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Semiosis and Catastrophes

René Thom’s Semiotic Heritage

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Edited By Wolfgang Wildgen and Per Aage Brandt

The French mathematician René Thom (Fields medal 1958) died in 2002. In this volume his contributions to biology, semiotics and linguistics are discussed by a group of scholars who have continued his work and have shaped the new paradigm of dynamic semiotics and linguistics. Thom’s heritage is full of revolutionary ideas and deep insights which stem from a rich intuition and a sharp awareness of the current state of the sciences, including their potentials and risks. The contributions to this volume are elaborations of papers given at a colloquium at the International Center for Semiotics and Linguistics of the University of Urbino (Italy), in 2005.
The central concern of this volume is semiogenesis, i.e. the evolution and differentiation of meaningful («pregnant») forms in the field of symbolic systems – from bio-communication to language and cultural forms like music, art, architecture or urban forms. The basic questions are: How are meanings created and further differentiated? Where do they come from? What kind of forces drive their unfolding? How can complex cultural forms be understood based on simple morphodynamic principles?
Applications concern the perception of forms by animals and humans, the categorization of forms e.g. in a lexicon, and predication or other complex symbolic behaviors which show up in grammar or in cultural artifacts like the unfolding of urban centers.

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ÁNGEL LÓPEZ-GARCÍA Catastrophes: What are we talking about? 127

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Catastrophes: What are we talking about? ÁNGEL LÓPEZ-GARCÍA The catastrophe theory (CT) developed by René Thom beginning in 1972 is the only mathematical model that has proved adequate to natural sciences and to human sciences at the same time. One might expect such a model to be highly successful given that unified consideration of empirical facts is an essential desideratum of science. Nevertheless, things have not turned out as expected. Natural scientists tend to consider CT as a qualitative model, hence, as a model that does not allow one to make predictions on the struc- ture of reality. By contrast, human scientists have frequently adopted it as an alternative formalization of semantic facts, together with much other formal- ization, passing over its mathematical complexity and using it in rather a clumsy way. Consequently, Thom’s model continues to be somewhat pe- ripheral to science even though there are several enthusiastic scholars that have done well within this paradigm. Mathematicians are rarely interested in natural language. Sometimes they consider the relationship between Mathematics and Logics, as Russell and Whitehead did, but natural language is too vague, metaphorical and am- biguous for formalization purposes. Except for specifically formal grammars, which content themselves with the formal aspects of syntax, the remaining current grammatical theories have evolved from a more formal approach to a less formal one. It seems as if linguists had repeatedly discovered that for- malism does not work in linguistics and that natural scientific methods can- not be transferred to...

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