Tag Archives: actions

Dialogue of the deaf

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Dialogue of the deaf

I had a stimulating discussion with a neuroscientist the other day. I tried to explain to her that my interest in children’s cognitive development is linked to my interest in epistemology, that is, to what I refer to in this blog as the normativity of thought.

For example, I argue that researchers who try to explain children’s knowledge of math from a nativist point of view, can only explain the starting point of cognitive development. The starting point is innate mathematical knowledge, which is mostly implicit, and basically consists in an ability to identify the numerosity of collections of objects found in the outside world. In other words: researchers have shown that animals (humans included) have the innate ability to assess the size of a collection of perceived objects (for example, they can notice that a collection of 15 pebbles is greater than a collection of 10 pebbles). They can also discriminate among exact quantities, but only when dealing with small sets (two, three, and perhaps four objects). Also, some animals and human babies can perform elementary arithmetic operations on small sets (adding two plus one, subtracting one from two, etc.) I am referring here to studies by Dehaene (2011), Izard, Sann, Spelke, & Streri (2009), Spelke (2011), and many others.

This basic capacity is certainly different from fully-fledged “human math.” The latter involves, at the very least, the symbolic representation of exact numbers larger than three. We (humans) can represent an exact number by saying its name (“nine”), or by using a gesture that stands for the number in question (depending on the culture, this might be done by touching a part of one’s body, showing a number of fingers, etc. – see Saxe ( 1991) and also http://en.wikipedia.org/wiki/Chinese_number_gestures). And, of course, we can write down a sign that represents the number (for example, with using the Arabic numeral “9”).

Scholars agree on the fact that advanced math is explicit and symbolic, and that it builds on (and uses similar brain areas to) its precursor, innate math. Once they operate on the symbolic level, humans can do things like: performing operations (addition, subtraction, multiplication, division, and others), demonstrating mathematical propositions, proving that one particular solution to a mathematical problem is the correct one, etc. To sum up: our symbolic capacities allow us to re-describe our intuitive approach to math on a precise, normative, epistemic level.

Now, here’s when it gets tricky. I argue that the application of algorithms on the symbolic level is not merely mechanical. Humans are not computers applying rules from a rule book, one after the other (like Searle in his Chinese room). Rather, as Dehaene (2011) argues, numbers mean something for us. “Nine” means nine of something (anything). “Nine plus one” means performing the action of adding one more unit to the set of nine units. There is a core of meaning in innate math; and this core is expanded and refined in our more advanced, symbolic math.

When executing mathematical operations (either in a purely mental fashion, or supported by objects) one gets a feeling of satisfaction when one arrives to a right (fair, correct, just) result. Notice the normative language we apply here (fair, correct, right, true, just). We actually experience something similar to a sense of justice when both sides of an equation are equal, or when we arrive to a result that is necessarily correct. (Note to myself: talk to Mariano S. We might perhaps do brain fMRIs and study if the areas of the brain that get activated by the “sense of justice” in legal situations, also light up when the “sense of justice” is reached by finding the right responses in math. If a similar region gets activated, that might suggest that there is a normative aspect to math that corresponds to the normative aspect of morality).

For me, then, the million dollar question is: how do humans go from the implicit, non-symbolic, automatic level to the explicit, symbolic, intentional and normative level? What is involved in this transition? What kind of biological processes, social experiences and individual constructions are necessary to achieve the “higher,” explicit level? (These are interesting questions both for the field of math and for the field of morality). And my hypothesis is that this transition necessarily demands the intervention of a particular type of social experience, namely, the experience of the normative world of social exchanges and rules of ownership (I’ve talked a little about such reckless hypotheses in other posts of this blog).

Now, when I try to explain all this to the neuroscientist, I lose her. She doesn’t follow me. For her, human knowledge is the sum of a) innate knowledge and b) learning from the environment. Learning is the process by which our brain acquires new information from the world, information that was not pre-wired, that didn’t came ready to use “out of the box.” Whether such learning involves a direct exposure to certain stimuli that represent contents (a school teacher teaching math to his or her students) or a more indirect process of exposure to social interactions is not an interesting question for her. It doesn’t change her basic view according to which there are two things, and two things only: innate knowledge and acquired knowledge. What we know is the result of combining the two. And this is the case both for humans and for other animals. Period.

