Computability in Developing Systems
P. B. Ivanov · 1996
Human activity and cognition cannot be modelled without accounting for development. The principal directions of incorporating development in production systems, abstract automata and practical problem solvers are discussed in this paper. A few generalisations of a physical definition of Turing machine are described, including and hierarchical models. Considering the modification of the machine's operation set and environment requires a new mathematics, which would incorporate self-modifying (reflective) axiomatic systems. Schemes of explicit and implicit definitions are discussed, and the necessity of a conceptual closure of hierarchical development in science is stressed. Universal features of development are described, distinguishing structural, systemic and hierarchical development. These features are indispensable to insure human-like behaviour in ensembles of Turing machines. Still, the ways science describes the world could be made the subject of a particular investigation, and nothing prohibits the formation of new sciences studying it. Actually, every science is aware of the limits of its applicability; moreover, the attempts to more exactly specify the applicability conditions often become a source of new discoveries. Such methodological study may be more obvious in sciences whose subject is originally related to the description of the observer. Thus, mathematicians intensely explore the foundations of mathematics, this activity being sometimes called metamathematics (Engeler 1983). The analogous branch in cybernetics is called second-order cybernetics (Foerster 1981). Also, many psychological works include an analysis of possible observer's involvement.