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Full Idea
An emergent property of a system is causally explained by elements of the system, but it is not a property of the elements, and cannot be explained by a summation of their properties. The behaviour of H2O explains liquidity, but molecules aren't liquid.
Gist of Idea
A property is 'emergent' if it is caused by elements of a system, when the elements lack the property
Source
John Searle (The Mystery of Consciousness [1997], Ch.1)
Book Ref
Searle,John R.: 'The Mystery of Consciousness' [Granta 1997], p.18
A Reaction
The genie is 'emergent' from the lamp, and so (in Searle's meaning) is the lamp's solidity. I agree that the mind is 'emergent' in Searle's very weak sense, if that only means that one neuron can't be conscious, but lots together can.