The Philosophy of Lines by Thorsten Botz-Bornstein

Author:Thorsten Botz-Bornstein
Language: eng
Format: epub
ISBN: 9783030653439
Publisher: Springer International Publishing

The Line as Cognition: Fichte

But let us first move back a century, and see what the situation was like just before non-Euclidean geometry emerged, that is, before Gauss, Bolyai, and Lobachevsky. Through Euclid, space had become abstract and homogenous, and thus all-penetrating. Philosophers of the late eighteenth century would expand this model by rethinking the connection between being and geometry. Compared to Descartes, the focus was now more on cognition. The idealist German philosopher Johan Gottlieb Fichte attempted to explain all human action in terms of geometry and found that even human thinking could only be conceived of as taking place in space. This idea would much later have some impact on Bergson. In his New Exposition of the Science of Knowledge (Darstellung der Wissenschaftslehre aus dem Jahre 1801), Fichte depicts action as a point, and the whole as a point extended to infinity. The single point is “a point in absolute emptiness, wherein it grasps and penetrates itself,” and the whole is “a point extended to infinite separability, and yet remaining a point.” More precisely, the point for Fichte is a “living and self-luminous form of line-drawing. In a line, the point is everywhere, for the line has no breadth. In a line, manifoldness is everywhere for no part of the line can be regarded as a point, but only as a line in itself, as an infinite separability of points.”2

A year earlier, Fichte had rather lengthily explained, in his The Vocation of Man, why the line model should be converted into a general model of cognition. It is a kind of Euclidean cognitive science. The following conversation between the author and a “spirit” (Geist) is supposed to make this clear:

Spirit: But what shape then is assumed, not by thy produced, but by thy inherited, knowledge, of which all specific thought is but the revival and farther definition?—How does this present itself to thee? Under what image does it appear?

I: Evidently as something in which one may draw lines and make points in all directions, namely, as space.3

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