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*To*: ablunden@mira.net, "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Subject*: Re: [xmca] In what sense(s) is mathematics a social construction.?*From*: Ed Wall <ewall@umich.edu>*Date*: Wed, 29 Apr 2009 22:41:05 -0400*Cc*:*Delivered-to*: xmca@weber.ucsd.edu*Domainkey-signature*: a=rsa-sha1; s=2007001; d=ucsd.edu; c=simple; q=dns; b=gbuybK3Jdi0KDz2sPkK4CNqtYo5B4PsFiByrvPSSHj/3gi+0wuNCkh9FYIS3X8Lse PfdvQqhDRwcknAsrQ5d7w==*In-reply-to*: <49F90605.1040504@mira.net>*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> <2C46D7A7-AD94-441C-AABD-269045835E3D@umich.edu> <0193A85F-03A7-4811-B912-217722A5770B@uvic.ca> <BDD722EC-3E52-48C1-829B-AD5053D51B78@umich.edu> <2B2B3D4D-462E-4654-8457-A1C4F21B2874@uvic.ca> <49F7DE9B.5050908@mira.net> <14a6419f0904290031g79f0f6aagaaaf6e9a906005b2@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>*Reply-to*: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Sender*: xmca-bounces@weber.ucsd.edu

Andy

Ed On Apr 29, 2009, at 9:59 PM, Andy Blunden wrote:

Ed,I have fretted over this question of whether mathematics is ascience of something objective (if so what) or is 'just' a socialconstruction ever since I studied Goedel's famous proof 43 yearsago. Answers to this question tend to tell us more about the speakerthan the problem I think. But my current thought would be this:All the natural sciences have an object which exists independentlyof human thought and activity, but all the sciences also createconcepts and artefacts and forms of activity which are peculiar tohuman life. THis is as true of mathematics as it is of physics andchemistry.This does not contradict the fact that mathematics is a socialconstruction. It is a social construction twice over inasmuch as itsobjects are already artefacts which are themselves tools. But thatin no way leads to any kind of arbitrariness in its conclusions anddiscoveries (as opposed to inventions). But the artefacts we createin order to explore this trange domain of Nature are artefacts, andas someone earlier said, the element of agency persists. Newton andLeibniz's simultaneous discovery (sic) and formulation of theCalculus kind of proves this.Andy Ed Wall wrote:Actually, I was wondering just the opposite ofThe issue for me is why the Western civilization prioritizes (andthenmathematizes) social relations described in the Arabic wisdom.If I look at a number of the intriguing 'rationalizations' Mike'squestion generated, I seem to see a tendency to, in a sense, almostanthropomorphize mathematics (hope that makes sense as I don'tquite know what the right word is). Social relations don't giverise to mathematics, but mathematics seems to give, perspectivally,a rise to social relations. In fact the West goes a step furtherin prioritizing the digital over the analogue as your exampleshows. A number of people have taken this 'mathematizing' (whichgoes far beyond the problematic of double negations) up in recentyears. I think recently of Michael Eldred and Stuart Eden (and, ofcorse, there is Heidegger and Lachterman among others) andAristotle is very important in this regard as he is deals withsimilar questions as regards 'real' and mathematics. It is possiblyworth wondering how the Arabs were contaminated by all this as theywere a major transmitter of Greek mathematics to the West andelsewhere.Ed Wall On Apr 29, 2009, at 4:44 PM, Eugene Matusov wrote:Dear everybody--In response to Mike's profound inquiry of why a minus times aminus is aplus, I was thinking that it is a mathematical model of the Arabicwisdomthat "an enemy of my enemy is my friend." Of course, the latter isnotalways true -- we have plenty of examples when enemy of our enemyis stillour enemy (or just indifferent) and, thus, for these types of socialrelations, the mathematical model of (-1) x (-1) =1 does not work.Justconsider, for an example, the relations among the US, Al-Qaida,and SaddamHussein.The issue for me is why the Western civilization prioritizes (andthenmathematizes) social relations described in the Arabic wisdom. Oneanswer isbecause "the real world" works according to these social relations(i.e.,the social relations is just an example of the truth out there). Analternative explanation is that the Western civilization canafford andmight be even benefit from imposing these social relations on "therealworld" that by itself is indifferent to any social relations (andthusmathematical models). Any other explanations? What do you think? Eugene-----Original Message-----From: xmca-bounces@weber.ucsd.edu [mailto:xmca-bounces@weber.ucsd.edu]On Behalf Of Ng Foo Keong Sent: Wednesday, April 29, 2009 12:23 PM To: ablunden@mira.net; eXtended Mind, Culture, Activity Subject: Re: [xmca] a minus times a plus Is Mathematics _merely_ socially constructed, or is there something deeper and inevitable?I think this deserves a new thread, but I couldn't manage tostart one.Let me try to draw out and assemble the line of discussion thatspunoff 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._______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca __________ Information from ESET NOD32 Antivirus, version of virus signature database 4043 (20090429) __________ The message was checked by ESET NOD32 Antivirus. http://www.eset.com__________ Information from ESET NOD32 Antivirus, version of virussignaturedatabase 4043 (20090429) __________ The message was checked by ESET NOD32 Antivirus. http://www.eset.com _______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca_______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca-- ------------------------------------------------------------------------ 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 xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca

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**References**:**[xmca] a minus times a plus***From:*Mike Cole <lchcmike@gmail.com>

**Re: [xmca] a minus times a plus***From:*Ed Wall <ewall@umich.edu>

**Re: [xmca] a minus times a plus***From:*Wolff-Michael Roth <mroth@uvic.ca>

**Re: [xmca] a minus times a plus***From:*Ed Wall <ewall@umich.edu>

**Re: [xmca] a minus times a plus***From:*Wolff-Michael Roth <mroth@uvic.ca>

**Re: [xmca] a minus times a plus***From:*Andy Blunden <ablunden@mira.net>

**Re: [xmca] a minus times a plus***From:*Ng Foo Keong <lefouque@gmail.com>

**Re: [xmca] a minus times a plus***From:*Andy Blunden <ablunden@mira.net>

**Re: [xmca] a minus times a plus***From:*Ng Foo Keong <lefouque@gmail.com>

**Re: [xmca] a minus times a plus***From:*Ng Foo Keong <lefouque@gmail.com>

**RE: [xmca] a minus times a plus***From:*"Eugene Matusov" <ematusov@UDel.Edu>

**Re: [xmca] a minus times a plus***From:*Ed Wall <ewall@umich.edu>

**[xmca] In what sense(s) is mathematics a social construction.?***From:*Andy Blunden <ablunden@mira.net>

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