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Re: [xmca] Types of Generalization: concepts and pseudoconcepts
Oops. Make that 5 colors and 6 geometric shapes (said it backwards
before). And now I remember how Paula describes the 2*2 solution: a
On Sep 12, 2009, at 8:05 PM, Steve Gabosch wrote:
Andy, thanks for your response to Davydov on concept formation and
efforts to get us to read Davydov, Vygotsky, Sakharov, etc. It has
certainly been effective in my case. And Jay, your comments have
also been very helpful.
Two questions on your essay, Andy.
One, what do you mean by "an absolutely non-empirical social factor"
when you say: "The transition from complex to concept is a
protracted and complex process, but one which necessarily involves a
complex leap, in which absolutely non-empirical, social factors
enter into the formation and enrichment of the concept."
Two, I am having difficulty understanding how Sakharov block
solutions for bik, cev, lag and mur are not "true concepts" in the
way Vygotsky used the term. A taxonomy formed out of formal rules
can be a true concept, yes? The Sakharov block test is really just
a puzzle where you have to figure out the taxonomic classification
system by observing the visible attributes of the blocks and
figuring out the only one that can be put into four logical groups.
Yes, the nonsense words are arbitrary and only have meaning to test
participants - but that is the case for any game. In chess, for
example, rooks and pawns are "concepts" - yes? If a rook is a
concept, then why not bik, cev, mur and lag?
Here are some details on the Sakharov test and its solution that
might help visualize this question of whether the solution groups to
the test are themselves "true concepts". In discussing details to
the solution to the test the way I do, I am arguing that the
solution groups are "true concepts." I am willing to be corrected
on this, of course. Perhaps there is a better way to interpret
The 22 Sakharov blocks were very cleverly designed. No two blocks
are exactly alike. They are comprised of 6 different colors, 5
different geometric shapes, 2 different heights (tall and flat) and
2 different sizes (large and small). There would be 120
(6*5*2*2=120) different blocks altogether if a full set of blocks
were created out of these parameters. The 22 that were selected
have the interesting characteristic of having one and one only
possible rule-based solution to the challenge of sorting them into 4
logical groups based on their physical attributes.
Since there are 4 groups that these 22 blocks are going to fall in,
one's first impulse is to look for a single parameter that all
blocks share that has 4 variations. As it turns out, this is
impossible. There is no 4*1=4 solution. That took some serious
design forethought. There are not even any clever, obscure
alternative solutions along these lines.
In one of Paula's earlier papers, she reports on a child who, after
deciding that neither color nor shape would work as solutions, began
counting numbers of **sides** of the blocks to see if **that**
parameter fell into 4 groups. It doesn't - they fall into 5
groups. That little inspiration got me me to try to come up with
some other way of grouping the blocks into 4 logical groups by
seeking unusual parameters, such as numbers of angles, numbers of
two-surface intersections, numbers of three-surface intersections.
However, no single parameter I have come up with has has only 4
variations. (As an aside, most of these parameters just mentioned,
interestingly, have 5 variations - the reason being that all the 6
different geometric shapes have different totals of these unusual
parameters except the square and trapezoid, which have the same
number of these - so consequently, the total of 5 keeps reappearing).
I don't think it is a coincidence that there are no alternative
solutions. I am guessing that Sakharov very deliberately designed
these blocks to avoid that distraction. This is part of this test's
very clever design.
What makes this test a puzzle even to most adults is that the
solution requires not finding one parameter with 4 variations, but
combining **2** parameters that each have **2** variations. I think
Paula calls this a dichotomous solution (Paula, do I have the right
word?). Running into this principle in the way this test presents
it is not an everyday occurrence, but the principle is actually very
familiar, for example, to modern consumers when they compare similar
commodities of different brands and models for desired (and
undesired) features, prices, etc. Once one understands this general
principle (multiplying the parameter variations to figure out the
total possible combinations) and that this is the way this Sakharov-
block puzzle works, the solution becomes completely obvious by just
observing the parameters and counting their variations. Since the
solution seeks 4 groups, and since there are no 4*1=4 solutions, the
one and only possible other solution would be to find a 2*2=4 way of
assembling the groups together. And wallah! There the solution is,
plain as day once you see it - tall/flat and large/small.
In theory, if one understands this principle clearly, one could
determine the different groups just by looking at the 22 blocks,
counting and calculating the parameters and their variations by eye,
and do so without picking up a single block. However, since the
nonsense words are arbitrarily assigned, it would still be necessary
to pick up a block in each of 3 different groups to determine the
precise names that correspond to each group. There probably are
people who could figure this all out just by staring at these blocks
and arriving at this reasoning, but they would have to be a pretty
experienced puzzle solver to do that in one shot, I would think.
However, there are many very bright people associated with this list
- anyone solved or seen the test solved in "one shot," so to speak?
(An interesting question to ask is, about those that do solve the
test - which solve it **conceptually**, and which stumble on the
solution as just a pseudoconcept?)
