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Re: [xmca] Types of Generalization: concepts and pseudoconcepts

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 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 puzzle.

Well, that's my argument for calling these nonsense words "true concepts" in the Vygotskyan (not necessarily the Davydovian) sense. Thoughts?

- Steve

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.


Jay Lemke
Professor (Adjunct)
Educational Studies
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 brilliance.

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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