The Mechanism And Meaning Of Incomputable Complexity

Complexity problem as well as the problem of complexity philosophy itself is a complex problem with many aspects and difficult to be grasped. The goal of this paper is to distinguish the domain of complexity philosophy from that of complexity science, to answer precisely what is complexity in a certain view, to demonstrate the ultimate progresses of complexity science, and investigate the philosophical and cognitive meaning of these progresses.In order to derive explicit results, this paper bases its view on the substantial mathematical concept of computability. The complexity concept including both algorithm complexity and incomputable complexity is presented. The mechanism of incomputable complexity and three typical phenomena, namely "Observed Chaos", "Self-organized Criticality" and "Adaptation Build Complexity" are investigated. Then the meaning of incomputable complexity to three problems including "Determinism & Indeterminism", "the Limitation of Mankind's Knowledge" and "Reductionism" is explored, as well as its enlightenment for the ultimate philosophical problem. The approach adopted in the paper is from the accepted mathematical concept (computability) to empirical scientific results (CHAOS, SOC, CAS), and then to the philosophical (ontological, epistemological, and methodological) meaning. Various methods such as mathematical proof, case analysis, logical inference, philosophical thinking and so on are used.