Philosophy and Geometry: Theoretical and Historical IssuesPhilosophers 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 the rich intrigue of this fascinating story of human knowledge, providing a new analysis of the ideas of many scholars (including Plato, Proclus, Kant, and Poincaré), and discussing conventionalist and neopositivist perspectives and the problem of the origins of geometry. The book also ties together the concerns of philosophers of science and cognitive scientists, showing, for example, the connections between geometrical reasoning and cognition as well as the results of recent logical and computational models of geometrical reasoning. All the topics are dealt with using a novel combination of both historical and contemporary perspectives. Philosophy and Geometry is a valuable contribution to the renaissance of research in the field. |
Contents
I | 1 |
II | 9 |
III | 11 |
IV | 15 |
V | 18 |
VI | 19 |
VII | 22 |
VIII | 27 |
XXXVI | 112 |
XXXVII | 114 |
XXXIX | 118 |
XL | 119 |
XLI | 123 |
XLII | 132 |
XLIV | 139 |
XLV | 148 |
IX | 29 |
X | 30 |
XI | 32 |
XII | 39 |
XIV | 47 |
XV | 54 |
XVI | 57 |
XVII | 59 |
XIX | 66 |
XX | 69 |
XXI | 70 |
XXIII | 73 |
XXIV | 78 |
XXV | 84 |
XXVI | 91 |
XXVII | 96 |
XXVIII | 97 |
XXIX | 99 |
XXXI | 100 |
XXXII | 105 |
XXXIII | 107 |
XXXIV | 108 |
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Common terms and phrases
abductive reasoning activity affirms analysis analytic angles applied apprehension axiomatic Axioms of Intuition body chapter cognitive computational concept considered constitutive conventional principles conventionalism deduction demonstrations diagrams discovery elements empirical epistemic epistemological etak Euclid Euclid's Elements Euclidean geometry Euclidean system example experience experimental explain extensive quantities external fact figure geometrical construction given heuristic Hintikka Husserl hypotheses illustrated imagination inference interpretation ISBN Kant Kant's Kantian kind logical Magnani manifold manipulative abduction mathematical means mediators metric model-based models Moreover nature non-Euclidean geometries ometry perception perspective Petitot phenomena philosophy physical objects Poincaré point of view possible postulate problem Proclus Proclus Diadochus proof properties propositions pure intuition reference Reichenbach representation represented role rule schematism scientific Sefirot sense sensible Socrates space spatial frameworks square structure synthesis synthetic a priori synthetic proposition tacit knowledge theorems theory tion Torretti trans transcendental triangle universal visual field