Designing interaction
The psychology of proof: deductive reasoning in human thinking
The psychology of proof: deductive reasoning in human thinking
Image and brain: the resolution of the imagery debate
Image and brain: the resolution of the imagery debate
Vision: A Computational Investigation into the Human Representation and Processing of Visual Information
Neuroanatomical Correlates of Human Reasoning
Journal of Cognitive Neuroscience
Journal of Cognitive Neuroscience
Fmri evidence for a three-stage model of deductive reasoning
Journal of Cognitive Neuroscience
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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.