[Xmca-l] Re: Objectivity of mathematics

[Julian Williams]

Dear all

I'm struggling to keep up here... Surely I didn't hear Andy Blunden say that 'objectivity' implies stuff that can't be transformed? I'm sure I must have misremembered that!.?

My feeble understanding of activity is that it involves transformations of (material and other) objects... In order to meet collective and individual human needs. 

Ok, Marx says such activity also thereby generates new human needs...

Mathemattics is being confrnted, criticised and transformed all the time ?  I hope this includes being critically subjected to practice, where it might be confronted by some objective, even material facts and 'firstness' (even the CIA found they could not walk through walls) or thirdnesses ( the naive practices of infants who claim that 7 and4 makes 10 sometimes... And surely they are right).

In particular, the Maths involved in early years may be confronted with the objective social practice of measurement ( Davydov)... This provides an objective basis for mathematics, which when symbolised in discursive forms ensures a degree of objectivity (not just social convention) for mathematics discourse itself.

Thus, the objectivity of the rules of mathematics (as with logic) rest ultimately on the validity of the social practices that ensure maths a wider validity, beyond the conventions of the clique of mathematicians who run the discipline. Thus the discipline is itself disciplined.

 Vygotsky cites Lenin re Hegels logic:

".. The practical activity of man had to lead his consciousness to  () the significance of axioms... "

I hope the relevance to objectivity and Davydov makes sense.

Julian

On 8 Nov 2014, at 21:22, "HENRY SHONERD" <hshonerd@gmail.com> wrote:

> Huw and Andy,
> I am jumping in now, because I think I might have understood almost entirely what you both have been saying. (Don’t go there!) To the extent that this stage of the dialog is about constraints, could we add an ethical note (no bullying) and an aesthetic note (don’t be ugly) as far as “constraints” on our discourse and activity. Or, we could just be creative. I am so blissfully sure of my brilliance that I propose we make creative projecting as our unit of analysis. Good for whatever ails you. (Don’t go there!)
> Henry’
> 
> 
>> On Nov 8, 2014, at 5:40 AM, Huw Lloyd <huw.softdesigns@gmail.com> wrote:
>> 
>> That seems fine to me.  Although I don't consider that objectivity to be
>> free-standing.  Once you have cars, you're going to need traffic
>> management.  Once you have practices of arithmetic, you're going to come
>> across the need for algebra.  That external objectivity seems to be the
>> same as stating that there are systemic implications.
>> 
>> Huw
>> 
>> On 8 November 2014 12:21, Andy Blunden <ablunden@mira.net> wrote:
>> 
>>> No Huw, I am not saying "there is no outside to discourse." On the
>>> contrary. I am saying that a properly developed discourse theory allows
>>> that the world has constraints which cannot be altered by discourse.
>>> Activity Theory, properly developed, also recognises that there are
>>> relations which are objective and cannot be changed by activity. And
>>> Vygotsky warned us against pitting act against word. My objections is only
>>> to those elaborations of Activity Theory or Discourse Theory which claim
>>> that there is nothing outside the Activity/Discourse.
>>> So *obviously* children learn mathematics by learning to participate in
>>> mathematical discourse according to social conventions applying to that
>>> specific discourse. But my point is only that that discourse is constrained
>>> by objective relations (and can therefore be rationally reconstructed), and
>>> social conventions can turn out to be wrong. Mathematics is not *just* a
>>> social convention.
>>> Interesting isn't it, that Leibniz and Newton each discovered calculus at
>>> the same time, but each gave it a completely different form.
>>> 
>>> Andy
>>> ------------------------------------------------------------------------
>>> *Andy Blunden*
>>> http://home.pacific.net.au/~andy/
>>> 
>>> 
>>> Huw Lloyd wrote:
>>> 
>>>> The simple problem here, Anna, is that actions require memory.  To act is
>>>> to exercise memory.  This may be why Andy is saying there's no outside to
>>>> discourse and is the reason why I proffered a way of construing discourse
>>>> that included action.
>>>> 
>>>> Best,
>>>> Huw
>>>> 
>>>> On 8 November 2014 07:16, anna sfard <sfard@netvision.net.il> wrote:
>>>> 
>>>> 
>>>> 
>>>>> Hi Huw,
>>>>> 
>>>>> I really like your metaphor of discourse as a plane with "kinds of
>>>>> mathematical knowledge ... traversing through that plane". It is for such
>>>>> metaphors, if anything, and for the kind of imagery that generates it
>>>>> that
>>>>> one should learn mathematics!
>>>>> 
>>>>> This metaphor shows me very clearly, however, that you and I are not at
>>>>> the same page when it comes to the use of the word discourse. I am
>>>>> insisting on this point because, unlike you, I think that "the
>>>>> distinction
>>>>> between when something is or isn't discursive" IS "a big deal". See, for
>>>>> me, discursive is tantamount to communicational. If so, when you say
>>>>> "memories derived from non-discursive actions ... are not discursive", I
>>>>> cannot agree. Having memories, no matter about what, is always a
>>>>> communicational act. The fact that memory is about something
>>>>> non-discursive
>>>>> cannot change this. When you say it does, you "collapse" the talk with
>>>>> what
>>>>> is being talked about (we commit  such "ontological collapses" all the
>>>>> time, so you're definitely not alone :-)).
>>>>> 
>>>>> And since Andy's post is coming just as I am about to send this email,
>>>>> let
>>>>> me add that while I agree with Andy that activity theory and the
>>>>> discursive
>>>>> framework are doing similar jobs in similar, but mostly parallel ways, I
>>>>> am
>>>>> wondering about why Andy thinks that the equation 'math = discourse'
>>>>> implies that 'there is no "outside" to discourse'. But this, probably,
>>>>> is a
>>>>> different story, and since I do have life beyond [this] discourse, I
>>>>> think
>>>>> I must leave it here :-)
>>>>> 
>>>>> 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 10:27 PM
>>>>> To: eXtended Mind, Culture, Activity
>>>>> Subject: [Xmca-l] Re: Objectivity of mathematics
>>>>> 
>>>>> 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
>>>>>>>> 
>>>>>>>> 
>>>>>>> 
>>>>>> 
>>>>>> 
>>>>>> 
>>>>> 
>>>>> 
>>>>> 
>>>> 
>>>> 
>>>> 
>>>> 
>>> 
>>> 
>