Andy Blunden, August 2010
I will preface a review of the ideas of the conceptual change movement in learning theory, by mentioning the work of Jean Piaget, whose Kantian theory of cognitive development triggered the cognitive revolution, and Thomas Kuhn, whose book “The Structure of Scientific Revolutions,” itself constituted a revolution in how conceptual change is understood. These currents are more concerned with understanding than with recognition and categorisation.
I mention Piaget only by way of his being an agent who inspired the developments in psychology and pedagogic research which are of interest to us here, rather than for his own outstanding contribution to developmental psychology. Piaget’s idea of equilibration is a powerful way of conceptualising how an organism (child) develops in the process of adaptation to its environment. Equilibration is a dynamic equilibrium between two opposite tendencies: assimilation and accommodation. In assimilation the child incorporates into its cognitive structure and behaviour a new experience or form of behaviour, acquired from its environment, thus making a power found in the environment into a power of their own. In accommodation, the child responds to a failure of adaptation by modifying their cognitive structure and behaviour in order to yield to the resistance offered by the environment. For example, in following a moving object with their eyes, they accommodate their eye movement to the object. When the object passes behind something, their eyes remain fixed at the point it disappeared. Later the object reappears on the other side of the obstruction, and they again accommodate to it in its new position. When they learn to continue to follow the path of the object until it re-appears on the other side, they have assimilated the object’s regular movement to their own cognitive scheme and behaviour. If the object fails to re-appear then this provides a new stimulus for further accommodatory searching until a new schema of object-following can be developed. This idea made it possible to understand the process of an organism’s adaptation to its environment, firstly as an active process, rather than one of passive reflection, and secondly as a process of development of the organism’s own activity, rather than one of mirroring arbitrary attributes of the environment. The result was a conception of the mind that went through successive waves of accommodation and assimilation, each time achieving a formal representation of its own activity through which it could be subject to control by the organism itself.
This allowed Piaget to represent the cognitive structure of a child, at any given stage in its development, with formal mathematical structures such as groups, according to the complexity of transformation of reality which the child can cognise. Each developmental stage corresponds to achievement of cognitive tasks corresponding to transformations describable by more and more sophisticated mathematical structures, irrespective of the context or content of the relevant ideas. This idea allows us to think of cognitive structures which are not just associations, images or metaphors, but incorporate the properties of something in the world through formally isomorphic structures of transformation, or if you like, a cognitive model of a type of reality. It also allows us to understand how cognitive dissonance may stimulate cognitive development.
Piaget made an interdisciplinary effort to transpose his conception from ontogenetic (child) development to phylogenetic (historical) development. This is a form of the ‘biogenetic hypothesis’ and it does not work. Partly this is because an individual person develops by growing into an existing culture and mode of activity, whereas societies, like species, develop principally by pulling themselves up by their own bootstraps. Also, the abstract mathematical structures which Piaget uses to describe stages of cognitive development are the outcome of a long history of logic and mathematics, which has uncovered successively deeper and more primitive relations. But in the development of science it is not at all the case that sciences begin with simple, abstract relations; mathematics began with Geometry and Arithmetic, not Group Theory. More likely a science begins with very concrete structure and content, and like mathematics and logic, burrow down to a conception of the basic underlying abstract forms only much later. Nonetheless, his venture into the history of science, introducing the idea of structural transformations in moving from one stage to another, proved, along with Gestalt Psychology, to be the inspiration that spurred Thomas Kuhn to develop his sociology of science, hinging around the idea of periods of gradual development punctuated by crises and revolutions in the natural sciences.
Kuhn’s theory of scientific revolutions is so well-known, I shall not bore the reader with a recapitulation of it. My aim is simply to bring out its importance for our theme, clarify the meaning of the term ‘paradigm’ and make some incidental comments about Kuhn’s theory.
The first thing to note about the theory, at least as it was first presented, is that a paradigm is an exemplar of scientific achievement, usually a book or a research report, or a family of such exemplars, which appears at a time of crisis in a science. Offering a novel and exemplary approach to the subject matter, the paradigm offers a way out of the impasse and serves as a model while leaving many open questions and matters of detail and application still to be clarified. Such an exemplar thus leaves in its wake a period of puzzle solving, working through the details, so to speak, which Kuhn calls ‘normal science’.
