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Thinking through drawing

Diagram constructions as epistemic mediators in geometrical discovery

Published online by Cambridge University Press:  30 July 2013

Lorenzo Magnani
Lorenzo Magnani*
Affiliation:
Department of Humanities, Philosophy Section, Computational Philosophy Laboratory, University of Pavia, Pavia, Italy; e-mail: [email protected]
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Abstract

The concept of manipulative abduction is devoted to capture the role of action in many interesting cognitive situations: action provides otherwise unavailable information that enables the agent to solve problems by starting and performing a suitable abductive process of generation or selection of hypotheses. We observe that many external things, usually inert from an epistemological point of view, can be transformed into epistemic mediators. I will present some details derived from the history of the discovery of the non-Euclidean geometries that illustrate the relationships between strategies for anomaly resolution and visual thinking. Geometrical diagrams are external representations that play both a mirror role (to externalize rough mental models) and an unveiling role (as gateways to imaginary entities). I describe them as epistemic mediators able to perform various explanatory, non-explanatory, and instrumental abductive tasks (discovery of new properties or new propositions/hypotheses, provision of suitable sequences of models as able to convincingly verifying theorems, etc.). I am also convinced that they can be exploited and studied in everyday non-mathematical applications also to the aim of promoting new trends in artificial intelligence modeling of various aspects of hypothetical reasoning: finding routes, road signs, buildings maps, for example, in connection with various zooming effects of spatial reasoning. I also think that the cognitive activities of optical, mirror, and unveiling diagrams can be studied in other areas of manipulative and model-based reasoning, such as the ones involving creative, analogical, and spatial inferences, both in science and everyday situations so that this can extend the epistemological, computational, and the psychological theory.

Type
Articles
Information
The Knowledge Engineering Review , Volume 28 , Special Issue 3: Visualization, Visual Representation and Reasoning , September 2013 , pp. 303 - 326
Copyright
Copyright © Cambridge University Press 2013 

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