Neste artigo o autor pretende mostrar como as reflexões filosóficas de Giordano Bruno sobre a Retórica foram fortemente influenciadas pelas concepções metafísicas e metodológicas de Raimundo Lúlio. Para tanto, são analisados especialmente os Escritos de Wittenberg, Artificium perorandi e De lampade combinatoria, onde Bruno discute a aplicação dos princípios do lulismo através da utilização da metáfora dos caracteres e da hierarquização do cosmos, bem como da operacionalização de um processo combinatório na construção de proposições e argumentos.

En este texto se examina críticamente la teoría combinatoria de las representaciones científicas de Andoni Ibarra y Thomas Mormann. El núcleo de la crítica va dirigido a mostrar que una serie de estudios sobre la ciencia, que ellos mismos mencionan, sugiere que la clasificación en tipos de representaciones propuesta es problemática. Es más, esos mismos estudios muestran que por lo menos muchas representaciones tienen una dimensión histórica que parece imposible capturar por medio del tipo de formalismo propuesto. /// Ibarra and (...) Mormann's combinatorial theory of scientific representations is subject to critical scrutiny. It is argued that the classification of types of representations offered cannot serve as a basis for an analysis of the variety of representations that happen to arise in science. Empirical studies on ways of representing used in science strongly suggest that a formal theory of representations of the kind proposed is not able to capture the historical dimension of the structure of representations. (shrink)

ResumoO artigo apresenta um estudo sobre as aplicações feitas por Leibniz de sua arte combinatória ao campomusical. Elucidamos inicialmente alguns conceitos fundamentais, bem como alguns procedimentos dacombinatória leibniziana, e mostramos os usos musicais sugeridos por Leibniz para esses procedimentos.Em seguida, discutimos o alcance geral da abordagem combinatória em música e concluímos que Leibnizantecipa, na Dissertatio, a introdução de procedimentos vinculados à música contemporânea.Palavras-Chave: Combinatória. Música. Pensamento Simbólico. Leibniz.Abstract.The paper presents a study on Leibniz’s applications of his combinatorial (...) art to the musical field. First, weelucidate some fundamental concepts, and some procedures of Leibnizian combinatory, and we show themusical uses suggested by Leibniz for these procedures. Then, we discuss the general scope of the combinatorialapproach in music, and we conclude that Leibniz anticipates, in Dissertatio, the introduction ofsome procedures related to contemporary music. (shrink)

The present paper analyses the proof of the existence of God given by Leibniz in his early work, the Dissertatio de arte combinatoria of 1666. Leibniz delivers a proof by an (infinite) distinction of cases that has not always been recognized by his translators and critics.

This paper focuses on the possibility of conceiving a form of ontological nihilism, starting from D. M. Armstrong’s combinatorialism. This possibility has been suggested by Efird and Stoneham, by means of proposing an alternative strategy to the ‘subtraction argument’. They claim that it is possible to sustain such nihilism trough the concepts of construction and totality state of affairs. However, this hypothesis will require the acceptance of non-instanciated universals, that is, platonic universals. Yet this is opposite to requirements that are (...) basic for a combinatorial theory, which should uphold that universals exist only in their instantiations. Then, the assumption of platonic universals results in high costs for a combinatorial naturalism, according to which only exists what is located in space and time. (shrink)

The combination of single material elements characterises Nespolo’s artworks since the 60s. The primacy of art factuality - to do art manually - emerges both in his geometrically structured works and in his machines and wooden uniconic structures. These are all combined and based on the strategy of puzzle and on a reflection about the mental attitude to do art. For these reasons, it is possible to consider Nespolo as a forerunner of Conceptual Art.

