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.

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)

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)

According to the nineteenth-century polymath William Stanley Jevons, natural phenomena were a series of combinations and permutations. The similarity between Jevons’s account and other instances of ars combinatoria has already been noticed, although this topic has never been extensively addressed in the literature. In this paper, I offer a novel interpretation of Jevons’s logic and philosophy of science as an art of combinations. Jevons’s position shall be compared with other theorizers in the ars combinatoria tradition. This study will (...) show that Jevons’s art of combinations differed from some of the examples here investigated because he did not believe that language could refer to the primal constituents of reality. Rather, his art of combinations relied on the order of combinations, displaying a syntactical nature. Consequently, I will argue that Jevons’s logic presents some relevant similarities to Leibniz’s characteristica. Moreover, this analysis offers a contribution to the study of Jevons’s logic, highlighting the ontological implications embedded in his logical thought. (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 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.

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 36.2 (2003) 168-172 [Access article in PDF] Logic and the Art of Memory: The Quest for a Universal Language. Paolo Rossi. Trans. Stephen Clucas. Chicago: University of Chicago Press, 2000. Pp. xxviii + 333. $32.00 cloth. Of the traditional five canons of rhetoric—inventio, dispositio, elocutio, memoria, and actio—the most circuitous and fascinating history belongs to memoria. From its propulsion of Homeric lore to its grounding of (...) rhetorical invention to its exile under print culture to its recent revival in public memory studies, the promiscuous and perplexing history of memory in the West may be one of the least appreciated, and perhaps least understood, elements of rhetorical and intellectual history. The publication in 1966 of Frances Yates's highly praised The Art of Memory drew the attention of contemporary scholars to the importance of mnemotechnics to the culture of late medieval and early modern Europe. 1 Yates persuasively argued that the art of memory is an integral element of European intellectual history, one that can enrich our understanding of everything from Dominican theology to Shakespearian theater. However, six years earlier, in 1960, the Italian intellectual historian Paolo Rossi published in Italian an important precursor to Yates's work entitled Clavis Universalis: Arti Della Memoria e Logica Combinatoria da Lullo a Leibniz. The book traces the encyclopaedic and mnemotechnical traditions from Aristotle through Cicero and Raymond Lull and into the early-modern period, arguing that the art of memory provides an important antecedent to the advent of method in seventeenth-century philosophy, especially in the works of Bacon, Descartes, and Leibniz. Yates, in her preface to The Art of Memory, acknowledges her debt to Rossi's work, and now this work has been made available in English translation. Stephen Clucas's translation, under the title Logic and the Art of Memory, will no doubt stimulate and supplement research into the mnemotechnical tradition in the English-speaking world, and perhaps lead us to reconsider the relationship between philosophy and rhetoric.Rossi argues that the neglect of the mnemotechnical tradition in its Ciceronian and Lullian strands has distorted our understanding of the "new" science and philosophy of the seventeenth-century, which is often interpreted as constituting, in a Kuhnian sense, a drastic paradigm shift from a [End Page 168] Renaissance worldview that still retained occult elements. Rossi places the work of Bacon, Descartes, and Leibniz within the historical strand of the logico-encyclopaedic and mnemotechnical traditions, suggesting that these figures culminate late medieval and early modern intellectual and cultural ambitions as much as they give rise to new ones. Rossi makes his argument by providing a history of mnemotechnics from Aristotle into the fifteenth century in chapter one; by examining the fascination with encyclopaedism, combinatoria, and memory in the sixteenth century in chapters two and three; by investigating the role of artificial memory in the works of key intellectual figures in the late sixteenth and seventeenth centuries in chapters four through six; and by tracing the impulse toward universal knowledge and its connection to mnemotechnics among seventeenth-century Cartesians, Baconians, and in the work of Leibniz, in chapters seven and eight.Chapter one, after showing the pervasiveness of Renaissance mnemotechnical literature, surveys its classical and medieval antecedents in philosophy and rhetoric. Rossi argues that Aristotle's De memoria et reminiscentia, Cicero's De oratore, Quintilian's De institutione oratoria, the Rhetorica ad Herennium, and the works of Albertus Magnus and Thomas Aquinas were each important to the mnemotechnical tradition into the seventeenth century. Fourteenth- and fifteenth-century treatises on the ars memorativa and the ars predicandi, drawing on these classical and medieval theories, emphasize the importance of memory places (loci), images (imagines), and order or arrangement (dispositio) in mnemotechnics. Additionally, they intimately link the memory to the imagination, stressing the importance of exciting and stimulating the imagination in memorization. The Italian Pietro da Ravenna, for example, attributed the might of his memory to, in his own words, turning "the images of the most beautiful virgins into memory places" (22). Such imaginative mnemonic techniques were considered to... (shrink)

There are two accounts of the relation between subject and predicate in Leibniz's writings. The former, which appears in De arte combinatoria, is based on an interpretation of this relation in terms of sum and parts and can be viewed as an anticipation of mereology. The latter, which operates after 1686, is based on an interpretation of this relation in terms of inherence. Metaphysical reasons, linked with the discovery of infinitesimal calculus, explain this shift.

