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Semiosis and Catastrophes

René Thom’s Semiotic Heritage


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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SVEND ØSTERGAARD René Thom: The Recognition of Forms. An Apologia for Realism 35


René Thom: The Recognition of Forms. An Apologia for Realism SVEND ØSTERGAARD In a few short statements I will present René Thom’s philosophical commit- ments. As is well known, René Thom was the discoverer of catastrophe the- ory, but more generally, we can say that he made substantial contributions to the theory of dynamical systems (mathematical analysis) and to the theory of differential manifolds (topology). These fields influenced his conception of mathematics: he was very much against set theory, partly because it did not contribute to any understanding of the perceptual world and partly because it led to incomprehensible paradoxes. He was not a formalist, but he accepted of course formal representations in mathematics insofar as they led to in- sights in geometry, topology and dynamics. So, mathematics is not primarily a formal system, but a method to obtain realistic representations of space and dynamic processes. One can perhaps say that he reverted to Newton’s under- standing of mathematics: The mathematical laws were predicates of the ob- jects, i.e. not anything imposed from outside. If mathematics describes struc- tural properties of space/dynamics on the one hand, then on the other it also describes the structural conditions for the subject’s recognition of the exter- nal world. René Thom almost favors a mirroring effect where the dynamics of the external world correlates with a dynamics of the human brain, and this correlation makes recognition possible. This is a position which underlies a philosophy that contains the following assumptions. The continuum The only...

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