Euclides ab omni naevo vindicatus

The issue is obscured by the fact that the word `space' can be used in four different ways. It can be used, first, as a term of pure mathematics, as when mathematicians talk of an `n-dimensional phase-space', an `n-dimensional vector-space', a `three-dimensional projective space' or a `twodimensional Riemannian space'. In this sense the word `space' means the totality of the abstract entities-the `points'-implicitly defined by the axioms. There is no doubt that there exist, iii this sense, non-Euclidean spaces, because all that is claimed by such an assertion is that sets of non-Euclidean axioms constitute possible implicit definitions of abstract entities, that is to say that some sets of non-Euclidean axioms are consistent. If Kant or any other philosopher had denied this, he would have been wrong; but Kant himself took care not to deny it, 2 and there is little reason to suppose that any philosopher concerned about space has been using the word in this, the pure mathematician's, sense
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/bjps/20.1.1
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,530
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Contemporary Arguments for a Geometry of Visual Experience.Phillip John Meadows - 2011 - European Journal of Philosophy 19 (3):408-430.
Poincaré's Conventionalism of Applied Geometry.F. P. O'Gorman - 1977 - Studies in History and Philosophy of Science Part A 8 (4):303-340.
Comments: Reality and Time.J. R. Lucas - 1997 - International Studies in the Philosophy of Science 11 (1):97 – 108.

Add more citations

Similar books and articles
Thomas Reid and Non-Euclidean Geometry.Amit Hagar - 2002 - Reid Studies 5 (2):54-64.
Wave Function Ontology.Bradley Monton - 2002 - Synthese 130 (2):265 - 277.
Life in Configuration Space.Peter J. Lewis - 2004 - British Journal for the Philosophy of Science 55 (4):713-729.
Quinus Ab Omni Naevo Vindicatus.John P. Burgess - 1998 - In Ali A. Kazmi (ed.), Meaning and Reference. University of Calgary Press. pp. 25--66.
Two Spaces Looking for a Geometer.Giorgio Parisi - 2003 - Bulletin of Symbolic Logic 9 (2):181-196.
Added to PP index

Total downloads
268 ( #13,345 of 2,210,880 )

Recent downloads (6 months)
4 ( #115,657 of 2,210,880 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature