Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Understanding ImaginationThe Dynamically Imaginative Cognition of Descartes

Understanding Imagination: The Dynamically Imaginative Cognition of Descartes [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Understanding ImaginationThe Dynamically Imaginative Cognition of Descartes

Download PDF
62 pages

Loading next page...
 
/lp/springer-journals/understanding-imagination-the-dynamically-imaginative-cognition-of-041T8O0Ubq

References (18)

Publisher
Springer Netherlands
Copyright
© Springer Science+Business Media Dordrecht 2013
ISBN
978-94-007-6506-1
Pages
267 –329
DOI
10.1007/978-94-007-6507-8_6
Publisher site
See Chapter on Publisher Site

Abstract

[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.]

Published: Apr 1, 2013

Keywords: Pineal Gland; Analytic Geometry; Mathematical Truth; Algebraic Formula; Primitive Notion

There are no references for this article.