Referring to Reichlin’s reflections, the author analyzes the aporias arised in the debate on euthanasia, proposes to establish some general principles (e.g. inviolability of human life, the prohibition of extend unnecessary suffering, the principle of autonomy) and a method of application of them to controversial cases. The combinatorial ethics that emerges can probably solve the aporias and can harmonize the common sense (about the possibility of euthanasia in extreme cases) with Catholic doctrine – specifically referring to the Natural Moral Law (...) theory – in an attempt to integrate the results of combinatorial ethics with the principles established in this doctrine. The conclusions, although admittedly provisional, are translated into indications for an hypothetical legislator, in order to overcome the legislative aporia. In the final part, analyzing the religious aporia, the author proposes to include some forms of euthanasia in a total rethinking of the meaning of death, starting with the teachings of Christian faith. Basandosi sulle riflessioni di Massimo Reichlin e James Rachels, l’Autore intende analizzare le principali aporie che emergono nella riflessione etica sull’eutanasia – quella filosofico-metodologica, deontologica, legislativa e religiosa. Attraverso quest’analisi, l’Autore propone di riprendere alcuni principi generali (tra cui l’indisponibilità della vita, il divieto di prolungare sofferenze inutili e il principio di autonomia), fornendo poi un metodo d’applicazione ai casi concreti. L’etica combinatoria che emerge da questa impostazione, riesce in buona misura a risolvere le aporie analizzate, armonizzando alcune intuizioni comuni (circa la liceità dell’eutanasia in casi particolarissimi ed estremi) con la dottrina cattolica corrente in materia. Nel confronto con la morale cattolica, in particolare, viene analizzata e discussa la teoria della legge morale naturale, nel tentativo di integrare i risultati dell’etica combinatoria con i principi affermati in questa dottrina. Le conclusioni teoretiche, anche se dichiaratamente provvisorie, si traducono poi in indicazioni praticate per un ipotetico legislatore, nel tentativo di superare l’ultima grande aporia, quella legislativa. Nella parte conclusiva, analizzando l’aporia religiosa, l’Autore propone di iscrivere la liceità di alcune forme di eutanasia all’interno di un complessivo ripensamento del significato della morte, partendo dal dato di fede cristiano, nel tentativo di superare la “logica della rimozione” che sembra caratterizzare la nostra contemporaneità. (shrink)

The Lambdoma, considered the most important harmonical pattern of order is to be understood as a further development of a figure attributed to the Pythagoreans "in the shape of the capital letter Lambda" -therefore named Lambda . Diagrams similar to the Lambdoma without explicit harmonical significance can be found in the writings of several medieval and modern authors, including Ramon Llull , whose influence on Leibniz is already evident in the Dissertatio de arte combinatoria , Leipzig 1666. Leibniz and Llull (...) are linked particularly by the idea of Kombinatorik as ars inveniandi in the sense of a universal language, whose extension of knowledge is self-creating . In the larger context of LlulPs historical influence, Kombinatorik as structural logic and harmonical Lambdoma we also have to see Leibniz's genealogical scheme in his academic dissertation . The harmonical analysis of this model contains convincing parallels to the structural build-up of the Lambdoma . However, the analogies go further, as is shown by the reference to Leibniz's Dyadik, to the 64 hexagrams of the /Ging and the comparison of the /Ging with the genetical code. Harmonically structured systematized thought reveals itself as that possibility of an interpretation of the universe, which Leibniz did not really have in mind. However, we can find that thought at the decisive points of his theory of philosophical principles so to speak as the pythagorean-platonic inheritance. (shrink)

In seiner Dissertano de arte combinatoria entwickelt G. W. Leibniz eine Methode, um Prädikate von einem Subjekt und Subjekte zu einem Prädikat zu finden, und er stellt eine Formel auf, um deren Anzahl zu berechnen. Ich möchte im Folgenden erläutern, wie diese Methode funktioniert und warum sie sowohl einen Teil der, wie Leibniz es nennt, logica inventiva als auch eine direkte Folge seiner Variationslehre bildet, die den zentralen Teil seiner Dissertano ausmacht. Im letzten Abschnitt dieses Beitrages werde ich auf einige (...) theoretische und historische Zusammenhänge zwischen der logica inventiva und der aristotelischen Logik eingehen. Insbesondere werde ich erläutern, in welcher Weise Leibniz' Methode mit einigen traditionellen Versuchen in Verbindung steht, die tota minora eines gegebenen Terms zu bestimmen, und ob die aristotelische Theorie der kategorischen Propositionen in der Lage war, Leibniz' Methode zum Auffinden von Subjekten und Prädikaten innerhalb der logica inventiva zu begründen. (shrink)

