[Xmca-l] Re: Objectivity of mathematics

[Andy Blunden]

Activity Theory and Discourse Theory both have chequered histories, but 
if fully developed both can arrive at the same place. I think the 
Japanese martial arts people probably have a saying similar to that. 
Vygotsky's article circulated earlier, hints at this. I prefer Activity 
Theory, but only on condition that it is developed to the point where it 
matches what Discourse Theory can tell us.
My only objection is to claims that maths (for example) is *only* a 
discourse, that is, that there is no "outside" to discourse. The same 
would go for Activity.
Thus the subject line for this thread.
Andy
------------------------------------------------------------------------
*Andy Blunden*
http://home.pacific.net.au/~andy/


Huw Lloyd wrote:
> Hi Anna,
>
> I think with that clarification about how you're referring to discourse the
> point may be put more simply.  That is, that memories derived from
> non-discursive actions contribute towards thinking and these memories are
> not discursive (although they could be made to be discursive in a limited
> manner).
>
> For me, the distinction between when something is or isn't discursive isn't
> a big deal.  But if you're presenting a sense of mathematical competence
> upon discourse, then it becomes more important to demonstrate that
> discourse offers a sufficient explanation.  Personally, I would see
> discourse as a plane, and the kinds of mathematical knowledge being
> referred to as often traversing through that plane.  That would mean that
> discourse contributes to specific links in that genetic development, but
> that discourse was not the source of that genesis, but that, however, the
> social situations established through discourse may promote such
> development and that interesting event that are non-discursive may be
> reported discursively.  Those circumstances could give the illusion that it
> was all happening discursively.
>
> Best,
> Huw
>
>
>
> On 7 November 2014 17:01, anna sfard <sfard@netvision.net.il> wrote:
>
>   
>> Hi Huw,
>>
>>
>>
>> You say:
>>
>>
>>
>> Well, I think I pointed to the source of the issue with respect to the
>> fabric of actions.  If you say that the entirety of actions are discursive,
>> rather than mediated by discursive means, that's fine.  But it means you're
>> introducing phenomena typically inaccessible to the analysis of discourse
>> into this terminology.  Actions communicate, but they also interact with
>> the world of objects.
>>
>>
>>
>> I didn't mean to say that "the entirety of actions are discursive", this
>> would be strange. There are non-discursive actions, of course. Sometimes,
>> they may be mediate by discourses. But it is important to remember that
>> discourses are not just talking – there is also gesturing, drawing etc. But
>> including those in discourse (communication) does not mean putting there
>> "phenomena inaccessible to analysis within this terminology". I think your
>> tacit assumption was that discourse is exclusively a language thing, and
>> can thus be analyzed only with the methods used by linguists?
>>
>>
>>
>> You also say:
>>
>>
>>
>> Particular important points with respect to competence include notions of
>> independently solving tasks.  You can call that an inner discourse, but
>> note that in a developed form there may not actually be any internal
>> discourse but rather simply a memory, a knowing about consequences of a
>> considered action and what is required.  And this memory is not only
>> derived from participants but from our interactions with objects -- things
>> going on beneath the stratum of communication.  The use of discourse can be
>> a rather coarse medium.  A toddler learning to put a jumper on does not do
>> it through talking, though talking may help organise it a little.
>>
>>
>>
>> Is there a contradiction between the claims "this person is recalling
>> things" and "this person is involved in a discourse (communication with
>> herself)"? I don’t think so. Recall may be not (always) the kind of inner
>> discourse the teacher would like to see, but it is a discourse
>> nevertheless. Learning to walk or dress, in itself, is not discursive, so
>> it doesn't belong to the debate what is and what is not inner discourse
>> (thinking). By the way, we may do this learning of walking or dressing a
>> bit more "discursive" by talking or gesturing to the kid, thus giving her
>> advice.
>>
>>
>>
>> You say:
>>
>>
>>
>> Re reductionism.  I think its often the case that people will reduce
>> whenever there is opportunity to.  I don't know whether the adjective