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)

On trouvera en ces Etudes l'examen de Quelques notions fondamentales sur la langue allemande, le fondement du Droit, l'épistémologie, la naissance de la Dynamique, l'harmonie, l'erreur, la réflexion, la perception, le simple et le composé, l'espace. On y suivra l'héritage leibnizien au XVIIIe siècle en France, en particulier chez Voltaire et chez Diderot, mais surtout, plus tard, en Allemagne, par l'intermédiaire de Kant, chez Hegel, sur le problème de l'essence. On y verra enfin, sur deux exemples - parmi combien d'autres (...) -, se réaliser sous nos yeux, grâce à l'ordinateur, le rêve de note philosophe : De Arte Combinatoria Pourquoi Leibniz? Parce qu'en nous rattachant au passé, il ne cesse d'être moderne. (shrink)

Ramon Llull y el secreto de la vida descubre el enigmático mundo de este filósofo, místico y visionario (Mallorca, 1232-1316) que escribió unos 300 libros en catalán, latín y árabe recorriendo las principales capitales europeas, el Mediterráneo oriental y el norte de África con el claro propósito de comunicar y predicar un modelo místico de contemplación. El descubrimiento del «ars combinatoria», un nuevo lenguaje que tenía sus paralelismos en las técnicas de cabalistas y sufíes, encontraría numerosos admiradores en Europa, (...) desde los filósofos del Renacimiento –que lo entendieron como un arte de la memoria– hasta los más recientes estudios, que lo ven como un precedente del lenguaje de la informática. Este libro quiere ofrecer una interpretación del pensamiento filosófico y religioso de Llull. La primera parte se vincula a la necesidad de comprensión de su propia experiencia extraordinaria. La segunda desarrolla la teoría de la contemplación mística. En la tercera se estudian los diversos usos del lenguaje empleados por Llull. Y la cuarta incluye una selección de sus textos más representativos. (shrink)

Artificial Intelligence, both as a hope of making substantial progress, and a fear of the unknown and unimaginable, has its roots in human dreams. These dreams are materialized by means of rational intellectual efforts. We see the beginnings of such a process in Lullus’s fancies. Many scholars and enthusiasts participated in the development of Lullus’s art, ars combinatoria. Amongst them, Athanasius Kircher distinguished himself. Gottfried Leibniz ended the period in which the idea of artificial intelligence was shaped, and started (...) the new period, in which artificial intelligence could be considered part of science, by today’s standards. (shrink)

Ramón Llull se propuso instruir y educar en las disciplinas más relevantes de su tiempo -artes liberales, teología, física, medicina, astronomía- a iletrados y no cristianos, y diseñó con ese fin un instrumento de aprendizaje al que llamó "Arte". El Arte, con sus principios, figuras combinatorias y símbolos fundó un camino especulativo interdisciplinario en el que diversas ciencias hallaron una convergencia epistémica, ética y religiosa. El propósito luliano se multiplicó en cerca de 270 obras: literarias, científicas, apologéticas y (...) en las distintas versiones del Arte. Uno de los aspectos más interesantes del pensamiento de Llull es el lenguaje de los correlativos: un conjunto de términos, acuñados al modo de la gramática especulativa del siglo XII, cuyo objetivo es la expresión de los principios del Arte. En el "Liber correlativorum innatorum", que aquí se presenta, Llull describe la formación de estos "nuevos nombres", su significado metafísico y su estructura lingüística, y enseña el modo de usarlos. Se trata de un modelo de lenguaje universal cuya estructura gramatical está vinculada con el contenido metafísico de los principios del Arte y su significación metafórica en la naturaleza y el orden intelectual. (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)

In this book, international experts from Europe and the United States address Lullism as a remarkable and distinctive method of thinking and experimenting. The origins and impact of Ramon Llull's oeuvre as a modern thinker are presented, and their interdisciplinary and intercultural implications, which continue to this day, are explored. Ars combinatoria, generative and permutative generation of texts, the epistemic and poetic power of algorithmic systems, plus the principle of unconditional dialogue between cultural groups and their individual members, are (...) the most important coordinates of this combinatorial-dialogical media and communication theory, which appeared very early in the history of science, technology, and art. It was developed in the work of Ramon Llull during the transition from the thirteenth to the fourteenth century when Arab-Islamic, Jewish, and Christian cultures intersected. The legacy of Lullism lives on in poetry and in the visual and electronic-based arts, as well as in research on the history of informatics, formal logic, and media archaeology. The primary idea of Llull's teachings--to enable rational and therefore trustworthy dialogue between cultures and religions through a universally valid system of symbols--is today still topical and of great relevance, especially in the tensions prevailing in globalized spaces of possibility. (shrink)

A collection of photographs depicts life on Chicago's west side between 1949 and mid-1960s.

Helps individual readers to overcome procrastination and build self-esteem Reveals how to create a culture of accountability, and how to hold someone accountable Gives leaders a step-by-step process for helping team members become more self-responsible Explains commitment reluctance and how to encourage self-responsibility among team members Uncovers why we blame others and shows how to defeat a blame culture Provides an easy read with no consultant-speak In recent years, HORN Training and Consulting was awarded the distinguished Gold Medal by the (...) Canadian Society for Training and Development for its leadership development program designed for one of the world’s largest international banks; and HORN is currently executing leadership development projects on a global scale for companies in the consumer packaged goods and pharmaceutical industries. (shrink)

Business ethics courses have been launched with professors from business pulling on one oar, and professors of philosophy pulling on the other, but they lack a sense of direction. Let's begin with the basics: What is an ehtical decision? More fundamentally, why the interest in professional ethics in the first place?There are over 300 centers for the study of appIied ethics in this country-why? The events which face our society today are outside the business-oriented collection of shared beIiefs that set (...) our pubIic policy agenda. Cur beIiefs are too narrow, thus we see, understand, and control small slices of life.Business ethics should be the study of the structure and impact on us of what we call "business science," e.g., accounting, marketing, economics, law, etc., and the corresponding study of the process of what Carl Jung called individuation: learning to become one's own uniqueself in the face of these bodies of professional knowledge which have structured our lives and charted the direction for our sensibilities for too long. (shrink)