A shorthand symbolism for the relational mapping of categories is introduced and developed on the basis of Nelson Goodman's structural methodology. Through a reconstruction of extensional isomorphism that Goodman introduces as a criterion for definitional accuracy, and a brief reminder of the argument structure behind his ‘new riddle of induction’, Goodman's radical ontological relativism is turned into a protological principle of what I call ‘domain constituting philosophy’. MSS is demonstrated with reference to Goodman's symbol theory, particularly his notion of exemplification, (...) as well as in a final structured comparison of Frege's ‘sense’ with Goodman's straightforward construction of ‘secondary extension’. (shrink)

Gian-Carlo Rota a su concilier un travail mathématique exemplaire et des recherches philosophiques largement inspirées par la phénoménologie husserlienne. Son œuvre philosophique nous semble avoir de fait deux composantes : l’une s’intéresse majoritairement à des phénomènes universels. L’autre se déploie de façon plus subtile en filigrane de ses travaux mathématiques ; sans être thématisée comme telle – comme contribution philosophique –, elle alimente très lar-gement l’aura de Rota dans la communauté mathématique et justifie le rôle qu’il y joue de père (...) fondateur d’une école combinatoire. L’analyse de ces différents moments de sa pensée permet de mieux en cerner les ressorts, l’unité et la portée.Gian-Carlo Rota was able to combine a remarkable mathematical work with philosophical research largely inspired by Husserl’s phenomenology. His philosophical work has two components. One focuses mainly on universal phenomena in mathematics. The other unfolds in a more subtle way in his mathematical work; without being characterized as a proper philosophical contribution, it feeds largely the aura of Rota in the mathematical community and contributes to justify his role of founder of a school of combinatorics.The analysis of these different moments of his thought allows to understand better its origins, unit and scope. Gian-Carlo Rota ha saputo coniugare il propio lavoro matematico esemplare ad una ricerca filosofica in gran parte ispirata dalla fenomenologia di Husserl. La sua opera filosofica ha secondo noi due componenti: una riguarda principalmente i fenomeni universali. L’altra si sviluppa in modo più sottile nel suo lavoro matematico e, senza diventare un tema in quanto tale – come vero e pro-prio contributo filosofico –, alimenta in gran parte l’aura di Rota nella co-munità matematica, contribuendo a giustificare il suo ruolo di fondatore di una scuola combinatoria. L’analisi di questi diversi momenti del suo pensi-ero permette di identificarne meglio le origini, l’unità e la portata.This article is in French. (shrink)

This volume offers the first-ever complete English translation of Leibniz’s Dissertatio De Arte Combinatoria together with a critical edition of the original Latin text on fa...

The meaning of the term “analysis” in Leibniz’s work is multifarious and it is doubtful that one could ever succeed in gathering this variety of meanings into a unified whole. However it has long been remarked that a landmass seems to detach itself from these moving waters – an island sometimes called by its inventor “The Most General Analytics of Human Thoughts”. Already sketched in the De Arte Combinatoria (1666) as a reform of the “analytical part” of Logic (pars logices (...) analytica), it rested on a very simple intuition: the possibility of developing, in parallel, three analyses, namely an analysis of thoughts (analysis notionum et veritatum), an analysis of the structure of language by which we express these thoughts (analysis linguarum or analysis grammatica) and an analysis of the symbols by which we represent them (analysis characterum). This “General Analytics” achieved, any human thought could be related to a catalog of simple notions expressed by basic characters (the so called alphabetum cogitationum humanarum) and, as a direct consequence, any truth could be expressed as a combination of these primitive symbols. (shrink)

Ultrafilters are very important mathematical objects in mathematical research [6, 22, 23]. There are a wide variety of classical theorems in various branches of mathematics where ultrafilters are applied in their proof, and other classical theorems that deal directly with ultrafilters. The objective of this article is to contribute (in a divulgative way) to ultrafilter research by describing the demonstrations of some such theorems related (uniquely or in combination) to topology, Measure Theory, algebra, combinatorial infinite, set theory and first-order logic, (...) also formulating some updated open problems of set theory that refer to non-principal ultrafilters on N, the Mathias’s model and the Solovay’s model. -/- Resumen: Los ultrafiltros son objetos matemáticos muy importantes en la investigación matemática [6, 22, 23]. Existen una gran variedad de teoremas clásicos en diversas ramas de la matemática donde se aplican ultrafiltros en su demostración, y otros teoremas clásicos que tratan directamente sobre ultrafiltros. El objetivo de este artículo es contribuir (de una manera divulgativa) con la investigación sobre ultrafiltros describiendo las demostraciones de algunos de tales teoremas relacionados (de manera única o combinada) con topología, teoría de la medida, álgebra, combinatoria infinita, teoría de conjuntos y lógica de primer orden, formulando además algunos problemas abiertos actuales de la teoría de conjuntos que se refieren a ultrafiltros no principales sobre N, al Modelo de Mathias y al Modelo de Solovay. (shrink)

El discurso de individuos diagnosticados con trastorno del lenguaje como en el caso de la esquizofrenia, ha sido alta y comúnmente estudiado desde enfoques que observan el procesamiento cognitivo en la memoria, la atención o el acceso léxico o la localización y funcionamiento neuronal. El presente artículo en cambio, presenta y propone una reflexión y análisis de la forma de la información en las representaciones mentales a partir de una Semántica Conceptualista que incluye la combinatoria de interfaz físicas/perceptivas y de (...) inferencia o razonamiento para la formación del pensamiento y del lenguaje. A partir de un método de análisis deductivo indirecto sobre las sustituciones que operan en las estructuras conceptuales mediatizadas por las interfaces de la percepción, y el proceso de recursividad en la reparación de la referencia, se infiere que no necesariamente se trata de un trastorno del lenguaje o del pensamiento sino más bien de procesos relacionados directamente con la racionalización de los conceptos en las estructuras conceptuales; donde la sustitución es una forma común de representar la identidad de objetos. Identidad que resulta abstracta e inteligible a los oyentes en tanto que no se han satisfecho las necesidades de referencialidad. (shrink)

Este trabajo se encuadra dentro de una nueva visión de la lógica de Leibniz, la cual pretende mostrar que sus escritos fueron ricos no solamente en proyectos ambiciosos (Característica Universal, Combinatoria, Mathesis) sino también en desarrollos lógico-matematicos concretos. Se demuestra que su “Caracteristica Numerica” que asigna pares de números a las proposiciones categóricas es una semántiea para la cual la silogística aristotélica es correcta y completa, y que el sistema algebraico presentado en Fundamentos de un Cálculo Lógico es una lógica (...) algebraica similar a la de Boole.This work is a contribution to a new view of Leibniz’s logic, pretending to show that his writings were not only rich in projects (Characteristica, Combinatoria, Mathesis), but also in concrete logico-mathematical developments. We prove that his “Numerical Characteristic” assigning pairs of numbers to terms of categorical propositions, is a complete and correct semantics for aristotelian syllogistic, and the algebraic system presented in Fundamentals of Logical Calculus is essentially a complete version of boolean algebraic logic. (shrink)

