RE: [xmca] concept as gambit

From: Peter Moxhay (
Date: Tue Nov 15 2005 - 08:13:11 PST

Anna (& Victor & Vera & all):

Yes, I would very much like to read your (Anna's) paper on concepts in mathematics.

Also, does anyone have the reference to Gordon's paper or chapter?

Though perhaps this is off the main line of interest for most on the list, I think that the current discussion of Anna's paper has helped me start to resolve some difficulties I have had in understanding and correlating:

- everday concepts vs. scientific concepts (Vygotsky)
- theoretical concepts vs. empirical concepts (Davydov)
- Ilyenkov's knowledge of the object vs. verbally expressed conceptions

I would be most grateful if anyone could send me (perhaps off the list) references to any recent literature on this topic of concept formation. (Perhaps Anna and Eduardo's paper has comprehesive references?)



>>> 11/15/05 10:41 AM >>>
I find you points on concepts very much in tune with previous argumentation. Indeed, this can be seen as an important grounding for the more general points previously made (at the level of a worldview) in analysing conrete interactions of teaching-and-learning. Especially for the worldview level point about the centrality of contribution by each individual to the flow of social practice unfolding in history.
Vygotsky's discussion of everyday and scientific concepts is very relevant here, I would think. Gordon Wells has an excellent paper (or was it chapter?) reflecting on this distinction.
Knowing how important such grounding of general ideas in concrete concepts is, I have written a paper comparing various models of teaching-and-learning concepts in mathematics (Nunes and Cobb versus Davydov-Elkonin). With the notion of individual contribution to social practice at the center (also making an argument how worldview level ideas get chanelled into practice and vice versa). This paper was written together with Eduardo Vianna who is my doctoral student and of whom I am very proud -- he works precisely at the juncture of general ideas and practice -- in the context of a Group Home for boys (he presented in Seville). Could send you a paper, if you like - it's in press for Theory&Psychology.


From: on behalf of Peter Moxhay
Sent: Mon 11/14/2005 2:36 PM
To: Activity eXtended Mind Culture
Subject: Re: [xmca] concept as gambit

Anna -- thanks for your comments on my query; I've finding it very
useful in understanding your article to think in terms of concept
formation .

And Victor -- thanks so much for the references, especially for
sending me to reread Chapter VI of Andy's "The Meaning of Hegel's

where I found this, in particular:

> Even (or rather especially) when what we see sharply contradicts
> what we know it to be, truth lies neither in abandoning our former
> opinion nor in ignoring the evidence of the senses but in forming a
> unity of the two: modifying our former opinion and seeing it in a
> new light, finding in immediate perception what was formerly so but
> now is not so.

Andy gives the example of one's immediate perception of "the Moon"
taken together with the accumulated human knowledge of the Moon:

> When we look at "the Moon", we do not question the immediacy of
> this perception. A murky cloud-covered view we would unhesitatingly
> refer to as "the Moon" equally as the Moon on a clear night. The
> Moon itself is inseparable from our concept of it, and has
> reflected sunlight on to countless generations of people. And in
> apprehending the Moon, we apprehend that which is referred to in
> the word "lunacy" and the words "romantic moonlit night" and which
> causes the tides.

Now what this puts me in mind of is a conversation I had a few years
ago with Sergei Gorbov, who is one of Davydov's co-authors of the
Elkonin-Davydov mathematics curriculum for elementary schools. He
told me that one of the most important moments of the teaching-
learning process is when the children come forward and express their
_subjective_ reactions to a given mathematical problem situation.
That is, the children may have in common certain ways of acting when
faced with a mathematical problem, but then they are confronted with
some new problem situation where what they know so far doesn't work.
A particular child will then tell what he or she thinks is the action
to be performed to solve the problem. In some cases, the child's
suggested action will not solve the problem, but even this "mistake"
gets folded back into and enriches the socially-shared mathematical
ways of acting. In other cases, the child's suggested action does
solve the problem, and so is successful in pushing forward the
collective knowledge of the classroom of children. The child takes a
risk (gambit?) of suggesting some new action, and the class as a
whole evaluates whether this new action solves the mathematical
problem or not.

