ABSTRACT
This chapter argues that Charles Sanders Peirce’s conception of a diagram is fundamentally and inseparably both conceptual and spatial insofar as reasoning by diagrams engages the continuum of spatial extension in the reasoning process. The perception of icons and diagrams in mathematics is found to be linked with human spatial reasoning more generally. Benjamin Peirce’s “pictures on the imagination” become, in the context of Charles’s later semiotics, icons, geometric images, and diagrams in the imagination. Peirce’s concept of a diagram is fundamentally and inseparably both a cognitive and spatial notion. Peirce often notes that the action of the mind in thought is best captured by iconic images and diagrams, and not by words. Peirce leaves open, by omission, that Topical Geometry is concerned with spatial quality. The essence of topical geometry is the interrelationship between ourselves and our mathematical entities. The practice of mathematics directs our attention to these interrelationships.
