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*To*: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Subject*: [Xmca-l] Re: Objectivity of mathematics*From*: Martin John Packer <mpacker@uniandes.edu.co>*Date*: Fri, 7 Nov 2014 22:04:54 +0000*Accept-language*: es-CO, en-US*In-reply-to*: <00b201cffa88$f03a1bb0$d0ae5310$@net.il>*List-archive*: <https://mailman.ucsd.edu/mailman/private/xmca-l>*List-help*: <mailto:xmca-l-request@mailman.ucsd.edu?subject=help>*List-id*: "eXtended Mind, Culture, Activity" <xmca-l.mailman.ucsd.edu>*List-post*: <mailto:xmca-l@mailman.ucsd.edu>*List-subscribe*: <https://mailman.ucsd.edu/mailman/listinfo/xmca-l>, <mailto:xmca-l-request@mailman.ucsd.edu?subject=subscribe>*List-unsubscribe*: <https://mailman.ucsd.edu/mailman/listinfo/xmca-l>, <mailto:xmca-l-request@mailman.ucsd.edu?subject=unsubscribe>*References*: <CAGVMwbUV9Jdf2XpAshWE0dCNcT1kHRTrpxGy=Ci2M3xR9N3rhQ@mail.gmail.com> <9A0CD8DC-7A92-4561-A550-EF5900B9B1CE@umich.edu> <CAGVMwbUcnDxvMbpfha4QVHKtU6mi+igRvxZhzFFj8hyynkDiwg@mail.gmail.com> <5883D78B-B4BC-4EB7-987E-06C3C2D22EB1@umich.edu> <CAGVMwbVugt4Mqh_jLosUdHNyRmg19dEaULa7weLj8y7jHSXn6g@mail.gmail.com> <5451DB76.7010007@mira.net> <CAGVMwbWSmg+0X=VvUQMojAtX911Hg6jmfYqkx3a2EoTjCq2OxA@mail.gmail.com> <54520634.9080302@mira.net> <CD06F23C-D0F7-4169-AB99-E025679FDA4A@umich.edu> <5452C9B0.70505@mira.net> <32EF9A39-CDDA-4258-BBDE-7D7658C85A03@umich.edu> <5455DA75.9040906@mira.net> <8EB7C6A3-BA03-469A-A2A5-94274633BE10@umich.edu> <CAHCnM0CGp_qJU5mVEt0ieiK8r-A7qvg0N=5-Fd5eqjOkaTqWqA@mail.gmail.com> <54585A04.8020708@mira.net> <AE980414-2565-49C5-881F-C1A33995A1D6@umich.edu> <3B024BCD-D68E-474C-A83A-35864F9C3027@gmail.com> <00ac01cff988$5b8fe860$12afb920$@netvision.net.il> <CAG1MBOFphRCuiDqhJMU34UZRcVPEzbCG-im91b2dxJuEesbBCA@mail.gmail.com> <006101cffa79$8f551b60$adff5220$@net.il> <9DD4F91DCF90@uniandes.edu.co> <006901cffa81$183a41b0$48aec510$@net.il> <2939B2A3-72DC-43BB-9E3E-E5B23CC9A482@uniandes.edu.co> <00b201cffa88$f03a1bb0$d0ae5310$@net.il>*Reply-to*: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Sender*: <xmca-l-bounces+comm-xmca=mail.ucsd.edu@mailman.ucsd.edu>*Thread-index*: AQHP+obQ7P9Bw4z1/0C1X+h1y8KLtQ==*Thread-topic*: [Xmca-l] Objectivity of mathematics

