The Foundations of Geometry and the Concept of Motion
Helmholtz and Poincaré
Bibliographic Data
| ID | 4516101 |
|---|---|
| Authors | Gerhard Heinzmann (Archives Henri-Poincaré - Philosophie et Recherches sur les Sciences et les Technologies, corresponding author) |
| Year | 2001 |
| Volume | 14 |
| Issue | 3 |
| Pages | 457-470 |
| Publication date | 2001-09-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Science in Context (JOURNAL) |
| Journal identifiers | ISSN: 0269-8897 • E-ISSN: 1474-0664 |
| Publisher | Cambridge University Press (CUP) (PUBLISHER) |
| DOI | 10.1017/s0269889701000163 |
| OpenAlex | W2105812188 |
| Language | EN |
| Citations received | 4 |
ArgumentAccording to Hermann von Helmholtz, free mobility of bodies seemed to be an essential condition of geometry. This free mobility can be interpreted either as matter of fact, as a convention, or as a precondition making measurements in geometry possible. Since Henri Poincaré defined conventions as principles guided by experience, the question arises in which sense experiential data can serve as the basis for the constitution of geometry. Helmholtz considered muscular activity to be the basis on which the form of space could be construed. Yet, due to the problem of illusion inherent in the subject's self-assessment of muscular activity, this solution yielded new difficulties, in that if the manifold is abstracted from rigid bodies which serve as empirical justification of the geometrical notion of space, then illusionary bodies will produce fictive manifolds. The present article is meant to disentangle these difficulties
Argument (complex analysis · Basis (linear algebra · Classical mechanics · Constitution · Epistemology · Geometry · Helmholtz free energy · Motion (physics · Physics · Political science · Action Observation and Synchronization · Law · Mathematics · Motor Control and Adaptation · Philosophical and Theoretical Analysis · Philosophy
| Unique citing works | 4 |
|---|---|
| Citations per year | 0,21 |
| Citation span | 2007 - 2024 (18) |
| Citation velocity | recent |
| Highly cited | No |
| Citation types | Neutral: 4 |