El presente artículo trata de mostrar la presencia del pensamiento de Ireneo de Lyon en el sustrato del pensamiento de Gregorio de Nisa en una de sus obras cumbres: el Comentario al Cantar de los Cantares. Esta obra refleja la confluencia de una profunda reflexión a partir del texto bíblico y la filosofía de la época. El niseno se ubica en la tradición de los autores eclesiásticos que han comentado este bello poema de amor veterotestamentario. Si bien es cierto que (...) en la edición crítica de la obra no aparece nunca citado el lugdunense se pueden encontrar ciertos núcleos conceptuales y temáticos que ayudan a descubrir una recepción de Ireneo en el Comentario al Cantar de Gregorio. Esos elementos permiten poner de relevancia la relación existente entre estos dos autores patrísticos que se conectan para mostrar la realidad esponsal de la iglesia que posee un dinamismo pneumático-salvífico abierto a toda la humanidad. The purpose of this article is to show how Ireneus of Lyon´s thought was present in one of Gregory of Nyssa´s fundamental works: Commentary on The Song of Songs. This work reflects a convergence of deep biblical reflection and the philoshophy of the time. Gregory is among the ecclesiastical writers who have commented on this beautiful love poem in the Old Testament. Even though there is no mention of the Lugdunian in the critical edition of the work, some concepts and themes may be found which help identify an influence form Ireneus on Gregory´s Commentary on the Song of Songs. These elements allow us to give relevance to the relationship between these two patristic authors, who come into contact in order to show the church´s spousal reality, which has a pneumatological-salvific dynamics, open to all mankind. (shrink)
In a recent article in this journal, Kingsley has tried to show that the postulates of special relativity contradict each other. Here we show that the arguments of Kingsley are invalid because of an erroneous appeal to symmetry in a non-symmetric situation. The consistency of the postulates of special relativity and the relativistic kinematics deduced from them is restated.
In this paper we study the axiomatic system proposed by Bourbaki for the Theory of Sets in the Éléments de Mathématique. We begin by examining the role played by the sign \(\uptau \) in the framework of its formal logical theory and then we show that the system of axioms for set theory is equivalent to Zermelo–Fraenkel system with the axiom of choice but without the axiom of foundation. Moreover, we study Grothendieck’s proposal of adding to Bourbaki’s system (...) the axiom of universes for the purpose of considering the theory of categories. In this regard, we make some historical and epistemological remarks that could explain the conservative attitude of the Group. (shrink)
In the present article two possible meanings of the term mathematical structure are discussed: a formal and a nonformal one. It is claimed that contemporary mathematics is structural only in the nonformal sense of the term. Bourbaki's definition of structure is presented as one among several attempts to elucidate the meaning of that nonformal idea by developing a formal theory which allegedly accounts for it. It is shown that Bourbaki's concept of structure was, from a mathematical point of (...) view, a superfluous undertaking. This is done by analyzing the role played by the concept, in the first place, within Bourbaki's own mathematical output. Likewise, the interaction between Bourbaki's work and the first stages of category theory is analyzed, on the basis of both published texts and personal documents. (shrink)
Saunders Mac Lane famously remarked that "Bourbaki just missed" formulating adjoints in a 1948 appendix (written no doubt by Pierre Samuel) to an early draft of Algebre--which then had to wait until Daniel Kan's 1958 paper on adjoint functors. But Mac Lane was using the orthodox treatment of adjoints that only contemplates the object-to-object morphisms within a category, i.e., homomorphisms. When Samuel's treatment is reconsidered in view of the treatment of adjoints using heteromorphisms or hets (object-to-object morphisms between objects (...) in different categories), then he, in effect, isolated the concept of a left representation solving a universal mapping problem. When dualized to obtain the concept of a right representation, the two halves only need to be united to obtain an adjunction. Thus Samuel was only a now-simple dualization away for formulating adjoints in 1948. Apparently, Bodo Pareigis' 1970 text was the first and perhaps only text to give the heterodox "new characterization" (i.e., heteromorphic treatment) of adjoints. Orthodox category theory uses various relatively artificial devices to avoid formally recognizing hets--even though hets are routinely used by the working mathematician. Finally we consider a "philosophical" question as to whether the most important concept in category theory is the notion of an adjunction or the notion of a representation giving a universal mapping property (where adjunctions arise as the special case of a bi-representation of dual universal mapping problems). (shrink)
The group of mathematicians known as Bourbaki persuasively proclaimed the isolation of its field of research – pure mathematics – from society and science. It may therefore seem paradoxical that links with larger French cultural movements, especially structuralism and potential literature, are easy to establish. Rather than arguing that the latter were a consequence of the former, which they were not, I show that all of these cultural movements, including the Bourbakist endeavor, emerged together, each strengthening the public appeal (...) of the others through constant, albeit often superficial, interaction. This codependency is partly responsible for their success and moreover accounts for their simultaneous fall from favor, which, however, can clearly be seen as also stemming from different internal problems. To understand this dynamics, I argue that Bourbaki’s role can best be captured by using the notion of cultural connector, which I introduce here. (shrink)
La storia della filosofia come frontiera. L’itinerario di Nicola Abbagnano - ASBTRACT: L’articolo ricostruisce i momenti fondamentali del percorso storiografico di Nicola Abbagnano, a partire dalla sua tesi di laurea del 1923, Le sorgenti irrazionali del pensiero, fino all’articolo Il lavoro storiografico in filosofia : l’intento di questa analisi è mostrare la centralità e la complessità della Storia della filosofia , non riducibile a semplice "appendice" storiografica del periodo esistenzialistico dell’autore. Vengono esaminate in tale prospettiva le premesse teoriche (...) dell’impostazione storiografica di Abbagnano e le difficoltà che sorgono nel concreto lavoro storiografico: la Storia della filosofia si rivela così anche opera teoretica decisiva nel passaggio al neoilluminismo, che risulta caratterizzato da un profondo ripensamento dei rapporti tra storia e filosofia. (shrink)
This article reconstructs the personal and intellectual friendship between two cosmopolitan intellectuals: Andrea Caffi and Nicola Chiaromonte , who met while in exile in Paris in 1932. After a brief recapitulation of their previous biographies, and an overall presentation of their participation in the revolutionary antifascist group ‘Giustizia e Libertà’ in the thirties, this article provides a detailed analysis of their dialogues and disagreements in the forties and fifties on the topics of socialism and revolution, antifascism and anti-totalitarianism, utopia (...) and history. Particular attention is devoted to their contribution to the debates in the antifascist journal of GL and in the radical journal of Politics . Examined closely, the friendship between Caffi and Chiaromonte appears as a sequence of convergences and divergences, understandings and ruptures, which reflect the tensions and lacerations of the European civil war and its post-war legacy . Looked at again from a distance, however, it reveals a fundamental intellectual unity—a profound apolitical affinity in a century of radical politics which had fed wars, revolutions and totalitarian regimes. (shrink)