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Re: [xmca] Types of Generalization: concepts and pseudoconcepts
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- Subject: Re: [xmca] Types of Generalization: concepts and pseudoconcepts
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- Date: Tue, 15 Sep 2009 12:51:57 +1000
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Steve, here is Vygotsky commenting on how children play chess:
"Although initially the investigator's task was to disclose
the hidden rules in all play with an imaginary situation, we
have received proof comparatively recently that the
so-called pure games with rules (played by school children
and late preschoolers) are essentially games with imaginary
situations; for just as the imaginary situation has to
contain rules of behavior, so every game with rules contains
an imaginary situation. For example, what does it mean to
play chess? To create an imaginary situation. Why? Because
the knight, the king, the queen, and so forth, can move only
in specified ways; because covering and taking pieces are
purely chess concepts; and so on. Although it does not
directly substitute for real-life relationships,
nevertheless we do have a kind of imaginary situation here.
Take the simplest children's game with rules. It immediately
turns into an imaginary situation in the sense that as soon
as the game is regulated by certain rules, a number of
actual possibilities for action are ruled out."
What do you make of that?
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 these details.
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
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
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
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
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 puzzle.
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 institutional level.
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 play out?
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 synopsis.
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 else's words.
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
Andy Blunden (Erythrós Press and Media) Orders:
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