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Re: [xmca] In what sense(s) is mathematics a social construction.?
Hi, everyone.
Can I say something naive in three lines that will make any difference?
Let's see.
Platonic? What is Platonic after Godel proved "incompleteness"?
Here is a book by Lakoff/Nunez _Where Mathematics Comes From_ which
posits a mind in a body which has such things as symmetry and
development and ten fingers. Then the whole gestalt thing giving rise
to Polanyi and tacit knowledge - and Vygotsky's internalization...
To chime in on the most amazing and wonderful discussion I've seen in
eons,
so much depends on the starting point and how you build from there.
(Weren't many of us likely to be Euclidean in our early mathematical
habits?)
Well, we need something like a system,
even if we know it isn't THE system and never will be; otherwise we
have mush.
The trick is we all do really have systems and epistemologies and all
that,
we just don't know that we do, let alone how to talk about it
articulately (well some of us can).
We don't know what we know, and when someone comes up with 0 (zero),
gives a name to nothing - wow. Far exceeded my three lines.
Valerie Wilkinson
On 2009.May.1, at 01:02 PM, Andy Blunden wrote:
Fichte didn't have a problem with people even having different
epistemologies, let alone mathematical formalisms. According to
Fichte, people have a theory of knowledge according to the type of
person they want to be. But it was Hegel that really built that up
into a proper cultural psychology, rather than it being a matter of
personal choice.
Recognizing that there are many different mathematical theories is not
an -ism, it's just a fact.
Andy
Ng Foo Keong wrote:
Can Fichte account for the many different mathematical theories
that have emerged (re. my three examples) in human history?
What "-ism" do you call this?
F.K.
2009/5/1 Andy Blunden <ablunden@mira.net>:
No FK I am not a Platonist.
We cannot think of or describe nature other than through labour
processes of
some kind. But this does not imply that there are "nature's labour
processes" out there somewhere in a Kantian Jenseits, which we
mirror. It
simply means that we discover objective limits to our subjective
will and
this takes the form of activity which is both subjective and
objective. This
goes back to Fichte strangely enough.
Nominalism and Platonism are not the only choices.
Andy
Ng Foo Keong wrote:
so are you saying that the different forms / brands of maths
(small 'm') of different traditions/civilisations are just
human maps of _The_ Mathematics (big 'm')?
"The maps are not the territory", right?
is there a magic Book, Somewhere Up There, where we can download
all the maths that humans need, and maybe download instant
understanding of maths, so children (and adults) are spared
the pain of trying to work out their understanding of maths?
F.K.
2009/5/1 Andy Blunden <ablunden@mira.net>:
Eric,
the cosmos existed without humans and will exist after us. But we
invented
physics, and fairly recently at that. Physics (like mathes) is a
human
practice, practiced in a certain community of practice
(institutions,
procedures), using a certain range of artefacts (symbols, words,
apparatus).
That the material from which artefacts are made and the object of
hte
enquiry exists independently of human activity does not prove that
the
activity itself exists without humans.
*All* artefacts and forms of activity rest upon a natural world
which
exists
independently of us. Our practice is constrained by nature,
always, and
is
never in that sense capricious. I think I can fly ... but I still
come
crashing to the ground. Same with maths.
Andy
--
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Andy Blunden http://home.mira.net/~andy/
Hegel's Logic with a Foreword by Andy Blunden:
From Erythrós Press and Media <http://www.erythrospress.com/>.
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Andy Blunden http://home.mira.net/~andy/
Hegel's Logic with a Foreword by Andy Blunden:
From Erythrós Press and Media <http://www.erythrospress.com/>.
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Valerie A. Wilkinson, Ph.D.
Professor of Communication
Faculty of Information, Shizuoka University
3-5-1 Johoku, Hamamatsu, Japan 432-8011
http://www.ia.inf.shizuoka.ac.jp/~vwilk/
vwilk@inf.shizuoka.ac.jp
phone 81 (53) 478-1529
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