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 Ed Wall wrote:
Actually, I was wondering just the opposite ofThe issue for me is why the Western civilization prioritizes (and then mathematizes) social relations described in the Arabic wisdom.If I look at a number of the intriguing 'rationalizations' Mike's question generated, I seem to see a tendency to, in a sense, almost anthropomorphize mathematics (hope that makes sense as I don't quite know what the right word is). Social relations don't give rise to mathematics, but mathematics seems to give, perspectivally, a rise to social relations. In fact the West goes a step further in prioritizing the digital over the analogue as your example shows. A number of people have taken this 'mathematizing' (which goes far beyond the problematic of double negations) up in recent years. I think recently of Michael Eldred and Stuart Eden (and, of corse, there is Heidegger and Lachterman among others) and Aristotle is very important in this regard as he is deals with similar questions as regards 'real' and mathematics. It is possibly worth wondering how the Arabs were contaminated by all this as they were a major transmitter of Greek mathematics to the West and elsewhere.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 a minus is a plus, I was thinking that it is a mathematical model of the Arabic wisdom that "an enemy of my enemy is my friend." Of course, the latter is notalways true -- we have plenty of examples when enemy of our enemy is stillour enemy (or just indifferent) and, thus, for these types of social relations, 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 (and thenmathematizes) social relations described in the Arabic wisdom. One answer isbecause "the real world" works according to these social relations (i.e., the social relations is just an example of the truth out there). An alternative explanation is that the Western civilization can afford and might be even benefit from imposing these social relations on "the real world" that by itself is indifferent to any social relations (and thus mathematical models). Any other explanations? What do you think? Eugene-----Original Message----- From: firstname.lastname@example.org [mailto:email@example.com] On Behalf Of Ng Foo Keong Sent: Wednesday, April 29, 2009 12:23 PM To: firstname.lastname@example.org; 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 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._______________________________________________ xmca mailing list email@example.com 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 virus signaturedatabase 4043 (20090429) __________ The message was checked by ESET NOD32 Antivirus. http://www.eset.com _______________________________________________ xmca mailing list firstname.lastname@example.org http://dss.ucsd.edu/mailman/listinfo/xmca_______________________________________________ xmca mailing list email@example.com http://dss.ucsd.edu/mailman/listinfo/xmca
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