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Between ‘reality’ and the ‘imaginary’ there is the intermediary world of graphical artifacts like writing, notations, diagrams, graphs and maps. What are the epistemological functions of these diagrammatical inscriptions, situated between language and the pictorial? The guiding hypothesis here is that the ‘diagrammatical’ provides a link between the perceptible and the rational, insofar as it not only bridges the gap between these two realms but also gives rise to the very possibility of differentiating between the ‘aisthetic’ and the ‘noethic’. Starting from a reflection on exemplary forms of diagrammatical reasoning in philosophy (Platon, Descartes, Wittgenstein) first steps in the direction of an ‘ epistemology of the line’ will be sketched: (i) Surface, lines, and points are the building elements of diagrammatic graphism. (ii) The diagrammatic space is not an ‘illustrative’ but an operative space within which eye, hand and mind work together: thus the ‘mind’s eye’ is born. (iii) Diagrammatical spatiality has a dual character: it is both a perceptible concrete surface and a rational abstract space. This duality is the dodge of the diagrammatical. (iv) In this dual character it functions as a means for visualizing the non visual and for ‘spatializing’ the non-spatial. Thus bringing theoretical entities to intuition. Placing the theme within a cultural perspective: Could the invention of inscribed surface perhaps have meant for the mobility and productivity of the mind what the invention of the wheel meant for the mobility and productivity of the human body?

‘The Mind’s Eye’: Visualizing the Non-visual and the ‘Epistemology of the Line’