[Xmca-l] Re: Objectivity of mathematics

[Martin John Packer]

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
>>> 
>>> 
> 
> 
>