What is Complexity? - The philosophy of complexity per se with application to some examples in evolution

Abstract

It is argued that complexity has only a limited use as a paradigm against reductionist approaches and that it has a much richer potential as a comparable property. What can complexity be usefully said to be a property of is discussed. It is argued that it is unlikely to have any useful value as applied to real object or systems. Further that even relativising it to an observer has problems. It is proposed that complexity can be only usefully applied to constructions within a given language. It is argued that complexity is usefully differentiated from the concepts of size, ignorance, variety, minimum description length and order. A definition of complexity is proposed which can be summarised as follows: That property of a language expression which makes it difficult to formulate its overall behaviour even when given almost complete information about its atomic components and their inter-relations.. Some of the consequences of this definition are discussed. It is shown that this definition encompasses several existing varieties of complexity measures and is then applied to some examples pertaining to the evolution of complex' systems including: "What is the complexity that has evolved in organisms and has it increased?".