[Xmca-l] Re: Objectivity of mathematics

[mike cole]

How about sending me the reviews.
Who was the editor at the time?
mike

On Fri, Nov 7, 2014 at 2:04 PM, Martin John Packer <mpacker@uniandes.edu.co>
wrote:

> 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
> >>>
> >>>
> >
> >
> >
>
>
>


-- 
It is the dilemma of psychology to deal with a natural science with an
object that creates history. Ernst Boesch.