The intrinsic indetermination observed in chaotic and quantum systems, together with the theoretical results from Gödel and Turing, set limits of different kinds on what can possibly be answered, computed and predicted. These bounds play a fundamental role in the scientific practice, bearing on our theories and models, and therefore on the overall reach of our knowledge. If scientific explanations are considered as transition maps between observed phenomena and mathematical or logical relations preserving some relational structure, one has to deal ideally with three operational wards. First of all, the space of the observed phenomena, a subsample of what we conceive as the physical world: observed regularities, series of happenings or chains of reactions, either natural or arranged in the lab. Then there is the space of the abstract concepts and conceptual tools, conceived either ad hoc for the specific purpose of description, or independently from possible applications. Finally there is the process itself of finding meaningful correspondences between regions of these spaces, preserving properties, morphologies and connections. In this essay the role of the theoretical and practical limitations relative to each of these three domains are investigated, trying to portray the intrinsic limits of our knowledge, their implications, and what sense can be made of them.
Paolo Bellan