D-III-1 Diagrams

Sybille Krämer, Jan Wöpking

Abstract


a) Topics and Objectives. This research group investigates the history and theory of thinking with the help of diagrams. Diagrams are conceived as cognitive instruments which exploit spatial relationships paradigmatically in order to represent, analyze, and generate knowledge. We use the term »diagram« in both a narrow and in an extended sense: defined more narrowly, diagrams are schematic figures such as geometric constructions or chemical structural formulae; defined in an extended sense, the term may also refer to texts, charts, mathematical formulae, in short: all types of inscriptions upon a delimited surface which display diagrammatical aspects. The guiding presuppositions of our research are: (1) by means of spatial logics and topological orders, diagrams are preferred forms for representing non-spatial, theoretical relationships.
(2) Diagrams do not display simple ›objects,‹ but instead relationships within a conceptual or knowledge field. (3) As a consequence, diagrams not only open up spaces of representation, but also experimental, explorative, and operational spaces, in many cases involving abstract, non-sensory, or ideational contents. Diagrams render theories susceptible to experience in sensory terms. (4) On the whole, the capacity for graphism may be ranged alongside the capacity for language as a universal anthropological trait. Against this horizon, our research project – whose orientation is epistemological and philosophical – pursues two problems. The first involves the basic contours of a general theory of diagrammatics and – starting from the ›cartographic impulse‹ embodied in Plato’s parable of the line and in Ptolemy’s »handbook of geography« – an ›epistemology of the line‹ as a philosophical reconstruction of the implicit and explicit diagrammatical aspects of philosophical texts. The second problem involves the diagram as a cognitive artifact which is examined from historical and systematic perspectives. b) Methods: Philosophical analysis of texts, case studies of individual thinkers and specific types of diagrams. c) Current state of the discussion within the research group: Basic concepts related to diagrammatics have been elaborated, central episodes in the Occidental theory of the diagram identified and analyzed, and central elements of a general theory of diagrammatic cognition developed. Planned for the future is on the one hand deepened work on historical case studies, and on the other the integration of the hitherto developed modules into a consistent, overarching theory.


Keywords: Diagrammatics • Knowledge Production • Plato • Oresme, Galileo • Aristotle • Geometry • Physics


Keywords


Diagrammatics; Knowledge Production; Plato; Oresme; Galileo; Aristotle; Geometry; Physics



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eTopoi. Journal for Ancient Studies (ISSN 2192-2608)