Radical Constructivism: A Way of Knowing and Learning

By Ernst Von Glasersfeld | Go to book overview

Chapter 9

Units, Plurality and Number1

For some fifty years Piaget was saying that the process of perception does not seem feasible unless we assume that the perceiver has some prior structure to which he can assimilate his sensory experience. Though there are empirical findings that corroborate this hypothesis, it draws its strength from the epistemological foundation on which Piaget has built his entire theory of cognition. The notion that what we come to know is to a large extent selected and shaped by what we already know, has cropped up independently in the philosophy of science.

A century ago, most scientists and ordinary people believed that what they called ‘data’ was there to be found by anyone who looked closely enough. This belief has been shaken. Today, a new generation of scientists is more inclined to think that the finding of data presupposes a specific theoretical structure to direct and inform search and observation. Hanson (1958, p. 19) said it very simply: ‘Observation of x is shaped by prior knowledge of x’ (see also Bridgman, 1961; Kuhn, 1962; Feyerabend, 1975). This view was couched in the phrase ‘All data is theory-laden’.

Nonetheless, there is still a widespread belief that good data has to be objective and, therefore, independent of any observer’s perceptual habits, theories, and beliefs. How, otherwise, could data serve as the material from which a true representation of the environment can be produced? Throughout this text, I have argued that this belief is not a useful one because it leads to a paradox in epistemology and hence to an unsatisfactory model of cognition. I suggested that the constructivist view provides a more promising approach by positing that all knowledge is constructed from subjective experience. This might appear to be quite incompatible with the experiential fact that mathematics produces a host of results that are eminently ‘objective’ in the sense that no individual subject can question them. Clearly, this is a problem that has to be resolved before the constructivist model can claim to be viable.


An Elusive Definition

Consequently, I shall outline a constructivist method of conceptual analysis, and apply it to the three concepts that are basic to the development of arithmetic and mathematics: unit, plurality, and number. What I am going to

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