A brill - noether theory for k-gonal nodal curves by Ballico E.

By Ballico E.

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CoJ, p. 388)13 In this passage, the pure science of geometry is transformed into practical action, which results from the imagination’s ability to produce sensible forms of experience, independently of the understanding. Here, therefore, geometry is transformed from a pure theoretical reason (idea) into a series of actions, instruments or enactments which constitute the different forms of ‘practical’ or applied geometric methods. Importantly, it is the imagination’s powers that provide the conduit for this passage, from the ‘pure’ geometric relations to the technical acts of artistic production, so that each is brought into harmony with the other, and which establishes heterogeneity in geometric thinking.

Kant’s investigations into the productive imagination also continue beyond the third Critique; for example, it is explored in some depth in the later text, the Anthropology from a Pragmatic Point of View (1798). , perceptions, notions or projections) that are in harmony with a ‘higher level’ of cognition. Thus, the Anthropology studies the structure of sensibility, the senses and the imagination in the individual, in a way that we will see is implied in the imagination’s production of reflective judgment in the Critique of Judgment.

Kant therefore defines it as an ‘AESTHETIC judgment of reflection’ (CoJ, p. 409). Thus, the relationship between the subject and the world is brought about in the act of making aesthetic judgments in the First Introduction of the Critique, so that the procedures which might previously have been defined as deterministic knowledge become understood as aesthetic acts. As a result, scientific or technical procedures, such as geometry, are understood as ‘technical’ forms of aesthetic activity, and spatial and geometric judgments are defined in terms of their ability to express the powers of the sensing reflective subject, and his 22 Space, Geometry and Aesthetics or her experiences in the world, not as formal concepts or general ideas.

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