A Philosophical Analysis of Chaos Theory

Over the last 40 years, chaos theory has had a huge impact on science and philosophy. This is evidenced by the astonishing volume of chaos-related publications; even a cursory survey shows that chaos has been detected virtually everywhere, from cardiac rhythms to Joyce’s Ulysses (e.g. Kellert, 2008). Given the high export appeal of chaos theory, it is surprising that there are fundamental aspects of the field that still remain poorly understood and, in some cases, permanently debated. In particular: (i) it is still not clear how chaos should be defined and how the large number of coexisting chaos definitions relate to each other (e.g. Smith, 1998; Werndl, 2009c); (ii) there are still (largely unarticulated) questions about the faithfulness and predictiveness of the numerical and theoretical models on which chaos theory is based; and, finally, (iii) it has not been unequivocally resolved whether there is chaos in nature (e.g. Kellert, 1993) and how it should be diagnosed (e.g. Pool, 1989; Hastings et al., 1993). The three aspects are not independent of each other and it is evident that difficulties (i) and (ii) contribute to difficulty (iii). Together, they have made it very difficult to judge the diverse contributions to chaos theory comparatively and to enforce universal standards of quality and rigour. This book aims to clarify aspects (i)–(iii) by providing a structured survey of the construction, diagnosis and evaluation of chaotic models. Although the book follows a survey approach in that it aims to achieve a certain degree of comprehensiveness and to comparatively cover different aspects of chaos theory, it is not a mere review. I will pursue a modelling-centred strategy and thereby aim to provide the first in-depth analysis of all three stages, i.e. construction, diagnosis and evaluation, of modelling in chaos theory. This allows me to draw on a large amount of recently developed work on the use of models in science, which has so far not been applied to the field of chaos theory. In particular, the book uses, and develops further, several results of both the fictionalist approach to modelling (e.g. Frigg, 2010; Toon, 2012; Suarez, 2013) as well as the work on horizontal modelling by Bokulich (2003), which were not available to authors of earlier philosophical analyses of chaos theory (e.g. Kellert, 1993; Smith, 1998).