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 Early interpreters, especially, have criticized Bruno's mathematics for being “outdated” or too “concrete”.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)

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics education. (...) By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (shrink)

Education for Empire: American Schools, Race, and the Paths of Good Citizenship (Stratton, 2016) is much more than a history book about American education. It is a critical work that provides philosophical undertones that challenge our perception about the imperial roles of the U.S. school system. Stratton very clearly and meticulously presents the intricate relationship between history, civics, and geography within school curricula and textbooks. He shows us how these subjects have been manipulated by those in power to promote a (...) hidden agenda. One that instills national pride, American loyalty, and patriotism, and is designed to turn students into supporters of U.S. imperialism and of their racial and class hierarchies. An example of this is Stratton’s own examination of the content of books like, Complete Geography written in 1899. Stratton claims this text was widely used in American public schools and it explicitly states that, “the Caucasian or white race is most intelligent and most powerful of all races.” Education for Empire: American Schools, Race, and the Paths of Good Citizenship helps us understand why it has taken so much time for people of color, like me, to occupy academic spaces and to begin the dismantling of oppressive governmental and pedagogical systems that have intentionally kept us from having a dignified education. (shrink)

El libro El Feminismo es un Humanismo escrito por Rubí de María Gómez Campos es un trabajo literario sobre la urgencia y la complejidad del feminismo. La autora utiliza su vasta experiencia como educadora y filósofa en el contexto mexicano para presentar esta colección de ensayos, resultado de varias décadas de su carrera académica. En estos escritos explora las diferentes vertientes filosóficas del feminismo desde varios ángulos críticos y teóricos.

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)

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)

Mimesis can refer to imitation, emulation, representation, or reenactment - and it is a concept that links together many aspects of ancient Greek Culture. The Western Greek bell-krater on the cover, for example, is painted with a scene from a phlyax play with performers imitating mythical characters drawn from poetry, which also represent collective cultural beliefs and practices. One figure is shown playing a flute, the music from which might imitate nature, or represent deeper truths of the cosmos based upon (...) Pythagorean views (which were widespread in Western Greece at the time). The idea that mimesis should be restricted to ideals was made famous by Plato (whose connections to Pythagoreanism and Siracusa are well-known), and famously challenged by his student Aristotle (not to mention by the mimetic character of Plato’s own poetry). This volume gathers essays not only on the philosophical debate about mimesis, but also on its use in architecture, drama, poetry, history, music, ritual, and visual art. The emphasis is on examples from Hellenic cities in Southern Italy and Sicily, but the insights apply far beyond – even to modern times. Contributors include: Thomas Noble Howe, Francisco J. Gonzalez, Gene Fendt, Guilherme Domingues da Motta, Jeremy DeLong, Carolina Araújo, Marie-Élise Zovko, Lidia Palumbo, Sean Driscoll, Konstantinos Gkaleas, Anna Motta, Jure Zovko, Alexander H. Zistakis, Christos C. Evangeliou, Dorota Tymura, Iris Sulimani, Elliott Domagola, Jonah Radding, Giulia Corrente, Laura Tisi, Ewa Osek, Argyri G. Karanasiou, Rocío Manuela Cuadra Rubio, Jorge Tomás García, Aura Piccioni, and José Miguel Puebla Morón. (shrink)