>> "acquisitionist" applies, though I do know of one mathematics professor
>> communicating some rather negative gestures about mathematics as
>> communication.  Personally, I thought that was rather interesting, because
>> the wide use of one of this professor's books helped me to realise that
>> there was a problem with generalisation in the way mathematics is taught.
>>
>>
>>
>> Hmmm, I don't know what to say. I'm afraid I'm not clear enough about what
>> you meant.
>>
>>
>>
>> But anyway, this is helpful, so thanks, Huw. Hope my response is helpful
>> too J
>>
>>
>>
>> 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 5:57 PM
>> To: eXtended Mind, Culture, Activity
>> Subject: [Xmca-l] Re: Objectivity of mathematics
>>
>>
>>
>> Hi Anna,
>>
>>
>>
>> Well, I think I pointed to the source of the issue with respect to the
>> fabric of actions.  If you say that the entirety of actions are discursive,
>> rather than mediated by discursive means, that's fine.  But it means you're
>> introducing phenomena typically inaccessible to the analysis of discourse
>> into this terminology.  Actions communicate, but they also interact with
>> the world of objects.
>>
>>
>>
>> Particular important points with respect to competence include notions of
>> independently solving tasks.  You can call that an inner discourse, but
>> note that in a developed form there may not actually be any internal
>> discourse but rather simply a memory, a knowing about consequences of a
>> considered action and what is required.  And this memory is not only
>> derived from participants but from our interactions with objects -- things
>> going on beneath the stratum of communication.  The use of discourse can be
>> a rather coarse medium.  A toddler learning to put a jumper on does not do
>> it through talking, though talking may help organise it a little.
>>
>>
>>
>> Re reductionism.  I think its often the case that people will reduce
>> whenever there is opportunity to.  I don't know whether the adjective
>> "acquisitionist" applies, though I do know of one mathematics professor
>> communicating some rather negative gestures about mathematics as
>> communication.  Personally, I thought that was rather interesting, because
>> the wide use of one of this professor's books helped me to realise that
>> there was a problem with generalisation in the way mathematics is taught.
>>
>> As far as I can tell, if you spell out the details of "internalised
>> discourse" then I expect you won't get the same kind of reaction...
>>
>>
>>
>> Is that any clearer?
>>
>>
>>
>> Best,
>>
>> Huw
>>
>>
>>
>>
>>
>>
>>
>> On 7 November 2014 10:57, anna sfard < <mailto:sfard@netvision.net.il>
>> 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:  <mailto:xmca-l-bounces@mailman.ucsd.edu>
>>>       
>> xmca-l-bounces@mailman.ucsd.edu [mailto:
>>
>>     
>>>  <mailto:xmca-l-bounces@mailman.ucsd.edu>
>>>       
>> 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
>>>       
>>> On 6 November 2014 06:10, anna sfard < <mailto:sfard@netvision.net.il>
>>>       
>> sfard@netvision.net.il> wrote:
>>
>>     
>>>> Hi,
>>>>         
>>>> I have not been aware of this super-interesting (for me) thread, and
>>>>         
>>>> now, when I eventually noticed  it, I cannot chime in properly. So I
>>>>         
>>>> am doing this improperly, simply by attaching my own paper. Those
>>>>         
>>>> who are interested enough to open the attachment will see the
>>>>         
>>>> relevance of its theme to the present conversation. And although I
>>>>         
>>>> mention Davydov only in an endnote, he is very much present. The
>>>>         
>>>> theses I'm arguing for seem to substantiate his request for taking
>>>>         
>>>> the quantitative discourse, rather than the numerical, as a point of
>>>>         
>>>> departure for the process of  developing child's mathematical
>>>>         
>>>> thinking (we cannot help it, but in our society, these two
>>>>         
>>>> discourses appear in the child's life separately and more or less in
>>>>         
>>>> parallel, with the quantitative discourse free from numbers and the
>>>>         
>>>> numerical one innocent of any connection to quantities; at a certain
>>>>         
>>>> point, these two discourses coalescence, thus giving rise to the
>>>>         
>>>> incipient mathematical discourse; but at the pre-mathematical stage,
>>>>         
>>>> quantitative discourse is meaningful to the child on its own, as it
>>>>         
>>>> supports the activity of
>>>>         
>>> choosing, whereas numerical discourse is but a way to bond with
>>>       
>> grownups).
>>
>>     
>>>> anna
>>>>         
>>
>>
>>     
>
>