Recently, however, some philosophers have argued that, on the contrary, the development of non- Euclidean geometry has confirmed Kant's views, for since a demonstration of the consistency of non- Euclidean geometry depends on a demonstration of its equi-consistency with Euclidean geometry, one need only show that the axioms of Euclidean (. Kant's arguments for the synthetic a priori status of geometry are generally taken to have been refuted by the development of non- Euclidean geometries. It is argued that far from clinging to an outdated paradigm, programs based on new conceptions of intuition should be seen as motivated by important philosophical desiderata, such as the truth, apriority, distinctiveness and autonomy of mathematics. ) philosophical responses to these changes, focusing on the idea of modifying Kant’s conception of intuition in order to accommodate the increasing abstractness of mathematics. Mathematics seemed increasingly detached from experience as well as its form moreover, with advances in symbolic logic, mathematical inference also seemed independent of intuition. Similarly, advancements in algebra challenged the view that temporal intuition provides a foundation for both it and arithmetic. Non- Euclidean geometries challenged Kant’s view that there is a spatial intuition rich enough to yield the truth of Euclidean geometry. The mathematical developments of the 19th century seemed to undermine Kant’s philosophy.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |