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[Xmca-l] Re: Objectivity of mathematics
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.
[mailto:firstname.lastname@example.org] 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
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).
On Nov 7, 2014, at 6:50 AM, anna sfard <email@example.com> 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...
> -----Original Message-----
> From: firstname.lastname@example.org
> [mailto:email@example.com] On Behalf Of Martin John
> 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
> On Nov 7, 2014, at 5:57 AM, anna sfard <firstname.lastname@example.org> wrote:
>> Hi Huw,
>> Thanks for your thoughts. I agree with much of what you say. I would
> 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".
> 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...
>> -----Original Message-----
>> From: email@example.com
>> [mailto:firstname.lastname@example.org] 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
> 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
> 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
> 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
>> I don't think these issues conflict with your account, but perhaps
> quite a bit that is skimmed over (such as the bit about individualized
> discourse, perhaps).
>> I enjoyed your paper. :)