ONT Manifolds of Sensuous Impressions
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
MSI. Note 1
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| 11. On the Hypotheses Which Lie at the Basis of Geometry
|
| On June 10, 1854, Bernhard Riemann delivered his probationary lecture
| as a candidate for an unpaid lectureship at Göttingen. The title of the
| paper was "Ueber die Hypothesen welche der Geometrie zu Grunde Liegen".
| It is reported that the lecture won enthusiastic praise from Gauss and
| after its publication in 1867 it won similar praise throughout the
| mathematical world. One of the first to appreciate its importance
| was the English mathematician and friend of the Peirce family,
| William Kingdon Clifford. A first-rate mathematician himself,
| Clifford recognized the great importance of Riemann's lecture
| and in 1873 he translated it into English. It is quite probable
| that Clifford's praise of Riemann's work influenced Peirce's judgment
| of it. Concerning him, Peirce wrote, "Bernhard Riemann is recognized
| by all mathematicians as 'the' highest authority upon the philosophy
| of geometry". Since Peirce's views on the foundations of geometry
| are based on Riemann's, we must examine the latter's theory in
| some detail. (MGM, p. 219).
|
| Murray G. Murphey,
|'The Development of Peirce's Philosophy',
| first published, Harvard University Press, Cambridge, MA, 1961.
| reprinted, Hackett Publishing Company, Indianapolis, IN, 1993.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o