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What imagination is cannot be answered apart from understanding its conceptual topology, the articulated framework of basic phenomena and concepts that govern our thinking about it. The Platonic ontology of the good (as well as the forms) imaging itself in all levels of reality and the Aristotelian psychology based on the claim there is no thinking without images exercised their influence for nearly two millennia, though chiefly in distorted forms that undermined their conception of imagination as dynamic. The third step in our historical investigation examines the work of René Descartes (1596–1650), who was strongly influenced by this heritage in surprising ways (e.g., the practice of spiritual exercises). His early work developed a universal method for using figures and images, both mathematical and nonmathematical, for representing the degree of similarity of things to natural forms. On this basis he developed techniques for resolving all kinds of questions and problems. His invention of analytic geometry was the most rigorous form of using images ever conceived. Marked positions in geometric figures are symbolically incorporated into algebraic formulas; algebra, conceived as a matrix field, allows manipulations of elements that are mapped back exactly into the geometric field. The biplanar character of imagination first discovered by Plato—that things on one level of reality embody and can be used to display relations on another level, and vice versa—was thus incorporated into, and became the basis for, the dynamism of modern analytical mathematics.

DOI: 10.1007/978-94-007-6507-8_6

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