Abstraction and Representation: Essays on the Cultural by Peter Damerow

By Peter Damerow

The writer of this ebook is affiliated with the heart for improvement and Socialization of the Max Planck Institute for Human improvement and Ed­ ucation in Berlin and heads its application on tradition and cognition which de­ votes its labors to the reconstruction of clinical strategies via heritage in a viewpoint of what will be referred to as "historical epistemology." he's additionally a member of a comparable examine staff within the newly based Max Planck Institute for the heritage of technological know-how in Berlin. possibly this double association throws a few gentle at the scope of Damerow's clinical pursuits. In any occasion it is going to clarify why representatives of either those associations take part an attempt to introduce Peter Damerow's writings to an English talking audi­ ence. Damerow's scholarship levels throughout greatly various parts together with philosophy and background of technological know-how, psychology, and schooling. between his fields of craftsmanship are the emergence of writing, early Babylonian mathe­ matics, the historical past of mathematics, the connection among natural and utilized arithmetic, the idea and techniques of arithmetic guide, the tran­ sition from preclassical to classical mechanics, and the background and concept of relativity.

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The theory is, however, more simple in the sense that Piaget consistently makes a conceptual distinction between the material actions and their ideal correlates in the cognitive schemata of consciousness. " The concept of assimilation " ... expresses the fundamental fact that any piece of knowledge is connected with an action and that to know an object or a happening is to make use of it by assimilation into an action schema" ([II], p. 6). " ([ II], p. 8) In the successful process of cognition assimilation and accommodation constitute a "dynamic equilibrium," in which the stabilization and generalization of the behavioral schema by means of the assimilation of ever new objects and the differentiation and expansion of the behavioral schema by means of accommodation to new circumstances maintain their equilibrium.

In other words, let us assume that the ability to order the sticks according to their lengths is the result of a simple learning process. Now, somebody with the ability to solve the problem without difficulty is convinced in advance that he or she will be able to solve the problem. Thus, if the ability to solve the problem were the result of a simple learning process as described above, then there could only be an empirical argument to support this conviction: In recent years he or she never failed to solve such a problem (although, according to the results of the seriation experiment, he or she had difficulties with such a task as a child).

As such they ought to be part of the logic of essence. In Hegel's classification which, incidentally, is not based on empirical considerations concerning the ontogenetic sequence of the categories, the theoretical tradition persists of perceiving space and time as categories of intuition and of basing mathematics on the forms of intuition (cf. the Kantian system). Hegel claims: "Mathematics is concerned with the abstractions of time and space. " ([3], p. 34) According to Piaget's experiments, however, only a "practical concept of space" and a "practical concept of time" are developed at the stage of sensori-motor intelligence represented by the material actions and their sensori-motor coordination and lacking precisely the structural details of the developed concepts of space and time characterized by quantity and measure.

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