The question Mike and Paula discussed, and I think David raised,
about what procedure or methodology does the test-giver use to guide
the test-taker during the test, is especially interesting. Which
block do they overturn under what circumstances to show the test-
taker the error of their ways during the test, and what other
"hints" and "prods" to they provide as the test proceeds? (The
younger the child, the more creative prods are needed, from what
Paula's reports!) This question is interesting on two levels. One,
obviously, relates to how these prompts influence what the test-
taker understands and does. But here is another level to look at
this from: **what concepts** are guiding the **test-giver** when
they are giving their prompts? (And if they are not being guided by
"true concepts," then what are they being guided by?)
My point in going into all this detail is to suggest that this
parameter-counting principle is a concept, (or combination of
concepts), and that the solution groups, which themselves are
organized according to this principle, being completely derivative
of this overall concept, are necessarily concepts as well.
Generalizing, I am suggesting that these are "concepts" within this
experimentally-designed system in the same sense that the numbers 1,
2 and 3 are "concepts" within the number system.
Bik, cev, lag and mur, according to this reasoning, are the made-up
names for specific concepts and are arbitrarily assigned - as are,
ultimately, all words for the things they correspond to. In this
game, these four nonsense words correspond to the concepts flat-
large, flat-small, tall-large, and tall-small, which are meaningful
concepts within the game's rules. These conceptual groups are an
integral part of that puzzle's internal taxonomy and its overall
conceptual system - even though this puzzle, in many ways, is just
about as artificial, rule-based, experimental, arbitrary and trivial
as you could probably invent and still get children and adults to
make sense out of. But lots of cool puzzles are kinda like that.
And this Vygotsky-Sakharov concept formation test really is a cool
Well, that's my argument for calling these nonsense words "true
concepts" in the Vygotskyan (not necessarily the Davydovian) sense.
On Sep 11, 2009, at 1:14 PM, Jay Lemke wrote:
A small follow-up, having now read at least Andy's comments on
Davydov, if not the Davydov itself.
I would agree very broadly with what Andy says, and highlight one
point and note one that is perhaps underemphasized.
Maybe it's because of Davydov's view, but it seems clear to me
that LSV emphasizes very strongly and consistently the key role of
verbal language, and so we ought really want to know more about
exactly how the ways in which children and early adolescents use
verbal languages changes as they come to mediate their activity
more along the lines we might call acting-with-true-concepts.
What struck me as very important, that Andy emphasizes (and Davydov
also?) is that the development of true concepts depends on their
use in social institutions. This limits the relevance of artificial-
concept experimental studies in ways that would not be apparent in
a more purely cognitive science paradigm (or old fashioned
empirical-concept ideology), because the similarity to natural true
concepts is only logical-formal, and not also social-institutional.
A lot of my own students tend to get this wrong, because they
identify the social with the interpersonal, such that there is
still a similarity (in the micro-social milieu of the experiment
itself as a social activity). But not at the macro-social
And here perhaps is also a clue to my query about how the modes of
mediation differ across the historical cases (Foucault), the cross-
cultural cases (Levi-Straus), the post-modern cases (Wittgenstein,
Latour), and even the everyday true concept vs. formal scientific-
mathematical true concept cases. The difference arises in and from
the institutional differences. Could we perhaps combine LSV's
insights into how this works in the developmental case (changes in
the social positioning of the child/adolescent), L-S on the
functioning of mytho-symbolic mediated activiity in rituals and
social structuration processes, F on changes in the historical
institutions (medieval-early modern), and L on heterogeneity of
mediation in relation to heterogeneity of actant networks? to
understand better how this institutional context and its processes
I left out Wittgenstein, but he may help with an intermediate
scale, not the large social institutions, but the game-like
activities of which they are composed.
I'll be looking at Davydov to see what he offers in these terms.
University of Michigan
Ann Arbor, MI 48109
On Sep 11, 2009, at 5:51 AM, Andy Blunden wrote:
I have prepared a response to Davydov's book, but it is 4,000
words, so I have attached it in a Word document. But here is a
Davydov claims that in his analysis of the Sakharov experiments,
Vygotsky fails to demonstrate any real distinction between a true
concept and an abstract general notion (what is usually and
mistakenly taken for a concept in non-Marxist thought).
I claim that he has a point, but Vygotsky is guilty only of some
unclarity and inconsistency in his language, and makes the
distinction very clear. And Davydov should pay more attention to
what Vygotsky says about the relationship.
Davydov works with a mistaken contrast between scientific concepts
and the general notions derived from everyday life. Scientific
concepts are by no means the only type of true concepts and
everyday life is full of concepts.
Nonetheless, Davydov has a point. It is evident that Sakharov, the
author of the orignal, oft-cited report evidently is guilty
exactly as charged by Davydov. And no-one seems to have noticed!
Although Paula and Carol are consistent and correct in everything
they say in their paper, they err on one occasion only when they
cite Kozulin citing Hanfmann. It is as if people equate logical
use of generalized empirical notions with conceptual thought,
never in their own words, but only by means of citing someone
I think this is the legacy of a lack of clarity in Vygotsky's
4,000 words attached. And apologies for not entering the
discussion of Paula and Carol's paper earlier, but I was not clear
in my own mind on these problems, and Davydov helped me get clear.
Better late than never!
Andy Blunden (Erythrós Press and Media) Orders: http://www.erythrospress.com/store/main.html#books
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