Kaspar Schott’s “encyclopedia of all mathematical sciences”

In 1661, Kaspar Schott published his comprehensive textbook “Cursus mathematicus” in Würzburg for the first time, his “Encyclopedia of all mathematical sciences”. It was so successful that it was published again in 1674 and 1677. In its 28 books, Schott gave an introduction for beginners in 22 mathematical disciplines by means of 533 figures and numerous tables. He wanted to avoid the shortness and the unintelligibility of his predecessors Alsted and Hérigone. He cited or recommended far more than hundred authors, among them Protestants like Michael Stifel and Johannes Kepler, but also Catholics like Nicolaus Copernicus. The paper gives a survey of this work and explains especially interesting aspects: The dedication to the German emperor Leopold I., Athanasius Kircher’s letter of recommendation as well as Schott’s classification of sciences, explanations regarding geometry, astronomy, and algebra

Spinoza

"Spinoza", second edition. Encyclopedia entry for the Springer Encyclopedia of EM Phil and the Sciences, ed. D. Jalobeanu and C. T. Wolfe

The Combinatorics of Alternating Tangles: from theory to computerized enumeration

We study the enumeration of alternating links and tangles, considered up to topological (flype) equivalences. A weight $n$ is given to each connected component, and in particular the limit $n\to 0$ yields information about (alternating) knots. Using a finite renormalization scheme for an associated matrix model, we first reduce the task to that of enumerating planar tetravalent diagrams with two types of vertices (self-intersections and tangencies), where now the subtle issue of topological equivalences has been eliminated. The number of such diagrams with $p$ vertices scales as $12^p$ for $p\to\infty$. We next show how to efficiently enumerate these diagrams (in time $\sim 2.7^p$) by using a transfer matrix method. We give results for various generating functions up to 22 crossings. We then comment on their large-order asymptotic behavior.Comment: proceedings European Summer School St-Petersburg 200

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Logic in Early Modern Thought

Logical reflection in early modern philosophy (EMP) is marked by the instability of the period, although it is more lasting (the Port-Royal Logic was nevertheless used as a handbook in philosophy courses until the end of the nineteenth century). It started in the sixteenth century and ended in the nineteenth century, a period of 300 years during which there were deep transformations in the conceptions of authority and scientific method. For the history of twentieth-century philosophy, it was the period of “classical logic,” which lasted from the Renaissance to the linguistic turn conducted by Gottlob Frege. The period was used to be thought of as centuries of little or no original contribution to logic, in which conceptions of logic were tainted by rhetoric, epistemology, and psychologism in the worst sense (Kneale and Kneale 1962; Michael 1997). From the last decades of the twentieth century, however, scholars began to regard this period more accurately with respect to reflection and changes in logic and semantics. It has recently become a promising field for historical and conceptual research; today we can say that the legacy of early modern logical reformism has a philosophical, logical, and semantic value in itself

glossaLAB: Co-Creating Interdisciplinary Knowledge

The paper describes the glossaLAB international project as a contribution to confront the urgent need of knowledge integration frameworks, as required to face global challenges that overwhelm disciplinary knowledge capacity. Under this scope, glossaLAB is devised to make contributions in three main aspects of such endeavor: (i) development of a sound theoretical framework for the unification of knowledge, (ii) establishment of broadly accepted methodologies and tools to facilitate the integration of knowledge, (iii) development of assessment criteria for the qualification of interdisciplinarity undertakings. The paper discusses the main components of the project and the solutions adopted to achieve the intended objectives at three different levels: at the technical level, glossaLAB aims at developing a platform for knowledge integration based on the elucidation of concepts, metaphors, theories and problems, including a semantically- operative recompilation of valuable scattered encyclopedic contents devoted to two entangled transdisciplinary fields: the sciences of systems and information. At the theoretical level, the goal is reducing the redundancy of the conceptual system (defined in terms of “intensional performance” of the contents recompiled), and the elucidation of new concepts. Finally, at the meta-theoretical level, the project aims at assessing the knowledge integration achieved through the co-creation process based on (a) the diversity of the disciplines involved and (b) the integration properties of the conceptual network stablished through the elucidation process.2019-2

Getting nowhere fast: a teleological conception of socio-technical acceleration

It has been frequently recognized that the perceived acceleration of life that has been experienced from the Industrial Revolution onward is engendered, at least in part, by an understanding of speed as an end in itself. There is no equilibrium to be reached – no perfect speed – and as such, social processes are increasingly driven not by rational ends, but by an indeterminate demand for acceleration that both defines and restricts the decisional possibilities of actors. In Aristotelian terms, this is a final cause – i.e. a teleology – of speed: it is not a defined end-point, but rather, a purposive aim that predicates the emergence of possibilities. By tracing this notion of telos from its beginnings in ancient Greece, through the ur-empiricism of Francis Bacon, and then to our present epoch, this paper seeks to tentatively examine the way in which such a teleology can be theoretically divorced from the idea of historical progress, arguing that the former is premised upon an untenable ontological privileging of becoming