...can anyone set out clearly what emergence is? — Banno
On my view
emergence makes the most sense when used to refer to a naturally occurring(evolutionary) process that began long before language use emerged.
Consider a specific example of knowledge...
It is only from the recognition of causality, that a capable language-less creature will learn and thus come to know that touching fire causes pain. A creature incapable of attributing meaning to the behaviour and the fire will avoid the danger nonetheless, because fire damages biological material regardless of whether or not the biological entity in question is capable of acquiring the aforementioned knowledge in the aforementioned way. So, to be clear, avoiding the danger does not always require knowing that touching fire causes pain. Very simple biological organisms do it just fine despite not having what it takes to correctly attribute causal relations between different things.
Emergence is
how the recognition of causality
results in knowing that fire hurts when touched. Knowing that fire hurts when touched emerges from correctly attributing(recognizing) the aforementioned causal relations.
Knowledge of biological machinery and physics results in knowing how fire hurts when touched.
Emergence is what's going on when such knowledge is
being formed.
Knowing that fire hurts when touched - as set out directly above - is existentially dependent upon more than just the fire and the biological creatures' behavior regarding that fire. The knowledge is not contained within, nor possessed by
merely the elemental constituents, nor is such knowledge possible without all of them. Without the fire, the behaviour cannot happen. Without the behaviour, the attribution of meaning cannot happen. Without the attribution of meaning, the knowledge cannot be formed/acquired. Without the capable creature, the meaningful attribution of causality cannot happen. Without the meaningful attribution of causality, the formation/acquisition of that bit of knowledge cannot happen.
Other notably emergent things include truth(all senses of the term) and meaning(all senses of the term).
Of course, although I'm not certain, I would strongly suspect that not much of this, if any, aligns with current academic notions of "emergence".
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Earlier you asked what the difference was between emergence and 'backwards reduction', or something to that affect/effect. Why does that question matter to you? Keep in mind what I just roughly outlined above.