broader historiographical shift between 1780 and 1830, in which Africa and Asia came to be excluded from the history of philosophy, and I suggest that Hegel's philosophy of history was decisive in this process. I examine how Hegel's account of history as the realization and actualization of freedom goes together with the development of cultural production culminating in philosophy, and how both of these processes (if they are really separate processes at all), can be mapped onto particular historical-geographical populations and cultures. I suggest that, even though this was not Hegel's intention, by the late nineteenth and early twentieth centuries this served as a cultural justification for political domination: those who are unfree are unfree because they are unthinking (unphilosophical), and those who are unthinking cannot be free. Finally in section III I connect this Hegelian conception to Conti Rossini's work, both his article on the Hatäta and as apologist for Italian imperialism. I conclude by reflecting on what this underexplored connection between Hegel and early twentieth-century theorists of culture might mean for attempts to construct global histories of philosophy. (shrink)

This chapter proposes a corpus-based investigation and a semantic analysis of the Italian word "altro" ‘other’, focusing on two values of "altro" identified in the previous literature: difference (D-interpretation) and increment along a scale (M-interpretation). In syntax-based studies, focused on cardinal noun phrases, the two values have been related to distinct syntactic positions occupied by "altro" within the NP’s extended projection (Cinque 2015, Kayne 2021): a lower position, associated with the D-interpretation (altro N = ‘other kind of N’), and a (...) higher position, associated with the M-interpretation (altri n N = ‘n more tokens of N’). Conversely, discourse-based studies assume that the two values are due to a lexical ambiguity of "altro", with the D-interpretation being triggered by a discourse relation of contrast and the M-interpretation by an additive relation (Gianollo and Mauri 2020). We examine the distribution of the two values in the CORIS corpus of contemporary Italian (Rossini Favretti et al. 2002) and consider the question of whether they are equally basic interpretations or one of them is derivable from the other. The analysis we propose relies on the idea that the semantic core of "altro" is the relation of non-identity. The D-interpretation and M-interpretation result from the interaction between this semantic core and features of the larger discourse context, with additive and contrastive features playing a major role. Non-identity is introduced in the semantic representation of the sentence irrespective of the syntactic position of "altro", while discourse context—including lexical properties of the noun—determines at what ontological level (whether type or token) non-identity is evaluated. The analysis is cast in the framework of Segmented Discourse Representation Theory (SDRT; Asher and Lascarides 2003), which allows a modular representation of the separate contributions of "altro" and discourse structure. (shrink)

In recent decades, the analysis of phraseology has made use of the exploration of large corpora as a source of quantitative information about language. This paper intends to present the main lines of work in progress based on this empirical approach to linguistic analysis. In particular, we focus our attention on some problems relating to the morpho-syntactic annotation of corpora. The CORIS/CODIS corpus of contemporary written Italian, developed at CILTA – University of Bologna (Rossini Favretti 2000; Rossini Favretti, (...) Tamburini, De Santis in press), is a synchronic 100-million-word corpus and is being lemmatised and annotated with part-of-speech (POS) tags, in order to increase the quantity of information and improve data retrieval procedures (Tamburini 2000). The aim of POS tagging is to assign each lexical unit to the appropriate word class. Usually the set of tags is pre-established by the linguist, who uses his/her competence to identify the different word classes. The very first experiments we made revealed how the traditional part-of-speech distinctions in Italian (generally based on morphological and semantic criteria) are often inadequate to represent the syntactic features of words in context. It is worth noting that the uncertainties in categorisation contained in Italian grammars and dictionaries reflect a growing difficulty as they move from fundamental linguistic classes, such as nouns and verbs, to more complex classes, such as adverbs, pronouns, prepositions and conjunctions. This latter class, that groups together elements traditionally used to express connections between sentences, appears inadequate when describing cohesive relations in Italian. This phenomenon actually seems to involve other elements traditionally assigned to different classes, such as adverbs, pronouns and interjections. Recent studies proposed the class of ‘connectives’, grouping all words that, apart from their traditional word class, have the function of connecting phrases and contributing to textual cohesion. From this point of view, conjunctions can be considered as part of phrasal connectives, that can in turn be included in the wider category of textual connectives. The aim of this study is to identify elements that can be included in the class of phrasal connectives, using quantitative methods. According to Shannon and Weaver’s (1949) observation that words are linked by dependent probabilities, corroborated by Halliday’s (1991) argument that the grammatical “system” (in Firth’s sense of the term) is essentially probabilistic, quantitative data are introduced in order to provide evidence of relative frequencies. Section 2 presents a description of word-class categorisation from the point of view of grammars and dictionaries arguing that the traditional category of conjunctions is inadequate for capturing the notion of phrasal connective. Section 3 examines the notion of ‘connective’ and suggests a truth-function interpretation of connective behaviour. Section 4 describes the quantitative methods proposed for analysing the distributional properties of lexical units, and section 5 comments on the results obtained by applying such methods drawing some provisional conclusions. (shrink)