Since Norbert Wiener presented a new research field called the study of control and communication in the animal and the machine, the biological and the artificial universes are each time more integrated as pieces of a game that involves science, philosophy, technology, arts, architecture and several other fields. It is astonishing to take a look at an imaginary non-linear timeline where it is possible to see the ancient Ars Mnemonica inspiring the Leibniz combinatoria and how all these virtual knowledge structures (...) inspired the development of a communication and control machine called the computer. A machine that is quite an exploded black box artificial systems integrated into biological systems in a cybernetic structure through which most diverse kinds of information flows. We are living in times in which the logic of this machine becomes the core of our post-biological era in its essence, the era in which the biological and artificial realms are immersed in one another. An era in which we see [] humans in fact integrating with the fiction of their imagination as conjured up digitally by the computer, and in which the digital arts emanating from the cosmology of number are also a link between digital finality and infinity imagination, defending man in his impossibility to be simulated (Weibel 1999: 222). Considering this panorama in the contemporary artistic context, it could be stimulating to think about interactive digital art installations as systems in which the elements are both organic and artificial, both physical and virtual, interconnected like they were performing a cybernetic ballet. The aim of the present research is to study this choreography using the complex sciences framework. Following this objective, a series of parameters based on systemic measures of organization and complexity were structured. Our intention is, obviously, not to say that the work of art is more or less systemic, more or less complex or organized, but to help in understanding and to conceive the installation as a system: a complex adaptive system (CAS). (shrink)

No início deste ano, contemporânea a uma edição comemorativa dos quarenta anos deexistência do lnstitutus-Rainnmdus-Lullus em Freiburg i. Br., um tanto atrasada, mas nem por isso menos importante, apareceu a tradução alemã do Liber de gentili et tribus sapientibus,. Duas circunstâncias tornaram importante o aparecimento deste livro para todos os que se interessam por Ramon Llull e pela cultura catalã. Em primeiro lugar, por ser esta não somente a primeira edição completa desta obra em alemão, que substitui a edição selecionada, (...) muito fragmentária, de Xosé e Elisabeth Scheible1 mas, ao mesmo tempo, por ser a primeira tradução completa em língua alemã desta obra.2 Além disso, o fato de este livro aparecer numa tão conhecida editora como a de Philipp Reklam indica que o Buch vom Heiden und den drei Weisen será, pelo menos nos próximos anos, a obra de Llull pela qual os leitores alemães terão o primeiro contato com o fascinante pensamento do maiorquino. Esta obra, que representa uma importante contribuição para o discurso inter-religioso na Idade Média, presta-se verdadeiramente como introdução ao pensamento do Doctor muminatus e apresenta as características essenciais da análise combinatória de sua Ars, de forma altamente explícita e igualmente estética e literária. Constituem seu guia e base narrativa os diálogos de três sábios, representando as três grandes religiões, enquanto caminham por uma selva até a descoberta dum locua amoenus, magistralmente descrito, em meio do qual encontram cinco grandes árvores, em cujas folhas se acham gravadas as combinações binárias dos princípios básicos Julianos. Aqui os três sábios, e com eles o leitor, são conduzidos pela dama Inteligência, e com ajuda das árvores, na funcionalidade da análise combinatória Juliana, antes de exporem racionalmente aos desconfiados pagãos a confortadora verdade salvífica da respectiva fé de cada um. Com isso o tradutor e editor Theodor Pindl, que já se distinguiu com diversos trabalhos, especialmente sobre o Breviculum, satisfaz na sua versão, com poucas exceções,3 as qualidades tanto filosóficas como literárias da obra e produz um texto bastante legível. No entretanto, nao baseou sua tradução na edição crítica do texto catalão feita por Antoni Bonner,4 publicada em 1993 na série Nova edició de les obres de Ramon Llull, mas recorreu à edição latina de 1721, de Ivo Salzinger, reeditada em 1965. O que é de se admirar, pois a edição feita em Mainz por Ivo Sa!zinger, como é sabido, sofreu numerosas modificações no que diz respeito à ordem das frases e à escolha das palavras feitas pelo editor. (shrink)