So, it is an individual's "subjective image" of "how to act in the
new situation" that drives forward the socially-shared body of
knowledge. If we think of the "concept" not as the existing body of
knowledge but as a kind of vector along which that knowledge
increases, then the concept is intimately tied to individuals'
subjective ways of acting. But it's a subjective suggestion for
action that is socially (intersubjectively?) evaluated.

Anna, Victor -- does this example make any sense? Is this the kind of
subjectivity we've been talking about in the discussion of Anna's


> [Anna wrote]: Yes, Peter, you are right, this is critical indeed
> and I was going to elaborate on this too as this agrees with my
> position very much (and the readings Victor suggested are also
> critical - but let me try to make some points already here).
> In my take on this issue, and in more Vygotskian terms, concepts
> are TOOLS that are embedded within (in the sense of them coming out
> and returning to) the reality they are meant to serve. Concepts are
> saturated with this reality they serve and never break away from it
> ((Of course, if twe are dealing with meaningful concepts)). The
> reverse dependency is also true - this is as an upshot of the
> argument in my paper.
> This reality often, and more immediately for many of those who do
> theorizing, is the reality of theoretical debates, approaches and
> so on. In this sense, concepts are inextricably dependent on the
> whole theoretical system under consideration (hence the point about
> each and every idea or principle making sense only within the whole
> system) - and this is something readily acknowledged by many
> (though certainly not all) who come to think about and work with
> concepts. As, for example, reflected in the argument we all like
> very much - about the importance of context. But then, as also
> argued in my paper, behind this seemingly abstract theoretical
> reality there are always practical engagements with some issues out
> in the world, beyond the ivory tower of science - hence the
> practical and ideological saturation of concepts and theories.
> This embedded nature of concepts comes through very clearly in
> works on science as a social construction (the best in psychology
> being by Danziger, I think, who was referred to before), and in
> works by Sandra Harding on positionality and standpoint
> epistemology, and in Morwaski and other feminist scholars (Mary has
> mentioned some too in a different context).
> There are many renditions of this position - varying from extreme
> views of social constructionism a la Gergen for whom constructs are
> only instruments of social discourse (and are ephemeral, leading to
> extreme relativism - in my view), to more dialectical views in
> which concepts do reflect real practical contingences, at the same
> time as they serve as tools within discourses (many in philosophy
> of science, e.g. Young and in psychology - e.g., Ian Paker make
> similar arguments). In history of science, it was Russian
> philosopher Hessen who argued for this quite passionately in the
> 1940s, shocking members of the then established positivistically
> oriented community of historians of science. Young gives a
> fascinating account of the storm Hessen caused at some
> international congress on history of science with his presentation
> on Newton. This is my very brief selection, but there are many many
> more - as Victor points to readings in this direction. For me
> personally, this social-practical and history-context embedded
> nature of concepts was one of the first stark realizations that
> helped me throughout all my subsequent work (being really one of
> the threads of all my works, starting from early 1980s, I apologize
> for making this allusions to earlier works - this is meant as
> adding to context).
> My take on all of this, again, is about the importance of seeing -
> and using - concepts as embedded within the flow of practical
> activity/ engagements with the reality out in the world and its
> challenges, as well as the reverse movements between concepts-
> practice (the two being in unity but not in equivalence).
> I don't know if this agrees with what Victor meant (will read his
> posting more closely now).
> Incidentally, this is the way to answer also Mike's question - why
> subjectivity? Because the explanation has to do with the context. I
> will refer to this in the next message.
> Thanks to all who are still following the discussion (if there are
> some such people),
> A Stetsenko
> ________________________________
> From: on behalf of Peter Moxhay
> Sent: Thu 11/10/2005 12:25 PM
> To: Activity eXtended Mind Culture
> Subject: [xmca] concept as gambit
> Victor,
> You wrote:
>> the concept, is a gambit that is in fact a subjective challenge to
>> objective social practice (the idea is Hegelian though Hegel as an
>> idealist had a much more restricted concept of the negating effect
>> of the concept than that implicit in Marxian dialectics).
> I find this comment extremely clarifying (with respect to the ongoing
> discussion) and exciting. Could you perhaps provide references for
> further reading on this? In what works/sections would you say Hegel
> touches on this? Do you have any papers that expand on this comment?
> Also, I'm wondering whether this idea was really refused by _all_
> Soviet dialecticians...
> Peter
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