Pasch entre Klein et Peano
Empirisme Et Idéalité en Géométrie
Bibliographic Data
| ID | 3889288 |
|---|---|
| Authors | Sébastien Gandon (Université Clermont Auvergne, corresponding author) |
| Year | 2005 |
| Volume | 44 |
| Issue | 4 |
| Pages | 653-692 |
| Publication date | 2005-01-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Dialogue (JOURNAL) |
| Journal identifiers | ISSN: 0012-2173 • E-ISSN: 1759-0949 |
| Publisher | Cambridge University Press (CUP) (PUBLISHER) |
| DOI | 10.1017/s0012217300000032 |
| OpenAlex | W2108585451 |
| Language | EN |
| Citations received | 1 |
| References cited | 14 |
Pasch is usually credited with having presented the first axiomatization of a geometrical theory, but theVorlesungen über neuere Geometrie (1882)contains many features which do not fit the Hilbertian paradigm. Thus Pasch, while axiomatizing his"elementary geometry,"claims that it is an empirically true theory. Scholars usually regard the discrepancies between Pasch and the post-Hilbertian standard method as mere inconsistencies of Pasch's theory. On the contrary, this article aims at reconstructing the coherence and originality of theVorlesungen.We will first display the historical background of this work and then try to reconcile Pasch's logical axiomatic claim with his empiricist stance. More importantly, we will insist on the remarkable logical procedures worked out by Pasch in order to adapt his mathematical development to the strictures of his broad philosophical position
Algorithm · Axiom · Axiomatic system · Calculus (dental) · Epistemology · Geometry · Humanities · Peano axioms · History and Theory of Mathematics · Mathematics · Mathematics and Applications · Medicine · Philosophy · Philosophy, Science, and History
| Unique citing works | 1 |
|---|---|
| Citations per year | 0,25 |
| Citation span | 2022 - 2022 (1) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 1 |