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**Kant on geometry and experience.**
*(English)*
Zbl 1336.00107

De Risi, Vincenzo (ed.), Mathematizing space. The objects of geometry from antiquity to the early modern age. Collected essays based on the presentations at the conference on space, geometry and the imagination from antiquity to the early modern age, Berlin, Germany, August 27–29, 2012. Cham: Birkhäuser/Springer (ISBN 978-3-319-12101-7/hbk; 978-3-319-12102-4/ebook). Trends in the History of Science, 275-309 (2015).

The author provides a close examination of I.Kant’s theory of space as related to geometry and experience. From a modern point of view there is a sharp distinction between a mathematical, perceptual and physical space. If one insists that conflating this distinction can be regarded as a fundamental error in Kant’s theory, we are inclined to deny the “the possibility of what he calls synthetic a priori of knowledge of the empirical around us” (p.275). From a historical point of view, the author argues, one has to remind, however, that the contemporary conception “evolved in explicit reaction to Kant” (p.276). The author investigates in a close reading of Kritik der reinen Vernunft (Critique of pure reason) and related work Kant’s considerations on the relation between the mathematical notion of space and perception. His primary aim is “to explain in detail exactly how, for Kant, purely intellectual concepts – and, indeed, the pure intellect itself – are realized or instantiated in geometrical space, and exactly how, as a result, they then make our experience of nature possible” (p.306).

For the entire collection see [Zbl 1309.01004].

For the entire collection see [Zbl 1309.01004].

Reviewer: Volker Peckhaus (Paderborn)

### MSC:

00A30 | Philosophy of mathematics |

01A50 | History of mathematics in the 18th century |

03A05 | Philosophical and critical aspects of logic and foundations |

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\textit{M. Friedman}, in: Mathematizing space. The objects of geometry from antiquity to the early modern age. Collected essays based on the presentations at the conference on space, geometry and the imagination from antiquity to the early modern age, Berlin, Germany, August 27--29, 2012. Cham: Birkhäuser/Springer. 275--309 (2015; Zbl 1336.00107)

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