Something similar happens when I talk to her about the difference between “cold processing” and “hot processing.” We were discussing the research I am conducting right now. I interview children about ownership and stealing. In my interview design, children watch a movie where one character steals a bar of chocolate from another, and eats it. The interviewer then asks the child a series of questions aimed at understanding her reasoning about ownership and theft. Now, the movie presents a third person situation. This means that the child might be interested in the movie, but he or she is not really affected by it. Children reason about what they see in the movie, and sometimes they seem to say what they think it’s the appropriate thing to say, echoing adults’ discourse. Because, after all, the movie is fiction, not the real world.

I believe that normativity emerges not from absorbing social information that comes from external events (watching movies, attending to teachers’ explanations) but from children’s real immersion in first person, real world, conflictive situations. When a child is fighting against another for the possession of a toy, there are cries and sometimes there even is physical violence. These encounters end up in different ways; sometimes children work out a rule for sharing the scarce resource, sometimes they just fight, and sometimes an adult intervenes and adjudicates in the conflict. The child’s reactions during these events is not dictated by cold reasoning but by deeper impulses. It is in these situations where we should look for the emergence of our basic normative categories, such as reciprocity (both social and logical, or “reversibility”), ownership (or the relationship between substance and its “properties”), quantity (used to implement equity and equality), etc.

But, again, my biologist friend does not feel that the distinction between the impulsive, intense, hot reactions we experience when involved in real conflicts and the kind of third person reasoning that is triggered by movies and artificial stimuli is an important one. In both cases, she argues, it’s the same cognitive system that is at work. What we think about third person characters is probably similar to how we reason about ourselves (thanks to our capacity for empathy, our mirror-neurons, etc.)

I don’t know who’s right and who’s wrong here.

 

Dehaene, S. (2011). The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition. The number sense How the mind creates mathematics rev and updated ed (p. 352). Oxford University Press, USA. Retrieved from http://www.amazon.com/dp/0199753873

Izard, V., Sann, C., Spelke, E. S., & Streri, A. (2009). Newborn infants perceive abstract numbers. Proceedings of the National Academy of Science, 106(25), 10382–10385.

Saxe, G. B. (1991). Culture and Cognitive Development: Studies in Mathematical Understanding. Hillsdale: Lawrence Erlbaum Associates.

Spelke, E. S. (2011). Quinian bootstrapping or Fodorian combination? Core and constructed knowledge of number. Behavioral and Brain Sciences, 34(3), 149–150.

 

Kitchener on Piaget as a sociologist

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This post presupposes many others. Don’t start here.

I’ve just read Richard Kitchener’s excellent paper on Jean Piaget as a sociologist (Kitchener, 1991). He rightly emphasizes the normative aspect in Piaget’s approach to knowledge. Part of the unfair criticism that the Piagetian legacy endures these days comes from authors who neglect or just don’t understand such normative aspect (A. Gopnik’s publications are good examples of this intellectually shortsighted attitude). I’ve insisted on this topic in previous posts such as this one or this one or this one, and will be writing more about it in the future.

What do we mean when we say that epistemic knowledge and logic have an inescapable normative component? Our point is that individuals engaged in the construction of epistemic knowledge are different from animals in that they are not simply trying to solve problems posed by their environment (that is, they’re not just trying to be effectively adapted to the world) but they are trying to produce valid, legitimate knowledge that they can defend by means of reasons when questioned by interlocutors or adversaries. Ideally, these interlocutors challenge each other as equals, that is, they don’t use the argument from authority. “The need to justify one’s beliefs or actions emerges only under the particular social conditions of equality” (Kitchener, 1991, p. 433). Under conditions of equality people tend to cooperate with each other rather than to constrain or force each other to do certain things or to accept certain propositions. Rationality, in Piaget’s and Kitchener’s view, is a byproduct of peer interaction: cooperation generates reason (Kitchener, 1991, p. 430). Logic, to sum up, arises from interactions between individuals: “The Cartesian solitary knower, separate from social interaction with others, cannot construct an equilibrated logic” (Kitchener, 1991, p. 435).

Similarly, objectivity results from mutual exchanges of subjective perspectives between individuals: being objective “…requires an awareness that what one thinks may not coincide with what is true” (Kitchener, 1991, p. 429). This self-vigilance or, as Kitchener calls it, self-consciousness, is the psychological activity of an individual thinking and arguing with others, and subjecting herself to the normative rules of reasoning. “Rules of reasoning are thus normative obligations binding upon the individual (…) Reasoning in general requires normative principles of inference and the most adequate one is normative reciprocity” (Kitchener, 1991, pp. 425-426).

Kitchener illustrates this last point with a famous example from Piaget’s Études sociologiques: “two individuals, on opposite banks of a river, are each building a pillar of stones across which a plank will go as a bridge”. This creates a problem of action coordination between individuals that can be characterized in logical terms (correspondence, reciprocity, addition or subtraction of complementary actions). But the bridge example is an instance of what I call the technological approach to human action. That is, Piaget (and Kitchener) focus here not on the structure of social relations (the rules and institutions that organize life in common) but on the practical, effective coordination of actions that are a (more or less effective) means toward an end (building the bridge). The bridge example could have as well came out of the desk of a Vygotskian scholar, since it fits with the features of activity as defined by the socio-historical school: people organized in order to achieve a common goal and using tools available in their cultural context. The emphasis here, to say it again, is on technical action and not in the sense of justice inherent to social relations.

So I have two (external?) criticisms of Kitchener-Piaget: 1) to understand normativity (of social relations, and epistemic normativity as well) you need to pay attention to social institutions as they embody a sense of justice; a technical or technological view of human action won’t do; 2) institutions come with many flavors, reciprocity being a characteristic of one particular (albeit important) institution (contract). But there are other institutions (some of them based on authority) that are legitimate and can therefore be a source of valid statements. (There was rational argumentation before the emergence of Athenian democracy).

Kitchener, R. F. (1991). Jean Piaget: The Unknown Sociologist? The British Journal of Sociology, 42(3), 421–442. doi:10.2307/591188

 

“Let’s trade” and “my turn”

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My son L. is 3y 1m old. He’s started recently to use the expression “let’s trade” (“te cambio”). That is: he produces speech acts aimed at swapping objects with another person. For instance, he gives away his glass of milk in order to obtain a yoghurt cup I have. We exchange goods. He seems to understand that the proto- contract we thus celebrate involves the mutual surrender and handing over of possessions. The rules of reciprocity are no doubt regulating this interaction. Which doesn’t mean that the child can understand conceptually, let alone articulate, such rules.

In addition, when playing with other children, L. knows how to claim his turn to use a toy (shouts “¡Turno mío!”). He also uses this expression in other contexts; for instance, to demand his turn to drink mate (in a mate round shared with adults). Again: his understanding of the reciprocity rules involved is perhaps incipient. But L. is clearly starting to master the rhetorical forms that allow efficient access to the desired objects.

My hypothesis: the child first masters the rhetorical forms, and only later the conceptual content. Piaget’s prise de conscience (the conceptual, explicit insight) is the final product of a process that starts with immediate, un-reflected action. The process goes from the periphery of action to the center of explicit, conceptual thinking. Differently from Piaget, however, in the periphery I do not see the actions of an organism but the utterances of a retor.

Piaget and the logic of action

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I’m reading Prof. Castorina’s lectures on Genetic Epistemology. They’re quite good.

One of the points he explains very clearly is that, for Jean Piaget, logic emerges out of the individual’s coordination of actions (or action schemata). Piaget considers that one of the basic features of all living forms is their tendency to self-organize. He thought that this principle or “functional invariant” applied to all levels of development, from basic organic forms to complex human behavior. It is an essential part of self-preservation that organisms produce complex and organized structures and that they maintain such organization actively throughout time in order to survive. Successful self-organization is thus the counter-part of successful adaptation; they are parallel processes, two sides of the same coin.

I buy it up to that point. But Piaget extends this biological framework further: intelligent life is manifestation of life as such; the same laws that apply to living forms also apply to intelligence and to cognitive development. Logic derives from action, and action is understood in biological terms. Logic reflects the inner organization of action. For example, the organized actions of babies that move, order and categorize objects are at the root of the (developmentally later) mental operations of classification, seriation, number, etc. The very logical principle of “conservation,” so central to Piaget’s theory, derives from the organism’s tendency to self-organize and self-preserve.

It is as if a logical instinct were inherent to human action. For Piaget, there’s a continuum that goes from biology, through action, up to logic and scientific knowledge.

In my opinion, Piaget underestimates the discontinuities between animal cognition and human knowledge. I consider the latter as an institutional phenomenon (I try to explain in other places). As I see it, the deontological nature of human knowledge is not reducible to biological action.