**What is Complexity?**

By **Bruce Edmonds**,

Senior Research Fellow in Logic and Formal Methods
Centre for Policy Modeling,
Manchester Metropolitan University
Aytoun Building, Aytoun Street, Manchester M1 3GH.
email: b.edmonds@mmu.ac.uk
tel.no: +44 161 247 6479
Full paper
**Abstract:**

This paper aims to discuss the definition and application of the concept of
complexity from a pragmatic philosophical perspective with some examples taken from evolution. A useful definition is proposed to clarify its use in
discussion.

Firstly 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 within which its use as such a paradigm can be retained as a limiting case.

Then, 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 argued that complexity is usefully differentiated from the concepts of
size, ignorance, variety, controllability and cost. Examples are given to
illustrate the intuitive differences as well some of the pitfalls of conflating
these ideas.

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.

Some of the consequences of this definition are discussed. In particular some
examples where we can not approach complete information about their components are presented as situations where the complexity is either impractically large or just inapplicable

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

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