Mathesis

Giordano Bruno and the Geometry of Language brings to the fore a sixteenth-century philosopher's role in early modern Europe as a bridge between science and literature, or more specifically, between the spatial paradigm of geometry and that of language. Arielle Saiber examines how, to invite what Bruno believed to be an infinite universe-its qualities and vicissitudes-into the world of language, Bruno forged a system of 'figurative' vocabularies: number, form, space, and word. This verbal and symbolic system in which geometric figures are seen to underlie rhetorical figures, is what Saiber calls 'geometric rhetoric.' Through analysis of Bruno's writings, Saiber shows how Bruno's writing necessitates a crafting of space, and is, in essence, a lexicon of spatial concepts. This study constitutes an original contribution both to scholarship on Bruno and to the fields of early modern scientific and literary studies. It also addresses the broader question of what role geometry has in the formation of any language and literature of any place and time.

This book contains a translation of the Eight Books of the Mathesis by the 4th century astrologer Julius Firmicus Maternus along with some useful Indexes of Occupations, the Causes of Death, and Personal Characteristics. Book I: An essay on what astrology is Book II: The twelve signs Book III: Aspects and house placement of planets Book IV: Chart Interpretation Book V: The angles and the terms Book VI: The aspects Book VII: Life and death Book VIII: The degrees of the signs The translator, James H. Holden, is a well respected astrological scholar who has translated more than twenty astrology books that were written between the 2nd and 17th centuries. He is also the author of A History of Horoscopic Astrology.

In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gründe”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.

This publication covers papers presented at AIED2009, part of an ongoing series of biennial international conferences for top quality research in intelligent systems and cognitive science for educational computing applications. The conference provides opportunities for the cross-fertilization of techniques from many fields that make up this interdisciplinary research area, including: artificial intelligence, computer science, cognitive and learning sciences, education, educational technology, psychology, philosophy, sociology, anthropology, linguistics, and the many domain-specific areas for which AIED systems have been designed and evaluated. AIED2009 focuses on the theme "Building learning systems that care: from knowledge representation to affective modelling". The key research question is how to tackle the complex issues related to building learning systems that care, ranging from representing knowledge and context to modelling social, cognitive, metacognitive, and affective dimensions. This requires multidisciplinary research that links theory and technology from artificial intelligence, cognitive science, and computer science with theory and practice from education and the social sciences.

This book offers a new type of working tool for Cartesian studies. It presents the literature of the last 160 years in alphabetical order (Part Two), combined with a systematic analytical survey (Part One) and a detailed topical index to the whole (Part Three). This organization makes it possible to turn bibliogra phy from a repository of references into a workshop of research. The system atic survey of Part One and the topical index of Part Three, together, offer a mise au point of Descartes studies over their full historical and topical range. The results have often been surprising and illuminating to the author, and if his experience is any guide, the reader, too, will begin to wonder about certain seemingly well-settled points, or marvel at the Protean shapes which our elusive philosopher assumes when mighty commentators force him to reveal his true nature. A work which has been in the making for fifteen years must show the traces of expansion in scope, and changes in evaluation. Bibliographia cartesiana amends my Descartes chapter in A Critical Bibliography of French Literature, v. 3, 1961 (see no. I9a), and supersedes an earlier version of Parts One and Two, published in 1959 under the main title Descartes and his Philosophy, v. 1 (set: no. I8a). Part I (Introduction to Descartes Studies) divides the field into eleven broad areas.