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Re: [xmca] In what sense(s) is mathematics a social construction.?

just to throw some spanners in the works to Andy's comments:-

(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?


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
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