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Re: [xmca] a minus times a plus

On the nature of mathematics, you might find helpful E. Husserl's text "On the origin of geometry" and the commentaries that J. Derrida and M.Merleau-Ponty have published. I think the latter has a copy of the text in English, the original text was in German, published in an otherwise French journal. Cheers, Michael

On 29-Apr-09, at 9:22 AM, Ng Foo Keong wrote:

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

I think this deserves a new thread, but I couldn't manage to start one.
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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