Because of its role in setting new puzzles for research, with a new understanding of the nature of the subject matter, of what constitutes a useful question and a valid answer, the paradigm gradually becomes generalised into a set of norms and rules, definitions and axioms. These constitute the formal domain representing a scientific theory, along with a disciplinary identity, a reconstituted scientific community, standard practices and specialised technology. But Kuhn is at pains to emphasise that a paradigm is first of all an exemplar, and only consequent upon its acting as an exemplar may a disciplinary matrix constituting a new kind of ‘world view’ develop. In the same spirit, Kuhn insists that induction into a science is not a matter of first learning a series of abstract theories, definitions, laws and then later learning how to apply these principles. Rather science education is primarily acquaintance with the paradigms of scientific practice from which the scientist can learn the substance and concrete meaning of the abstract principles, which in themselves have no obvious connection with experience.
If we say that for Kuhn a paradigm is both an exemplar and a matrix of concepts and practices, then we are looking at a process of development, both of the work of individual participants and of the overall objectification of the science as a whole. A new concept cannot but emerge in the form of a particular exemplar of scientific practice, but the work of ‘normal science’ is to ‘operationalise’ the exemplar and fill its original undeveloped form with practical content. This process somewhat resembles the way a new legal precedent becomes consolidated in judicial practice and law. The confusion over what Kuhn meant by ‘paradigm’ which has reigned since the first publication of “Scientific Revolutions” is probably explained by the need to define a concept as an entity with fixed attributes, rather than as a developing process. The paradigm is this process which begins with a spectacular exemplar and is gradually transformed into an intricate matrix of norms and rules.
The ‘normal science’ which constitutes the gradual working out of the paradigm takes the form of ‘puzzle-solving’. The paradigm settles what the legitimate questions are which need to be asked, sets puzzles for scientists to solve. The concretisation of the paradigm is achieved by the successful solution of all those problems which are set up by the paradigm. Kuhn says that “the unit of scientific achievement is the solved problem” (Kuhn 1962: 169). The paradigmatic exemplar itself solves more than a ‘puzzle’. Its role is to resolve a crisis or impasse into which the whole former science had fallen, and effectively found a new branch of science. It is said that the paradigm constitutes a new concept of the subject matter, and in this sense we see in the above definition exactly what Kuhn means by a scientific concept. It is a process of problem solving which begins with a solution to a problem in the development of the entire body of the science, which reveals the nature of the subject matter, and develops through the working out and concretisation of the initial solution in the form of a continuous process of puzzle-solving.
If a successful problem solution is a concept, then the paradigm is a concrete universal concept which includes the puzzle-solving activity of ‘normal science’ as subordinate parts. The reader may notice the similarity of this idea to Hegel’s approach exhibited in the Phenomenology of Spirit, to be discussed in Part II. Science and its special branches, each founded by a paradigmatic exemplar concept, constitute what Hegel calls a ‘formation of consciousness’. The puzzle-solving of ‘normal science’ are its subordinate concepts, the units of the formation of consciousness. Continuing this comparison, Hegel sees that every formation of consciousness is subject to sceptical critique which begins in matters of detail, but ultimately undermines the ideal or defining self-concept of the formation. This criticism arises from the activity of the concept itself, and sooner or later, according to Hegel, every formation of consciousness eventually comes into irresolvable contradiction with itself. The resulting crisis opens the way for a new formation of consciousness which is able to resolve the terminal crisis of its predecessor. All the concepts belonging to the formation of consciousness, its special principles, are then negated and sublated into the constituent concepts of the new formation.
Natural science reifies its concepts. That is the defining feature of natural science. It treats its concepts as things existing independently in the natural world. But in Kuhn’s analysis, a concept is a problem-solution, a practical solution to a problem which arises only within a system of activity defined by the paradigm, itself an exemplar of natural scientific practice. The puzzle solution is then reformulated, and taken as the discovery of some thing with an independent existence. Thus, progress is recorded in terms of the reified product of scientific activity, rather than the process of scientific activity itself.
