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

Well David, I think it does put a question mark over any simplistic understanding of "the material" though I think "domination" is not an appropriate word to use in connection with the constraints implicit nature, which are after all equally the conditions of freedom. There could no freedom if nature which was not subject to regularity.

But what is nature-constrained in mathematics is not just the utility of application. I think I was wrong to rely on that idea. Beyond utilitarian constraints, maths is not arbitrary. For example, Goedel's theorem is a theorem not an arbitrary declaration, and absolutely nothing of the kind of "material substrate" envisioned as underlying physics is entailed in the proof.


David H Kirshner wrote:
Oh, Andy, you're such an ontological realist!

Physics, as a science, is bound by the constraints of a material substrate. Although math often is inspired by scientific concerns, often it isn't. Even when it is, being inspired by science isn't the same as being bound by material constraints. As was mentioned earlier in this thread*, mathematics has a fascinating role in shaping our perceptions, not just in representing or codifying them. This seems to orient us intellectually beyond the domination of the material.

*The lovely contrast of social construction of mathematics with mathematical construction of the social.
-----Original Message-----
From: xmca-bounces@weber.ucsd.edu [mailto:xmca-bounces@weber.ucsd.edu] On Behalf Of Andy Blunden
Sent: Thursday, April 30, 2009 8:24 PM
Cc: eXtended Mind, Culture, Activity
Subject: Re: [xmca] In what sense(s) is mathematics a social construction.?

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.


ERIC.RAMBERG@spps.org wrote:
Thought I would throw my hat into the ring on this one. When discussing 9 minus negative 2 we are looking at negative 2 as being the opposite of 2. So in essence we are adding the opposite. Now, if we look at negative 2 multiplied by negative we have two opposites of 2. Working with opposites of negative numbers we move into the positive. Number lines are helpful but when I illustrate these I use an accounting ledger and show how piles of chips move back and forth across the ledger line. Really enjoying the discussion.

My opinion is that the rules of math exist without humans and it is merely something humans of discoverd. Soundwaves exist without humans our ears merely discover them.


	*Andy Blunden <ablunden@mira.net>*
Sent by: xmca-bounces@weber.ucsd.edu

04/29/2009 11:59 PM
Please respond to ablunden; Please respond to "eXtended Mind, Culture, Activity"

To: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu> cc: Subject: Re: [xmca] In what sense(s) is mathematics a social construction.?

I am not familiar with all of these theories FK, but let's
keep it in the "public domain": If someone had decided that
a minus times a minus was a plus, then they could do that,
but such an arithmetic would have had little practical use,
and sooner or later, most likely sooner, someone would have
discovered something (say "negus") which looked very much
like a minus in every way except when negus is times by
itself it gave a plus. And then everyone would have been
learning about negus in school and Mike's granddaughter
would be asking him why negus times negus = plus.

Famously of course, Riemann discovered his mathematics
before Einstein found a use for it, otherwise it may still
be rotting in the back room of some library. Does someone
(Jay?) know how Einstein found Riemann's paper?

On a side note, a lot of people calling on various metaphors
to justify -x-=+ have never addressed the question a kid
might ask as to why the example given doesn't prove that a -
when **added* to a - gives a +. I certainly had kids
confront me with that one. It is very easy to skate over the
hidden equation of multiplication with intersection and
compounding and so on which to a lot of non-mathematicians
looks much more like addition. The link between these
operations is obviously NOT arbitrary, is it? But nor is it


Ng Foo Keong wrote:
 > 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

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/>.

xmca mailing list