NDLI: Prolegomena to a Cognitive Investigation of Euclidean Diagrammatic Reasoning

Content Provider	Springer Nature Link
Author	Hamami, Yacin Mumma, John
Copyright Year	2014
Abstract	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.
Starting Page	421
Ending Page	448
Page Count	28
File Format	PDF
ISSN	09258531
Journal	Journal of Logic, Language and Information
Volume Number	22
Issue Number	4
e-ISSN	15729583
Language	English
Publisher	Springer Netherlands
Publisher Date	2014-02-09
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Diagrammatic reasoning Euclidean geometry Mathematical cognition Visuospatial relational reasoning Categorical and coordinate spatial relations Relational complexity Logic Semantics Information Systems Applications (incl. Internet)
Content Type	Text
Resource Type	Article
Subject	Philosophy Computer Science Linguistics and Language

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