Husserl and Jacob Klein
Bibliographic Data
| ID | 3970533 |
|---|---|
| Authors | Burt C Hopkins (0000-0001-8709-641X, Seattle University, corresponding author) |
| Year | 2016 |
| Volume | 21 |
| Issue | 5-6 |
| Pages | 535-555 |
| Publication date | 2016-08-17 |
| Open Access | No |
| Type | ARTICLE |
| Venue | The European Legacy (JOURNAL) |
| Journal identifiers | ISSN: 1084-8770 • E-ISSN: 1470-1316 |
| Publisher | Informa UK Limited (PUBLISHER • GB) |
| DOI | 10.1080/10848770.2016.1173480 |
| OpenAlex | W2338231175 |
| Language | EN |
| Citations received | 2 |
| References cited | 2 |
The article explores the relationship between the philosopher and historian of mathematics Jacob Klein’s account of the transformation of the concept of number coincident with the invention of algebra , together with Husserl’s early investigations of the origin of the concept of number and his late account of the Galilean impulse to mathematize nature. Klein’s research is shown to present the historical context for Husserl’s twin failures in the Philosophy of Arithmetic: to provide a psychological foundation for the proper concept of number (Anzahl), and to show how this concept of number functions as the mathematical foundation of universal (symbolic) arithmetic. This context establishes that Husserl’s failures are ultimately rooted in the historical transformation of number documented in Klein’s research, from its premodern meaning as the unity of a multitude of determinate objects to its modern meaning as a symbolic representation with no immediate relation to a concrete multiplicity. The argument is advanced that one significant result of bringing together Klein’s and Husserl’s thought on these issues is the need to fine-tune Husserl’s project in The Crisis of European Sciences and Transcendental Phenomenology of de-sedimenting the mathematization of nature. Specifically, Klein’s research shows that “a ‘sedimented’ understanding of numbers” “is superposed upon the first stratum of ‘sedimented’ geometrical ‘evidences’” uncovered by Husserl’s fragmentary analyses of geometry in the Crisis. In addition then to the task of “the intentional-historical reactivation of the origin of geometry,” recognized by Husserl as intrinsic to the reactivation of the origin of mathematical physics, Klein discloses a second task, that of “the reactivation” of the “complicated network of sedimented significances” that “underlies the ‘arithmetical’ understanding of geometry.”
Epistemology · Foundations of mathematics · Psychoanalysis · The Symbolic · Transcendental number · Phenomenology and Existential Philosophy · Philosophical and Theoretical Analysis · Philosophy · Philosophy and Historical Thought · Psychology
| Citations per year | 0.5 |
|---|---|
| Citation span | 2022 - 2022 (1) |
| Highly cited | No |