An innocent form of emergence—what I call "weak emergence"—is now a commonplace in a thriving interdisciplinary nexus of scientific activity—sometimes called the "sciences of complexity"—that include connectionist modelling, non-linear dynamics (popularly known as "chaos" theory), and artificial life.1 After defining it, illustrating it in two contexts, and reviewing the available evidence, I conclude that the scientific and philosophical prospects for weak emergence are bright.

In this paper, I put forward a benchmark account of emergence in terms of non-explainability and explicate the relationship that exists between its synchronic and diachronic declinations. I develop an argument whose conclusion is that emergence is essentially a “two-faceted” notion, i.e. it always encapsulates both synchronic and diachronic dimensions. I then compare this account with alternative recent accounts of emergence that define the concept through the notion of unpredictability or topological non-equivalence.

Complex systems research is becoming ever more important in both the natural and social sciences. It is commonly implied that there is such a thing as a complex system, different examples of which are studied across many disciplines. However, there is no concise definition of a complex system, let alone a definition on which all scientists agree. We review various attempts to characterize a complex system, and consider a core set of features that are widely associated with complex systems in (...) the literature and by those in the field. We argue that some of these features are neither necessary nor sufficient for complexity, and that some of them are too vague or confused to be of any analytical use. In order to bring mathematical rigour to the issue we then review some standard measures of complexity from the scientific literature, and offer a taxonomy for them, before arguing that the one that best captures the qualitative notion of the order produced by complex systems is that of the Statistical Complexity. Finally, we offer our own list of necessary conditions as a characterization of complexity. These conditions are qualitative and may not be jointly sufficient for complexity. We close with some suggestions for future work. (shrink)

I challenge the usual approach of defining emergence in terms of properties of wholes “emerging” upon properties of parts. This approach indeed fails to meet the requirement of nontriviality, since it renders a bunch of ordinary properties emergent; however, by defining emergence as the incompressibility of a simulation process, we have an objective meaning of emergence because the difference between the processes satisfying the incompressibility criterion and the other processes does not depend on our cognitive abilities. Finally, this definition fulfills (...) the nontriviality and the scientific‐adequacy requirements better than the combinatorial approach, emergence here being a predicate of processes rather than of properties. †To contact the author, please write to: Institut d'Histoire et de Philosophie des Sciences et des Techniques (CNRS/Université Paris I Sorbonne), 13 rue du Four 75006, Paris; e‐mail: [email protected]. (shrink)

I investigate the relationship between adaptation, as defined in evolutionary theory through natural selection, and the concept of emergence. I argue that there is an essential correlation between the former, and “emergence” defined in the field of algorithmic simulations. I first show that the computational concept of emergence (in terms of incompressible simulation) can be correlated with a causal criterion of emergence (in terms of the specificity of the explanation of global patterns). On this ground, I argue that emergence in (...) general involves some sort of selective processes. Finally, I show that a second criterion, concerning novel explanatory regularities following the emergence of a pattern, captures the robustness of emergence displayed by some cases of emergence (according to the first criterion). Emergent processes fulfilling both criteria are therefore exemplified in evolutionary biology by some so-called “innovations”, and mostly by the new units of fitness or new kinds of adaptations (like sexual reproduction, multicellular organisms, cells, societies) sometimes called “major transitions in evolution”, that recent research programs (Maynard-Smith and Szathmary 1995 ; Michod 1999 ) aims at explaining. (shrink)

A framework for representing a specific kind of emergent property instance is given. A solution to a generalized version of the exclusion argument is then provided and it is shown that upwards and downwards causation is unproblematical for that kind of emergence. One real example of this kind of emergence is briefly described and the suggestion made that emergence may be more common than current opinions allow.

Weak emergence has been offered as an explication of the ubiquitous notion of emergence used m complexity science After outlining the problem of emergence and comparing weak emergence with the two other weak objectivist approaches to emergence, the paper explains a version of weak emergence and illustrates at with cellular automata Then it explains the sort of downward causation and explanatory autonomy involved m weak emergence.

This paper proposes an extensionalist analysis of computer simulations (CSs). It puts the emphasis not on languages nor on models, but on symbols, on their extensions, and on their various ways of referring. It shows that chains of reference of symbols in CSs are multiple and of different kinds. As they are distinct and diverse, these chains enable different kinds of remoteness of reference and different kinds of validation for CSs. Although some methodological papers have already underlined the role of (...) these various relationships of reference in CSs and of cross-validations, this diversity is still overlooked in the epistemological literature on CSs. As a consequence, a particular outcome of this analytical view is an ability to classify existing epistemological theses on CSs according to what their authors choose to select and put at the forefront: either the extensions of symbols, or the symbol-types, or the symbol-tokens, or the internal denotational hierarchies of the CS or the reference of these hierarchies to external denotational hierarchies. Through the adoption of this extensionalist view, it also becomes possible to explain more precisely the reasons why some complete reduction of CSs to classical epistemic paradigms such as “experiment” or “theoretical argument” remains doubtful. On this last point, in particular, this paper is in agreement with what many epistemologists already have acknowledged. (shrink)

Weak emergence has been offered as an explication of the ubiquitous notion of emergence used in complexity science (Bedau 1997). After outlining the problem of emergence and comparing weak emergence with the two other main objectivist approaches to emergence, this paper explains a version of weak emergence and illustrates it with cellular automata. Then it explains the sort of downward causation and explanatory autonomy involved in weak emergence.

As brightly shown by Mainzer [24], the science of complexity has many distinct origins in many disciplines. Those various origins has led to “an interdisciplinary methodology to explain the emergence of certain macroscopic phenomena via the nonlinear interactions of microscopic elements” (ibid.). This paper suggests that the parallel and strong expansion of modeling and simulation - especially after the Second World War and the subsequent development of computers - is a rationale which also can be counted as an explanation of (...) this emergence. With the benefit of hindsight, one can find three periods in the methodologies of modeling in the empirical sciences: 1st the simple modeling of the simple, 2nd the simple modeling of the complex, 3rd the complex modeling and simulation of the complex. Our main thesis is that the current spreading (since the 90’s) of complex computer simulations of systems of models (where a simulation is no more a step by step calculus of a unique logico-mathematical model) is another promising dimension of the science of complexity. Following this claim, we propose to distinguish three different types of computer simulations in the context of complex systems’ modeling. Finally, we show that these types of simulations lead to three different types of weak emergence, too. (shrink)