Author | Magnani, Lorenzo. author |
---|---|
Title | Philosophy and Geometry [electronic resource] : Theoretical and Historical Issues / by Lorenzo Magnani |
Imprint | Dordrecht : Springer Netherlands, 2001 |
Connect to | http://dx.doi.org/10.1007/978-94-010-9622-5 |
Descript | XX, 256 p. online resource |
1 At the Origins of Geometrical Knowledge -- 1. Conceptual space, mental spatial models, latent geometry -- 2. Figures, symbols, and the Greek origins of geometry -- 3. The ritual origin of geometry -- 2 Geometry: the Model of Knowledge -- 1. Sensibility -- 2. Imagination -- 3. Understanding -- 4. Pure apprehension and geometry -- 5. Empirical apprehension and empirical schematism -- 6. Geometrical schemata and constructions: models of philosophy -- 7. Space as the object of geometry -- 3 Constructions, Logic, Categories -- 1. Space and logic -- 2. Intuition, construction, and the logic of singular terms -- 3. Pure and applied geometry -- 4. Why is geometry synthetic? -- 5. Categories and Axioms of Intuition -- 6. Mathematical schematism -- 4 The ???????? in Ancient Geometrical Knowledge -- 1. Geometry, drawing, and writing -- 2. Mathematical objects -- 3. Geometrical reasoning -- 4. The science that studies shapes: geometry -- 5. โHistory of geometryโ and โelementsโ of geometry -- 5 Geometry and Convention -- 1. Crude facts, relations, conventions -- 2. Pure and applied geometry -- 3. Sensible, geometric, and physical space -- 4. Geometrical intuition -- 5. Geometrical apriorism and empiricism -- 6. The genesis of geometry -- 7. The interchangeability of geometries -- 8. Withdrawing conventions -- 9. Withdrawing principles of coordination -- 6 Geometry, Problem Solving, Abduction -- 1. Geometrical constructions and problem solving -- 2. Model-based and manipulative abduction -- 3. Geometrical construction is a kind of manipulative abduction -- 4. Diagrams, abduction, and deductive reasoning -- 7 Geometry and Cognition -- 1. Geometry of visibles, protogeometry, manipulations -- 2. At the origins of geometrical knowledge II -- 3. Non-conceptual and spatial abilities -- 4. Computational geometrical constructions -- 5. Spatial imagery -- 6. Logical models of diagrammatic reasoning -- References -- Author Index