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*To*: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Subject*: Re: [xmca] In what sense(s) is mathematics a social construction.?*From*: Jay Lemke <jaylemke@umich.edu>*Date*: Fri, 1 May 2009 18:39:03 +0200*Delivered-to*: xmca@weber.ucsd.edu*Domainkey-signature*: a=rsa-sha1; s=2007001; d=ucsd.edu; c=simple; q=dns; b=ZDcU6ROJ5GVuUqnIpNyD6FU/TGAnJLIzwMG3yp39Zd5qHavAMv/7xu+vkk9V4ipvm igqXc1ZrDYxgdKEzJeTtQ==*In-reply-to*: <14a6419f0904301003q3926218t6d13cbb59bd8c76@mail.gmail.com>*List-archive*: <http://dss.ucsd.edu/mailman/private/xmca>*List-help*: <mailto:xmca-request@weber.ucsd.edu?subject=help>*List-id*: "eXtended Mind, Culture, Activity" <xmca.weber.ucsd.edu>*List-post*: <mailto:xmca@weber.ucsd.edu>*List-subscribe*: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:xmca-request@weber.ucsd.edu?subject=subscribe>*List-unsubscribe*: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:xmca-request@weber.ucsd.edu?subject=unsubscribe>*References*: <30364f990904271547o5b4df21eifca69bf8318483f2@mail.gmail.com> <49F8060B.6070401@mira.net> <14a6419f0904290117q6c0e8432xf78fe6d1b3e9012b@mail.gmail.com> <14a6419f0904290922h34790b99o3d43d176dba1ce9d@mail.gmail.com> <00a101c9c90b$55341670$ff9c4350$@edu> <FB3532C8-20AA-431C-9492-696F44337D75@umich.edu> <49F90605.1040504@mira.net> <14a6419f0904292135p72c22aadic29ca0de30818459@mail.gmail.com> <49F93025.80908@mira.net> <001701c9c9a7$0a81cd10$6501a8c0@atticus> <14a6419f0904301003q3926218t6d13cbb59bd8c76@mail.gmail.com>*Reply-to*: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Sender*: xmca-bounces@weber.ucsd.edu

JAY. Jay Lemke Professor Educational Studies University of Michigan Ann Arbor, MI 48109 www.umich.edu/~jaylemke On Apr 30, 2009, at 7:03 PM, Ng Foo Keong wrote:

the reason why I brought up this topic is that i have been brought up (indoctrinated?) with a Platonic view of mathematics, a view held by a majority of mathematicians. however, while studying learning-sciences and maths education, i encounter post-modernist views including social constructivism, which gave me the cognitive dissonance that i felt i need to get off my chest. so i analysed the issue into two parts:- (P) "if humans exist, then they create mathematics" (C) "if mathematics exists, then it must have been created by humans" I am definitely convinced about (P), but not so sure about (C), the converse of (P). reading literature trying to convince me of (C) by citing examples of (P) is not going to cut it. prior to coming to xmca i did not find many knowledgable people to discuss/debate this with, so I began debating with myself. Like Andy, I'm still very much tainted with the Platonic view, although as an educator I recognise the need for different learners to make personal sense of maths and share their understandings socially. i find the pointer to Derrida's phenomenological "différAnce" (why must he invent such a new bombastic word?) analysis and "deconstruction" interesting, although if i were Derrida, i would have invented the word "égalEte" (the other way round from Derrida, using an analysis of equitable equalities to study deferring differences, much like algebraic topologists using homotopy to distinguish a doughnut from a figure of '8'). the reason i brought up my three examples viz. (1) the non-Riemannian geometries (vs Riemannian Geometry) [i meant non-Euclidean, but it doesn't matter. Euclidean geometry was historically discovered/invented first. Riemannian is just one of the "alternatives". if Riemannian had come first, then Euclidean might have been named as one of the "alternatives". ] (2) "non-Standard" Analysis (vs Standard Analysis, the dorminant brand of higher calculus, thanks to Cauchy and other French mathematicians), (3) Henstock/Daniell integration (vs Lebesgue integration, the dominant brand of modern integration theory)is to consider the other side of the argument (i.e. against anobjectivemathematics). Mathematics can be thought of as a game with certain rules (like Jay Lemke hinted). Different rules have different consequences. Just like American football, soccer ("football") and vs basketball. What is allowed in one ball game (e.g. using your feet to handle the ball) is not allowed in another. All socially constructed. People happen agree to play by those rules. [BTW, logicians/mathematicians working at the foundations of mathematics explore set theory with and without Axiom of Choice. others advocate using Category Theory as a foundation for all mathematics.] So, it seems there are no "right" or "wrong" rules. Different rules, different games. What is wrong (if any) with this counter-argument? F.K.p/s: I have transfered Andy's side note for discussion in the otherthread.From: "Andy Blunden" <ablunden@mira.net>To: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu> Sent: Wednesday, April 29, 2009 10:59 PMSubject: Re: [xmca] In what sense(s) is mathematics a socialconstruction.?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 obvious, Andy_______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca

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