This is one of a group of essays (collected in this issue of the journal) about methodological considerations that have arisen for the project on the “Sanskrit knowledge systems on the eve of colonialism.” For the history of the exact sciences in Sanskrit, or Jyotiḥśāstra, in the early modern period, there are special problems. These have to do with the historically anomalous status of the exact sciences among the śāstras or Sanskrit knowledge systems, and with the predominantly “internalist” method by (...) which most recent research on Jyotiḥśāstra has been carried out. The essay considers the usefulness for tackling these problems of recent writing elsewhere in the history and philosophy of science, especially the work of Hacking. (shrink)

Eine Reihe von mittelalterlichen Schriften zur Landmessung (vom 9. islamischen Jahrhundert bis zu Fibonacci und Pacioli) enthält eine besondere Art von „algebraischen” Aufgaben. Darin werden z.B. die Summe der Fläche und einer oder alle vier Seiten eines Quadrates beschrieben und nach der Seite gefragt. Es zeigt sich erstens, daß dieser Aufgabentyp mindestens seit dem frühesten 2. vorchristlichen Jahrtausend von geometrischen Praktikern tradiert wurde, und zweitens, daß er die Entwicklung einer „Algebra” in der altbabylonischen Schreiberschule inspirierte. Der Aufsatz untersucht, in welcher (...) Weise die Überführung der „sub-wissenschaftlichen” Praktikertradition in einen systematischen Schulunterricht den mathematischen Inhalt und den Denkstil künftiger Praktiker präge. Im letzten Kapitel wird diskutiert, inwieweit es sinnvoll ist, innerhalb dieser Schulalgebra von „Schulen” zu sprechen. (shrink)

This article deals with the social production of knowledge in the exact sciences. After defining the term ?exact science?, it delineates the broad dynamic of its history. It, then, offers a socio-economic historical explanation of why the production of knowledge has become a major industry, if not the largest industry, in the last hundred years. The article concludes by drawing a detailed blueprint of the components, mechanisms, and specificities of the knowledge industry.

Tarski’s conceptual analysis of the notion of logical consequence is one of the pinnacles of the process of defining the metamathematical foundations of mathematics in the tradition of his predecessors Euclid, Frege, Russell and Hilbert, and his contemporaries Carnap, Gödel, Gentzen and Turing. However, he also notes that in defining the concept of consequence “efforts were made to adhere to the common usage of the language of every day life.” This paper addresses the issue of what relationship Tarski’s analysis, and (...) Béziau’s further generalization of it in universal logic, have to reasoning in the everyday lives of ordinary people from the cognitive processes of children through to those of specialists in the empirical and deductive sciences. It surveys a selection of relevant research in a range of disciplines providing theoretical and empirical studies of human reasoning, discusses the value of adopting a universal logic perspective, answers the questions posed in the call for this special issue, and suggests some specific research challenges. (shrink)

The Science Museum, London, has recently acquired four fragments of a portable sundial with associated calendrical gearing. All the fragments are made of low zinc brass of substantially the same composition. The sundial is of a type known in other examples, some the products of recent archaeological excavations and all dated to the Late Antique or Early Byzantine period. Dating by the place names included in the latitude table, by the style of the heads of the planetary gods used to (...) identify the days of the week, and by the style of the script, all indicate that the instrument dates from the late fifth century of the Christian era or the first half of the sixth.The gearing, of which two arbors survive, carrying four toothed wheels and one ratchet, seems to have resembled that of a calendrical device described by al-Bīrūnī in about AD 1000. Like al-Bīrūnī's device and the geared calendar associated with a Persian astrolabe of AD 1221/2 now in the Museum of the History of Science, Oxford, the Byzantine instrument displayed the shape of the Moon and its age in days. Probably the calendar further resembled its Islamic counterparts in also displaying the positions of Sun and Moon in the Zodiac.The emergence of Byzantine mathematical gearing indicates that the Hellenistic tradition attested by the Antikythera machine continued to be active in the Byzantine period, and suggests that it may have influenced the Islamic tradition. Once again an artefact has shown up the inadequacy of the evidence derived from literary sources. (shrink)