Prolegomena to a cognitive investigation of Euclidean diagrammatic reasoning

Yacin Hamami
Vrije Universiteit Brussel
Euclidean diagrammatic reasoning refers to the diagrammatic inferential practice that originated in the geometrical proofs of Euclid’s Elements. A seminal philosophical analysis of this practice by Manders (‘The Euclidean diagram’, 2008) has revealed that a systematic method of reasoning underlies the use of diagrams in Euclid’s proofs, leading in turn to a logical analysis aiming to capture this method formally via proof systems. The central premise of this paper is that our understanding of Euclidean diagrammatic reasoning can be fruitfully advanced by confronting these logical and philosophical analyses with the field of cognitive science. Surprisingly, central aspects of the philosophical and logical analyses resonate in very natural ways with research topics in mathematical cognition, spatial cognition and the psychology of reasoning. The paper develops these connections, concentrating on four issues: (1) the cognitive origins of Euclidean diagrammatic reasoning, (2) the cognitive representations of spatial relations in Euclidean diagrams, (3) the nature of the cognitive processes and cognitive representations involved in Euclidean diagrammatic reasoning seen as a form of visuospatial relational reasoning and (4) the complexity of Euclidean diagrammatic reasoning for the human cognitive system. For each of these issues, our analysis generates concrete experiment proposals, opening thereby the way for further empirical investigations. The paper is thus a prolegomenon to a research program on Euclidean diagrammatic reasoning at the crossroads of logic, philosophy and cognitive science
Keywords Diagrammatic reasoning  Euclidean geometry  Mathematical cognition  Visuospatial relational reasoning  Categorical and coordinate spatial relations  Relational complexity
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DOI 10.1007/s10849-013-9182-8
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Perceptual Symbol Systems.Lawrence W. Barsalou - 1999 - Behavioral and Brain Sciences 22 (4):577-660.
Proofs, Pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.

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