On 3/30/2013 9:38 PM, Shmuel (Seymour J.) Metz wrote: > In <D8OdnVFB9IWK6MvMnZ2dnUVZ_rSdnZ2d@giganews.com>, on 03/30/2013 > at 12:15 AM, fom <fomJUNK@nyms.net> said: > >> If one wishes to argue that "real" space is curved >> but that the curvature is so slight as to be negligible, > > That would be Physics rather than Mathematics. >
Which accounts for the scare quotes in my statements.
>> If the sensible impressions relate to each other in the Euclidean >> sense, that is precisely Kant's thesis. > > <http://en.wikipedia.org/wiki/Geometry#Geometry_beyond_Euclid>: > > "Immanuel Kant argued that there is only one, absolute, geometry, > which is known to be true a priori by an inner faculty of mind: > Euclidean geometry was synthetic a priori." > > <http://en.wikipedia.org/wiki/Non-Euclidean_geometry#Importance>: > > "The philosopher Immanuel Kant's treatment of human knowledge had a > special role for geometry. It was his prime example of synthetic a > priori knowledge; not derived from the senses nor deduced through > logic - our knowledge of space was a truth that we were born with." > > That doesn't sound like a pragmatic appeal to observation. >
Both of these excerpts refer to "truth" which is a semantical concept. Kant's concerns were epistemological. In
you can find a more complete discussion of the complexities involved with interpreting Kant.
But, when words like "absolute" are used to describe Kant's position, it is almost clearly by someone who has not read "Critique of Pure Reason". The following is excerpted from the web link:
Kant consistently writes in the Critique of ideality and reality in the more familiar modern sense, where mind-dependence is at issue. Kant's usage serves to shift the philosophical discussion concerning space from a focus on relationalism and absolutism to one on idealism and realism. Hence when he reflects on the Newtonian and Leibnizian conceptions of space and time in general terms in the Transcendental Aesthetic, he eschews a discussion of the relative merits of absolutism and relationalism in favor of discussing the common mistake of his predecessors. For instance, after outlining his conception of space and time, Kant claims: ?Those, however, who assert the absolute reality [absolute Realität] of space and time, whether they take it to be subsisting or only inhering, must themselves come into conflict with the principles [Principien] of experience? (A39/B56). The former group, also called ?the mathematical investigators of nature,? is clearly identified with the Newtonians, and the latter, the ?metaphysicians of nature,? with the Leibnizians (cf. Shabel 2005, 31, 45-9). So transcendental idealism is articulated as a kind of replacement for the Leibnizian and Newtonian conceptions of space and time, but it is not their status as relationalist and absolutist conceptions, respectively, that calls for their replacement. Rather, it is their status as representatives of a separate and overarching conception of space, a conception according to which space (like time) is said to bear an ?absolute reality.?