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Additional resources for Chauvenet's treatise on elementary geometry
163). So, despite considering time to be a pure intuition and, hence, a form of synthetic a priori judgment, Kant suggests its ‘general’ condition constitutes a relationship between internal and external sense-intuitions. However, ultimately, Kant’s insistence upon the formal limits of space and time prevents a strong genetic or discursive continuity in this relationship from being fully established; for example, in the following passage from the section, ‘Elucidation on Time’, the formal definition of limit which differentiates space and time is clearly visible: Time and space are accordingly two sources of cognition, from which different synthetic cognitions can be drawn a priori, of which especially pure mathematics in regard to the conditions of space and its relations provides a splendid example.
Space, then, can be similar and incongruent, whether it is derived from both an Drawing Figures 19 extended body or from the unextended principles of absolute space, and ‘inner differences’ are founded upon the different positions within an entity; for example, the different positions of the right and left hands, which are also related to absolute space. Yet, in absolute space their ‘true differences’ are determined by the specific constitution of the body. So absolute space is not constructed externally of our sensory perception, but is a ‘fundamental concept’, which grounds any outer perception which we might have (CDS, p.
So, in contrast to scientific understandings of space and geometry in which the ‘technical’ procedure is separated from the ‘aesthetic’ act, this discussion suggests that Kant’s reflective judgment sustains the link. 14 Geometric spaces therefore become embodied in the powers of reasoning, aesthetic judgment and the actions of the imagination, and are transformed into the mental, sensory and bodily actions of the subject. Moreover, these powers represent embodied forms of indeterminate geometric and spatiotemporal intuition.
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