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These files are maintained strictly for historical reference, research, and recordkeeping purposes,
and the content has not been altered or updated since archiving.
Content on this site may not meet current digital accessibility standards.
If you require an alternative, accessible format of any information found on this site,
please contact Bruce Jones, bjones@ucsd.edu to request an accommodation.
just to throw some spanners in the works to Andy's comments:- Consider (1) the non-Riemannian Geometries (vs Riemannian Geometries), (2) "non-Standard" Analysis (vs Standard Analysis), (3) Henstock/Daniell integration (vs Lebesgue integration) theory. seems like there is still some sense of 'arbitrariness' leading to different mathematicses (sic) instead of one universal mathematics ... !? no? F.K. 2009/4/30 Andy Blunden <ablunden@mira.net>: > Ed, > I have fretted over this question of whether mathematics is a science of > something objective (if so what) or is 'just' a social construction ever > since I studied Goedel's famous proof 43 years ago. Answers to this question > tend to tell us more about the speaker than the problem I think. But my > current thought would be this: > > All the natural sciences have an object which exists independently of human > thought and activity, but all the sciences also create concepts and > artefacts and forms of activity which are peculiar to human life. THis is as > true of mathematics as it is of physics and chemistry. > > This does not contradict the fact that mathematics is a social construction. > It is a social construction twice over inasmuch as its objects are already > artefacts which are themselves tools. But that in no way leads to any kind > of arbitrariness in its conclusions and discoveries (as opposed to > inventions). But the artefacts we create in order to explore this trange > domain of Nature are artefacts, and as someone earlier said, the element of > agency persists. Newton and Leibniz's simultaneous discovery (sic) and > formulation of the Calculus kind of proves this. > > Andy _______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca