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[xmca] Is Mathematics _merely_ socially constructed, or is there something deeper and inevitable?

I think this deserves a new thread.  Let me try to draw out
and assemble the line of discussion that spun off from the
"a minus times a plus" thread.

In her inaugural post to xcma, Anna Sfard about talked "rules
of the mathematical game" among other things.

Then Jay Lemke said:-
> ...
> I think it's important, however, to see, as Anna emphasizes,
> that there is a certain "arbitrariness" involved in this, or
> if you like it better: a freedom of choice. Yes, it's
> structure-and-agency all over again! Structure determines that
> some things fit into bigger pictures and some don't, but
> agency is always at work deciding which pictures, which kind
> of fit, which structures, etc. And behind that values, and
> culture, and how we feel about things.

Then I (Ng Foo Keong) said:-

> regarding structure and agency, arbitrariness:-
> i think now it's time for me to pop this question that has been
> bugging me for some time.  i am convinced that mathematics is
> socially constructured, but i am not so convinced that mathematics
> is _merely_ socially constructured.  if we vary across cultures
> and different human activities, we might find different ways
> in which patterns and structure can be expressed and yet we might
> find commonalities / analogies.  the question i am asking is:
> is maths just a ball game determined by some group of nerds who
> happen to be in power and dominate the discourse, or is there some
> invariant, something deeper in maths that can transcend and unite
> language, culture, activity .... ?

Foo Keong,
NIE, Singapore

Then Ed Wall said:-

> Ng Foo Keong
> As regards your question about mathematics being socially
> constructed, I'm not entirely sure what you mean by
> mathematics or what kind of evidence would convince you it wasn't.
> Suppose I said that there was evidence for innate subtizing.
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