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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: lmagnani@unipv.it
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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.

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Articles
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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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