Of course what would be nice is getting it published! ;) On Nov 7, 2014, at 7:47 AM, anna sfard <sfard@netvision.net.il> wrote: > Salam/shalom, Martin, > > You said it better than I did (some 15 years ago). Thanks! > > Your paper on fractions is very relevant to the study currently being done > by one of my young colleagues (a.k.a. students). Don't be surprised if she > writes to you one of these days. > > anna > > > > -----Original Message----- > From: xmca-l-bounces@mailman.ucsd.edu > [mailto:xmca-l-bounces@mailman.ucsd.edu] On Behalf Of Martin John Packer > Sent: Friday, November 07, 2014 2:32 PM > To: eXtended Mind, Culture, Activity > Subject: [Xmca-l] Re: Objectivity of mathematics > > Hola Anna, > > Well, here's our summary of your position at the time. Did we get it right? > > Sfard (1998) also gives an account of mathematics that can be > called postmodern. She recounts how the search for the elusive referents of > mathematical discourse motivated reconceptualizations of this relationship - > the move from realism to constructivism, and then the abandonment of the > classic dichotomy of symbol/referent in favor of interactionist views of > symbols and meaning, such as the semiotics of Saussure and Peirce. Sfard > builds on "Foucault's central claim that the objects 'referred to' by > symbols, far from being primary to signs and speech acts, are an added value > (or the emergent phenomenon) of the discursive activity. This is > particularly true for the evanescent objects of mathematics" (p. 14). The > "central theme" of her paper is "[t]he process through which the objects > 'represented' by the symbols come into being retroactively" (p. 15). She > suggests that discourse about mathematical referents is "Virtual Reality > discourse" rather than "Actual Reality discourse," a metaphor that "conveys > a message as to the particular rights and obligations the mathematical > discourse confers upon the participants.... Those who really wish to > communicate, not being able to help themselves with their senses, have to > use all their mental faculties in an attempt to reconstruct for themselves > the realm within which the moves of their interloctors make sense" (p. 2). > The task that faces us when we seek to understand mathematics, as she sees > it, "consists of not - or no longer - treating discourses as groups of signs > (signifying elements referring to contents or representations) but as > practices that systematically form the objects of which they speak" > (Foucault, 1969/1992, p. 40, emphasis added by Sfard). > > Martin > > On Nov 7, 2014, at 6:50 AM, anna sfard <sfard@netvision.net.il> wrote: > >> Ahoy Martin, >> >> How nice: so Rotman, Lachterman and the writer of these lines are >> mathematical figures? Positive or negative? :-) >> >> And while all the other folks you mention indeed view discourse as the >> heart of mathematics, I view it as more than that. Indeed, not just >> the heart - discourse includes all the other parts as well. In >> mathematical symbols, mathematics = [special kind of] discourse (and >> this is what Huw regards as reductionism, perhaps because he equates > discourse with languaging?). >> >> Must reread your paper. It's been awhile... >> >> anna >> >> -----Original Message----- >> From: xmca-l-bounces@mailman.ucsd.edu >> [mailto:xmca-l-bounces@mailman.ucsd.edu] On Behalf Of Martin John >> Packer >> Sent: Friday, November 07, 2014 1:29 PM >> To: eXtended Mind, Culture, Activity >> Subject: [Xmca-l] Re: Objectivity of mathematics >> >> Huw & Anna, >> >> I had forgotten, until I read the paper again, that Jenny and I based >> our analysis of the fractions class on three main figures: Rotman, >> Lachterman, and Sfard! All three see discourse at the heart of > mathematics. >> >> Martin >> >> >> On Nov 7, 2014, at 5:57 AM, anna sfard <sfard@netvision.net.il> wrote: >> >>> Hi Huw, >>> >>> Thanks for your thoughts. I agree with much of what you say. I would >>> like >> to know more, though, about why you think that if you talked about >> problem solving in discursive terms, "you'd quickly end up with >> linguists reducing it to wording, and various kinds of >> "acquisitionists" thinking that this is where you're going." I do >> think about these processes in discursive terms and feel, on the >> contrary, that this is what guards me against objectification and > acquisitionism. So why? >>> >>> And on this occasion, to the other debate, the one about "objective". >>> If >> you assume the discursive stance, this word becomes an oxymoron. >> Objective, as I understand it, means "mind independent", bound have a >> given form independently of one's tastes, values and judgments. But >> this adjective >> ("objective") refers to narratives, to what people say/think ("facts" >> are subcategory of narratives). So... >>> >>> anna >>> >>> -----Original Message----- >>> From: xmca-l-bounces@mailman.ucsd.edu >>> [mailto:xmca-l-bounces@mailman.ucsd.edu] On Behalf Of Huw Lloyd >>> Sent: Friday, November 07, 2014 3:24 AM >>> To: eXtended Mind, Culture, Activity >>> Subject: [Xmca-l] Re: Objectivity of mathematics >>> >>> Hi Anna, >>> >>> Perhaps you could also assert that quantitative choices, predicated >>> upon >> social commitments, offer a means to go beyond those tentative bonds >> formed in numerical rituals. >>> >>> Commitments, such as commitment to a task that makes it a problem, >>> seem to >> be important. Also, it seems to me that problem solving (mental >> searching >> etc) is something that should have a first class status in a theory >> about mathematics. The problem I'd have with referring to these >> processes as discourse is that I think you'd quickly end up with >> linguists reducing it to wording, and various kinds of >> "acquisitionists" thinking that this is where you're going. >>> >>> A second problem, for me, with fusing communication and cognition is >>> the >> distinct role that communication has in mediating actions, rather than >> comprising the fabric of actions. For me, the act of exercising that >> fabric, whether mentally or in relation to a present object, induces >> transformations. >>> >>> I don't think these issues conflict with your account, but perhaps >>> there's >> quite a bit that is skimmed over (such as the bit about individualized >> discourse, perhaps). >>> >>> I enjoyed your paper. :) >>> >>> Best, >>> Huw >>> >>> > > >

**Follow-Ups**:**[Xmca-l] Re: Objectivity of mathematics***From:*mike cole <mcole@ucsd.edu>

**References**:**[Xmca-l] Re: Apologies***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Objectivity of mathematics***From:*Andy Blunden <ablunden@mira.net>

**[Xmca-l] Re: Objectivity of mathematics***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Re: Objectivity of mathematics***From:*mike cole <mcole@ucsd.edu>

**[Xmca-l] Re: Objectivity of mathematics***From:*Andy Blunden <ablunden@mira.net>

**[Xmca-l] Re: Objectivity of mathematics***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Re: Objectivity of mathematics***From:*HENRY SHONERD <hshonerd@gmail.com>

**[Xmca-l] Re: Objectivity of mathematics***From:*anna sfard <sfard@netvision.net.il>

**[Xmca-l] Re: Objectivity of mathematics***From:*Huw Lloyd <huw.softdesigns@gmail.com>

**[Xmca-l] Re: Objectivity of mathematics***From:*anna sfard <sfard@netvision.net.il>

**[Xmca-l] Re: Objectivity of mathematics***From:*anna sfard <sfard@netvision.net.il>

**[Xmca-l] Re: Objectivity of mathematics***From:*Martin John Packer <mpacker@uniandes.edu.co>

**[Xmca-l] Re: Objectivity of mathematics***From:*anna sfard <sfard@netvision.net.il>

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