Something about science: Mulling over impredicative systems

Abstract

The science of the twenty-first century won't be less creative and surprising than the science of the twentieth. Both complexity and chaos show the unavoidability of uncertainty - whether it is embedded in feedback cycles and emergence or in the infinite precision of initial conditions. 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. Both linear and non-linear techniques are forms of predicative modeling. 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. 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.