The curious neglect of geometry in modern philosophies of mathematics

Shahshahani, S ; Sharif University of Technology | 2021

21 Viewed
  1. Type of Document: Article
  2. DOI: 10.1007/978-3-030-53654-1_14
  3. Publisher: Springer Science and Business Media B.V , 2021
  4. Abstract:
  5. From ancient times to 19th century geometry symbolized the essence of mathematical thinking and method, but modern philosophy of mathematics seems to have marginalized the philosophical status of geometry. The roots of this transformation will be sought in the ascendance of logical foundations in place of intuitive primacy as the cornerstone of mathematical certainty in the late 19th century. Nevertheless, geometry and geometrical thinking, in multiple manifestations, have continued to occupy a central place in the practice of mathematics proper. We argue that this, together with advances in the neuroscience of mathematical processes, calls for an expansion of the present limited remit of the philosophy of mathematics. © 2021, Springer Nature Switzerland AG
  6. Keywords:
  7. Geometry ; Ontology ; Arithmetization ; Riemann ; Manifold ; Set ; Arithmetic
  8. Source: Logic, Epistemology, and the Unity of Science ; Volume 49 , 2021 , Pages 379-389 ; 22149775 (ISSN)
  9. URL: https://link.springer.com/chapter/10.1007/978-3-030-53654-1_14