A lot of the discussion around Kuhn’s idea has hinged around the ‘Gestalt switch’ that is involved in traversing a scientific revolution, with a total transformation of how the world is seen, and the seeming impossibility of communication across paradigms. But as I read it, the absolute character of the transformation effected by a scientific revolution is by no means essential to his basic idea, which is just as applicable to the solution of small problems as to great revolutions like that of Copernicus or Einstein. The difficulty of communication is always relative. There is no concept in any language which absolutely defies translation. But as a problem-solution, a concept is meaningful only in the light of the paradigm to which it belongs and this is an necessary part of understanding what a concept is. A solution is always the solution to some problem, which can only arise within some system of practice.
However, I think Kuhn falls into the same error that Hegel fell into by his focus on the internal problems of a scientific community and its specific concerns. This focus implies that progress is the work of thought alone, and that the history of science can be understood solely on its own terms. Rather, any science to a large extent gets its questions and its concerns from its place within the larger community of which it is a part. In particular, the technical means that it uses in its own activity are provided from outside the science and it is above all the developing means of measuring and observing which continually disrupts science and poses for it new problems as well as new means for their solution. This tends to be over the horizon of Kuhn’s point of view, which gives the appearance of science being an entirely intellectual activity, self-contained within a system of unfolding logical puzzles. Science is a practical activity, whose participants are real individuals living in a real human community, and uses the technical means provided by that community to solve puzzles which in some measure arise from the practical concerns of that community. Kuhn is right to take as his unit of activity the problem-solutions of one specific scientific community, one paradigm, but in order not to misconstrue what is at work within it, it is still necessary to place that scientific community within its context. Kuhn’s observation that scientific creation is insulated from the judgment of the broader community, and confined to a finite group of co-workers, to a greater extent than the work of any other creative worker, is noteworthy. It is this fact that allows the character of concepts as problem-solutions within a definite system of practice defined by a more general concept to stand out in such relief. Over time scientific concepts make their way into the general life of the larger community, where they merge with the activity of everyday life, and take on the appearance of noumena.
Another fact about concepts which is thrown into relief by Kuhn’s focus on communities of practice which are relatively insulated from the judgment of the general community is how the significance of a concept is dependent on the project of which it is a part. This begs the question as to whether the consistency demanded of the problem-solving activity within a given paradigm is a feature of thinking in the wider community. That is: what takes the place of a scientific paradigm in the life of the general community? Since Kuhn never addressed this question, a question which raises very far-reaching questions, I will put this aside until the final section when I address the question: “What Is a Concept?”
Kuhn remarks that “unfortunately, the questions which [investigation of the crisis-state] leads to, demand the competence of the psychologist even more than that of the historian” (1962: 86). And indeed, the psychological processes of bridging the gap from one paradigm to another, either in the process of education or as a pioneer in science, has attracted the attention of psychologists, and it is to this work I shall now turn, rather than the analogies and metaphors of which Kuhn’s theory is so productive.
“Starting in the mid to late 1970s, a huge social movement, which we dub ‘misconceptions’, began modern conceptual change studies in educational research and in neighboring disciplines, including experimental psychology and developmental psychology” (diSessa 2006). Especially in subjects like physics and biology, rather than taking learning to be a matter of adding new ideas on to a blank slate representing no prior knowledge of the field in question, learning theorists began to look at learning as replacing formerly held misconceptions – naïve physics or naïve biology – with scientific conceptions of the same subject matter. Thus learners were seen as having to undergo a ‘paradigm shift’.
One outcome of this approach was to take seriously the concepts novices had of the processes studied by physics, biology, mathematics and so on, and investigate how children conceived of falling bodies, the difference between animals and inanimate objects, and so on. Since all children approach learning in these areas with one or more of a finite range of possible alternative (mis-)conceptions, mere awareness of how a child already understands a process will invariably make the teacher’s job easier. To explain the way science understands the process and assist the child in adopting science’s view is difficult if you are working on the mistaken assumption, that the child has no way of understanding heat and temperature or the shape of the Earth or whatever, at all.
The question is this. Is it valid to conceive of the novice’s naïve view of a process as a paradigm, and is it reasonable to expect that the novice’s view is part of an internally consistent worldview, from which a ‘gestalt switch’ is required? Does the schoolchild’s misconception have to be destroyed before it can be replaced with a new, scientific view? Concomitantly, is the novice’s spontaneous view of a topic an actual barrier to adopting the alternative, scientific view?
Drawing on Andrea diSessa’s (2006) excellent historical summary of this debate, it seems fair to conclude that there is no basis whatsoever for supposing that a child’s naïve physics, for example, is a ‘paradigm’ in the sense of a matrix of concepts and practices which exhibits any kind of internal consistency. It is fairly well established that children do not become aware of logical contradiction until learning the idea by engaging in argument with their peers, and even then, it takes a long time for this awareness to penetrate all domains of their thinking and activity. Even given this awareness, a lifetime may not be long enough for their knowledge to be restructured into anything resembling an internally coherent body of knowledge. But this does not mean that a child’s naïve physics is not paradigmatic in a different sense. A child’s naïve views rest on the use of words learnt through collaboration with adults and a practical intelligence acquired through manipulation of objects even before acquiring the use of language. Thus the child’s actions express the logic implicit in the culture they are being raised in, whether or not they are consciously aware of it. Until the child’s view of the world is sufficiently differentiated, the child must perforce extend a strategy which has been successful in one situation to use in other similar situations. So the general idea of a paradigm, as an exemplar on which a range of activities can be modelled is not necessarily misplaced. The empirical study of misconceptions sheds light on the kind of mistakes children make in the absence of access to the institutionalised experience of the entire community. But nothing like a gestalt switch is implied in correcting such mistakes. Generally speaking, a system of ideas is precisely what children lack. They have some kind of idea for everything they have learnt the name of, but these ideas will not be true concepts. More likely the child will set off from improvised extensions of concepts derived from practical sensori-motor experience or hearsay, and their ideas will be neither stable nor fit into any coherent system.
Piaget was influential in the formation of the conceptual change movement, on account of his discovery that children were required to successively restructure their cognitive framework in the course of their development. However, the idea of equilibration did not shed any light on how naïve conceptions come to be abandoned, under the influence of instruction, in favour of more scientific concepts. Nonetheless, Piaget promoted a constructivist view of mental development, that is, that revised views of the world have to be constructed on the basis of and by means of some earlier idea. His idea of mental structures which were independent of context or situation did not stand up to scrutiny however. Spontaneous concepts are domain specific.
Linguists have also made a substantial contribution to the study of concepts. Ray Jackendorf (Margolis & Laurence, 1999: 305) points to an important distinction: most linguists are concerned only with concepts as they are embodied in artefacts (especially words) in the world, whilst others, such as Noam Chomsky, approach concepts as mental formations:
On one hand, [a concept] is something out there in the world: ‘the Newtonian concept of mass’ is something that is spoken of as though it exists independently of who actually knows or grasps it. Likewise ‘grasping a concept’ evokes comparison to grasping a physical object. ... On the other hand, a concept is spoken of as an entity within one’s head, a private entity, a product of the imagination that can be conveyed to others only by means of language, gestures, drawing or some other imperfect means of communication.
Because “language is the immediate actuality of thought” (MECW v.5: 446), linguistics allows a more sophisticated and nuanced investigation of concepts and the relations between them, exploring avenues that remain closed to a psychology of concepts which concerns itself with hypothetical and imperceptible forms in the mind. It seems that there is little prospect of building a rich psychology of concepts without actively engaging with linguistics and semiotics generally and being able to appropriate its results. I will not venture into the vast domain of linguistics here, but part of our aim must be to open a door to allow the insights of linguistics to be accessed by a psychology of concepts and vice versa.
In addition, I would like to make the following note on linguistics. All specialists tend to apotheosise their own field of study and linguists are no different. Even though the subject matter of linguistics is merely the signs of concepts, linguists tend to see concepts as properties of words, whether spoken or written. As Marx said:
One of the most difficult tasks confronting philosophers is to descend from the world of thought to the actual world. Language is the immediate actuality of thought. Just as philosophers have given thought an independent existence, so they were bound to make language into an independent realm (MECW v.5: 446).
Ever since Saussure, linguistics has been hampered by a pervasive dualism, with a system of signifiers on one side, and the world of the signified on the other, presenting linguists with the insoluble problem of how to match up one side with the other. Nonetheless, the very difficulty of having to reconstruct a living activity from the evidence of texts, has led to linguistics becoming the source of a wealth of critical insights into the relation between words and concepts. I thank Jay Lemke for the following list of distinctions in the understanding of word meaning known to linguistics:
Our aim here is to clarify what a concept is, not the meaning of a word. Pragmatics and the place of language in activity and context is not our subject matter. I am concerned only with what pertains to an understanding of concepts. The problem of what is a concept is neither more nor less complex than the problem of word meaning, i.e., the relation of an expression to the concept for which it is a sign. The two problems are co-extensive, but nonetheless, two different problems.
Linguists and cultural critics working in their departments, the social behaviourists and sociologists in their departments, and historians and psychologists in theirs, each focus exclusively on just one aspect of concepts. The absence of an integrated theory and the dominance of one-sided approaches is a result of the modern fragmentation of science along disciplinary lines. Imagine if you had two different departments, one studying keys, the other locks. Each can describe the constitution of their subject perfectly well, but self-evidently no sense could be made of either locks or keys. Only if the systems of activity in which individuals participate, the constellation of artefacts used and constituted in that activity and the individual human actions are taken together as aspects of a single, indivisible whole, can we understand any one side of a concept.
We live in a humanised world. We live in Nature too, of course, but our relationship to Nature is mediated by the artefacts with which we surround ourselves and the collaborative forms of activity through which we interact with culture and Nature. Our concepts are necessarily part of this too, because our concepts are the basic units of this humanised world. Our concepts are the basic units, the threads, from which our consciousness is woven, and the basic units of which our culture is made, and the basic unit from which the systems of activity through which we interact with each other are made. If we can work out an approach to concepts like this, then it becomes possible to understand how concepts can truly reflect our actions and intentions, because they are basic units of both our mental world and the humanised world we share with others. Instead of a problem of matched pairs of ideas and things, we have an assembly of entities which are both mental and material, both subjective and objective. We don’t need a dichotomy, because we make no cut.
It is worth noting that if we take concept to mean a situation constituted by artefact-mediated activity, then concepts are as affect-laden and full of emotional content as is our activity. A concept is not a dead form of words, such as a definition, or any kind of reified object, but a living, active form of life, with all the vitality and emotion that belongs to real human activity: a real form of human life which is both subjective and objective.
The study of language and its relation to the study of concepts cannot go past the (later) work of Ludwig Wittgenstein, a renegade from Logical Positivism, who has provided an insider’s critique of the analytical approach to language and meaning.
Whereas I have said that a word (or expression) is the sign for a concept, the drift of Wittgenstein’s work is that it is a mistake to take a word as a sign for anything other than itself. Word meaning is just how the word is used. In §66 of the Investigations he demonstrates that the wide variety of concepts evoked by the word ‘game’, have no attribute which is shared in common by them all. That in itself should be no surprise. One would have to be a Logical Positivist to be surprised that word meanings don’t work like Set Theory. If a word simply named an attribute, then the concept itself would be empty.
But while a word may be a sign for concept, it would be untenable to also define a concept as the referent of a word, simply duplicating the world into signs and signifieds. A great deal of context, gesture and so on is required for a word to function as a sign for a concept in any locutionary act.
Wittgenstein goes on to suggest that we don’t have and don’t need to have any kind of definition of a word, beyond clarifying how we are using the word in the given instance. Taken in conjunction with his observations about ‘family resemblance’ and the impossibility of setting boundaries, this implies a move away from a taxonomy based on attributes, and towards a typology based on exemplars and as such has some merit. There is something to be said for the idea that a word gains its meaning from its use and can have no determinate meaning abstracted from the conditions of its use. But what does it mean to ‘use’ a word and what conditions of use determine meaning?
Wittgenstein also points out that it is empty to characterise an action by setting up a normative rule and taking the action as obedience to the rule. Wittgenstein shows that all this achieves is to set up a metaphysical model which more or less imperfectly reflects what it is supposed to explain. What is fundamental is the action itself, from which norms and rules can be abstracted, rather than rules and norms being deemed to underlie the action. People can behave normatively without being able to specify the relevant norm or even being aware that such a norm exists.
Like many others, Wittgenstein freely uses the word ‘concept’ but never says what he means by it. At one point, he suggests that “a concept is ... the application of a word” (PI §383), but at another that a concept is “a characteristic of human handwriting,” (PPF i) and that “Language is an instrument. Its concepts are instruments” (PI §569), implying that concepts are properties of language, if not exclusively of writing. I must agree, however, with his observation that “Concepts lead us to make investigations. They are the expression of our interest and direct our interest” (PI §570).
Word meanings are motivated or they are not meant at all. An action, such as word meaning, is obedient to its motivation, the end which the action serves, which is always something other than the action itself. It is this which is of interest to us, rather than just how speakers convey and evoke their meanings by selective and artful use of words. It is the concepts which motivate word meanings, and for which words are used. Where in Wittgenstein’s writings do we learn about how concepts function in mediating interaction?
The early paragraphs of “Philosophical Investigations” are set in the context of people collaborating in constructing a building, and the interlocutors make sense of each other’s words thanks to the fact that they are engaged in the same activity. In §23 he says:
the term ‘language-game’ is meant to bring into prominence the fact that the speaking of language is part of an activity, or of a form of life (Wittgenstein 1953 §23).
And this is the point. It is these extra-discursive activities which provide the ends towards which word meanings are oriented. Concepts are located within shared activities and forms of life, not just the transitory uses of words. A million disparate actions are required to build a house, but the meaning of all these actions is house building and derivative concepts (in the sense that Kuhn talks of normal science as derivative of a paradigm). Here is the real problem which Wittgenstein does not address.
Concepts are discursively constructed prior to any given utterance and have relative stability. We could not suppose that an environment (such as a building site) is sufficient for all the interlocutors to understand the activity they are engaged in, so that they are able to construe appropriate meanings to others’ words. That ‘context’ has to be evoked discursively. But everything about constructing a building: the various building elements, the skills and processes, the division of labour, plans and so on, pre-exist any given utterance or any of the actions which contribute to finally constructing a building.
Wittgenstein does not help us understand what it is in those activities and forms of life which create and maintain the concepts which allow language to be meaningful. The uttering of a word is a momentary, transient event, and it is surely only the activity and form of life of which it is a part which confers meaning on words, expressions and gestures?
I think Holzman and Newman had it right when they described “Wittgenstein’s work as therapy – for philosophers, whose obsession with philosophical problems is their pathology” (Newman & Holzman, 2006: 177).
In a similar vein, in the context of learning mathematics, Anna Sfard defines a concept, as “a word together with its discursive uses” (2008: 268). When we first learn a concept, then the concept is indeed inseparable from the word by which we first learned it. But over time, the concept becomes more and more independent of the word. At the same time, one and the same concept can be evoked by different words, differences in nuance and context notwithstanding. So I think it would a mistake to tie a concept to a word in this way. If every word marks a different concept, then we are led to the dualism of signifier and signified, even if by signified we mean “discursive uses” rather than some noumenon. Sfard is right to say that “one cannot get a sense of a person’s concept of number without considering the totality of this person’s discursive activities in which the term number may occur,” but there is no one-to-one relation between word and concept. The idea of a word unifying a disparate range of meanings has merit, but in my view, this definition is still too much oriented to personal meaning, and lacks normative content.
Wittgenstein argued forcefully that word meaning cannot be rationalised as conformance to a semantic norm, since semantic norms are derivative from discursive use. But by reminding us that language-use is part of an activity, Wittgenstein pointed to the source of semantic normativity. Wittgenstein remained a sceptic on the question of concepts, content with debunking the illusions of Logical Positivism. If we are to make any sense of the idea of ‘mathematical concepts’, we need to know what makes some uses of a word normative and not others. Anna Sfard sharply distinguishes her view from the interactionism of Wittgenstein and Brandom when she says: “with the whole discourse on numbers as the unit of analysis, we can now explain these phenomena as stemming directly from the systemic nature of discursive development” (2008: 268). But Sfard also evokes the idea of the ‘endorsed narrative’ as the criterion for having grasped a concept and being able to use a word in the socially approved manner. But an endorsed narrative can turn out to be wrong. Endorsed by whom? But if endorsement is the final court of appeal, then there can be no extra-discursive criteria for normativity. It makes sense for the concepts of everyday life, where semantic norms are always in play, but in the case of scientific concepts or other concepts belonging to definite forms of social practice, I think we must, as Sfard suggests, take “the whole discourse [of some activity] as the unit of analysis.”