Theories of the development of some phenomenon (e.g. life consciousness) where something emerges out of a background from which it could not have been predicted and in terms of which it cannot be fully explained.
What emerges may be a law of nature, or a science, though this would normally be because of emergent properties in the relevant sphere.
The existence of emergence theories contrasts with reductionism in the relevant sphere.
Also see: holism, vitalism
In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors which emerge only when the parts interact in a wider whole.
Emergence plays a central role in theories of integrative levels and of complex systems. For instance, the phenomenon of life as studied in biology is an emergent property of chemistry, and psychological phenomena emerge from the neurobiological phenomena of living things.
In philosophy, theories that emphasize emergent properties have been called emergentism.
Philosophers often understand emergence as a claim about the etiology of a system’s properties. An emergent property of a system, in this context, is one that is not a property of any component of that system, but is still a feature of the system as a whole. Nicolai Hartmann (1882-1950), one of the first modern philosophers to write on emergence, termed this a categorial novum (new category).
This concept of emergence dates from at least the time of Aristotle. The many scientists and philosophers who have written on the concept include John Stuart Mill (Composition of Causes, 1843) and Julian Huxley (1887-1975).
The philosopher G. H. Lewes coined the term “emergent”, writing in 1875:
Every resultant is either a sum or a difference of the co-operant forces; their sum, when their directions are the same – their difference, when their directions are contrary. Further, every resultant is clearly traceable in its components, because these are homogeneous and commensurable. It is otherwise with emergents, when, instead of adding measurable motion to measurable motion, or things of one kind to other individuals of their kind, there is a co-operation of things of unlike kinds. The emergent is unlike its components insofar as these are incommensurable, and it cannot be reduced to their sum or their difference.
In 1999 economist Jeffrey Goldstein provided a current definition of emergence in the journal Emergence. Goldstein initially defined emergence as: “the arising of novel and coherent structures, patterns and properties during the process of self-organization in complex systems”.
In 2002 systems scientist Peter Corning described the qualities of Goldstein’s definition in more detail:
The common characteristics are: (1) radical novelty (features not previously observed in systems); (2) coherence or correlation (meaning integrated wholes that maintain themselves over some period of time); (3) A global or macro “level” (i.e. there is some property of “wholeness”); (4) it is the product of a dynamical process (it evolves); and (5) it is “ostensive” (it can be perceived).
Corning suggests a narrower definition, requiring that the components be unlike in kind (following Lewes), and that they involve division of labor between these components. He also says that living systems (comparably to the game of chess), while emergent, cannot be reduced to underlying laws of emergence:
Rules, or laws, have no causal efficacy; they do not in fact ‘generate’ anything. They serve merely to describe regularities and consistent relationships in nature. These patterns may be very illuminating and important, but the underlying causal agencies must be separately specified (though often they are not). But that aside, the game of chess illustrates … why any laws or rules of emergence and evolution are insufficient. Even in a chess game, you cannot use the rules to predict ‘history’ – i.e., the course of any given game. Indeed, you cannot even reliably predict the next move in a chess game. Why? Because the ‘system’ involves more than the rules of the game. It also includes the players and their unfolding, moment-by-moment decisions among a very large number of available options at each choice point. The game of chess is inescapably historical, even though it is also constrained and shaped by a set of rules, not to mention the laws of physics. Moreover, and this is a key point, the game of chess is also shaped by teleonomic, cybernetic, feedback-driven influences. It is not simply a self-ordered process; it involves an organized, ‘purposeful’ activity.
Strong and weak emergence
Usage of the notion “emergence” may generally be subdivided into two perspectives, that of “weak emergence” and “strong emergence”. One paper discussing this division is Weak Emergence, by philosopher Mark Bedau. In terms of physical systems, weak emergence is a type of emergence in which the emergent property is amenable to computer simulation or similar forms of after-the-fact analysis (for example, the formation of a traffic jam, the structure of a flight of starlings or a school of fishes, or the formation of galaxies). Crucial in these simulations is that the interacting members retain their independence. If not, a new entity is formed with new, emergent properties: this is called strong emergence, which it is argued cannot be simulated or analysed.
Some common points between the two notions are that emergence concerns new properties produced as the system grows, which is to say ones which are not shared with its components or prior states. Also, it is assumed that the properties are supervenient rather than metaphysically primitive .
Weak emergence describes new properties arising in systems as a result of the interactions at an elemental level. However, Bedau stipulates that the properties can be determined only by observing or simulating the system, and not by any process of a reductionist analysis. As a consequence the emerging properties are scale dependent: they are only observable if the system is large enough to exhibit the phenomenon. Chaotic, unpredictable behaviour can be seen as an emergent phenomenon, while at a microscopic scale the behaviour of the constituent parts can be fully deterministic.
Bedau notes that weak emergence is not a universal metaphysical solvent, as the hypothesis that consciousness is weakly emergent would not resolve the traditional philosophical questions about the physicality of consciousness. However, Bedau concludes that adopting this view would provide a precise notion that emergence is involved in consciousness, and second, the notion of weak emergence is metaphysically benign. 
Strong emergence describes the direct causal action of a high-level system upon its components; qualities produced this way are irreducible to the system’s constituent parts. The whole is other than the sum of its parts. An example from physics of such emergence is water, which appears unpredictable even after an exhaustive study of the properties of its constituent atoms of hydrogen and oxygen. It follows then that no simulation of the system can exist, for such a simulation would itself constitute a reduction of the system to its constituent parts