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At first glance, twentieth-century science may be described as characterized by the move from a science primarily based on linear models to a science progressively based on non-linear ones. A subtler transformation is ongoing, however: a transformation at a deeper level than the move from linear to non-linear models and much less visible than it. This presently less visible transformation, if successful, may impact on the very idea of science in a vastly more important way than the move from linear to non-linear modeling techniques. In fact, both linear and non-linear techniques are forms of predicative modeling. The difference between predicative and impredicative systems (and models and definitions) is pervasive and often considered of marginal interest. The underlying unproven assumption is that the vast majority of systems are predicative, and only marginal, borderline systems are impredicative. Yet the transformation to which I am alluding directs attention to the opposite possibility: the unquestioned belief in the predicativity of most systems may prove to be illusory – a kind of self-inflicted groupthink. As a matter of fact, many disciplines, including sociology, anthropology, and biology, exhibit varieties of self-reference, which is the primary source of impredicativity. The idea that most systems are indeed impredicative opens new avenues for science. Moreover, it may help in addressing some of the most egregious failures of contemporary science. The possibilities to deepen and extend science as well as to address daunting obstacles of present science are serious enough reasons for thorough investigation of the difference between predicative and impredicative science.

DOI: 10.1007/978-3-319-63023-6_11

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