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Author: Hoffmann, Michael H. G. × End date: 2006 × Start date: 2006 ×

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Learning from People, Things, and Signs

2006-11-15 , Hoffmann, Michael H. G.

Starting from the observation that small children can count more objects than numbers—a phenomenon that I am calling the "lifeworld dependency of cognition"—and an analysis of finger calculation, the paper shows how learning can be explained as the development of cognitive systems. Parts of those systems are not only an individual’s different forms of knowledge and cognitive abilities, but also other people, things, and signs. The paper argues that cognitive systems are first of all semiotic systems since they are dependent on signs and representations as mediators. The two main questions discussed here are how the external world constrains and promotes the development of cognitive abilities, and how we can move from cognitive abilities that are necessarily connected with concrete situations to abstract knowledge.

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Seeing problems, seeing solutions. Abduction and diagrammatic reasoning in a theory of scientific discovery

2006-08-28 , Hoffmann, Michael H. G.

This paper sketches a theory of scientific discoveries that is mainly based on two concepts that Charles Peirce developed: abduction and diagrammatic reasoning. Both are problematic. While abduction describes the process of creating a new idea, it does not, on the one hand, explain how this process is possible and, on the other, is not precisely enough defined to distinguish different forms of creating new ideas. Diagrammatic reasoning, the process of constructing relational representations of knowledge areas, experimenting with them, and observing the results, can be interpreted, on the one hand, as a methodology to describe the possibility of discoveries, but its focus is limited to mathematics. The theory sketched here develops an extended version of diagrammatic reasoning as a general theory of scientific discoveries in which eight different forms of abduction play a central role.

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