Philosophy and Geometry Theoretical and Historical Issues

Philosophy and Geometry Theoretical and Historical Issues / by L. Magnani.

Philosophers have studied geometry since ancient times. Geometrical knowledge has often played the role of a laboratory for the philosopher's conceptual experiments dedicated to the ideation of powerful theories of knowledge. Lorenzo Magnani's new book Philosophy and Geometry illustrates t...

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Bibliographic Details
Main Author: Magnani, L. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht : Springer Netherlands : Imprint: Springer, 2001.
Edition:1st ed. 2001.
Series:The Western Ontario Series in Philosophy of Science, A Series of Books in Philosophy of Science, Methodology, Epistemology, Logic, History of Science, and Related Fields, 66
Springer eBook Collection.
Subjects:
Philosophy and science.
History.
Geometry.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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. “History of geometry” and “elements” 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.

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