I start with the observation that we often respond to a musical performance with emotion -- even if it is just the performance of a piece of absolute music, unaccompanied by text, title or programme. We can be exhilarated after a Rossini overture brought off with subtlety and panache; somber and melancholy after Furtlanger’s performance of the slow movement of the Eroica. And so forth. These emotions feel like the real thing to me – or anyway very close to (...) the real thing. When one experiences them, it takes time for them to wear off, and one gets irritated with the companion who, because not similarly moved, wants immediately to start discussing where to go for dinner. Like many others, I am drawn to the philosophy of music by a need to understand how such emotional responses are possible. How can absolute music move us in the way that it does, and to the extent that it does? (shrink)

This article—part of a Common Knowledge symposium titled “Between Text and Performance”—argues that the publication of a new edition of Il barbiere di Siviglia in Works of Gioachino Rossini (Bärenreiter-Verlag, Kassel) offers an excellent opportunity to reflect upon the written text of an opera and its relationship to the work that performers must do to realize the opera in the theater. Rossini wrote many passages that demand the intervention of performers (performing them “as written” is simply an error), (...) yet this does not mean necessarily that “anything goes.” The new edition not only gives Rossini's own variations for the opera, but also (in an appendix prepared by Will Crutchfield) indicates the nature of ornamentation and variations employed by singers before 1850. Many of the variations still heard today in the opera house reflect practices from the end of the nineteenth and early twentieth centuries. There is no moral obligation to avoid such practices, but one wants singers to be fully aware of what they are doing. This essay provides extensive examples of the kind of autograph notation that signals the obligatory intervention of performers and offers many examples from performers who were contemporaries of Rossini as to how they went about their task of representing the composer's work on stage. (shrink)

The existence of extensive written communications between Verdi and his librettists should have prompted scholars to prepare editions of the correspondence and to analyze its meaning and implications. Only rarely can we participate directly in the formative stages of an opera, and available material such as the correspondence between Richard Strauss and Hugo von Hofmannsthal is invaluable.1 Obeisance, at least, has been done to Verdi's correspondence. Alessandro Luzio calls the letters of Verdi to Antonio Ghislanzoni, "versifier" of Aida , "the (...) most marvelous course in musical aesthetics in action." Yet, for no opera do we have available a complete editions of the surviving letters between Verdi and a librettist. · 1. Willi Schuh, ed., Richard Strauss - Hugo von Hofmannsthal: Briedwechsel, 4th ed. . An English edition, made from an earlier German edition with many omissions, was published as A Working Friendship: The Correspondence between Richard Strauss and Hugo von Hofmannsthal, trans. Hans Hammelmann and Ewald Osers . Philip Gossett is the general editor of the critical edition of the works of Rossini and author of numerous articles on Renaissance music, Italian opera, Beethoven, and musical theory. (shrink)

In his great aria "La calumnia," Don Basillo, the music master of Rossini's Barber of Seville, graphically describes how evil whispers grow, with appropriate watering, into truly grand and injurious calumnies. For the less conniving among us, the same lesson may be read with opposite intent: in adversity, try to contain. The desire to pin evil deeds upon a single soul acting alone reflects this strategy; conspiracy theories have a terrible tendency to ramify like Basillo's whispers until the runaway (...) solution to "whodunit" becomes "everybodydunit." But conspiracies do occur. Even the pros and pols now doubt that Lee Harvey Oswald [202] acted alone; and everybody did do it on the Orient Express. 2.. (shrink)

If opera had existed in Elizabethan London, the world's Top Bard, as W.H. Auden called him, might have become the world's Top Librettist. As Gary Schmidgall shows in this illuminating study, Shakespeare's expressive ways and dramaturgical means are like those of composers and librettists in numerous and often astonishing ways. No wonder that well over two hundred operas have been based on Shakespeare's plays. Ranging widely through the Shakespearean canon and the standard operatic repertory, Schmidgall presents a fascinating comparison, focusing (...) on similarities of expressive style, scenic structure, staging, and performance practice. Shakespeare and Opera offers extended discussions of issues central to both theatrical genres, including their shared demand for virtuoso display, the comparable functions of set speeches and arias, and the similarities of verbal and musical rhetoric, and the charges of unreality and melodrama that have dogged them both. In addition, Schmidgall provides concise essays on the most intriguing Shakespeare-based operas, including works of Verdi, Wagner, Bellini, Rossini, Berlioz, Thomas, Vaughan Williams, Barber, and Britten. He enriches his argument with the insights of the great composers who never set Shakespeare (Mozart, Puccini, and Strauss among them), major observers of the legitimate stage (from Samuel Johnson to Eric Bentley) and the musical stage (from Joseph Addison to Joseph Kerman), as well as the incisive views of influential artists, critics, and performers as diverse as Walt Whitman, H.L. Mencken, and Laurence Olivier. For all who love the stage, Shakespeare and Opera offers endless insight and fascination. Schmidgall's extended comparison of the two dramaturgies provides a fresh perspective on Shakespeare, musical theater, comparative drama, and theater history. (shrink)

La discussione delle grandi narrazioni storiografiche del pensiero medievale. Il definirsi di una prospettiva teorica e di una storiografica attraverso il confronto con Scoto Eriugena. La ricerca di un senso e il problema di Dio. Gli anni della guerra e l'importanza della prassi.