 The denial of remedial, weaker forms of reductionism is the basis for the concept of emergence (Humphreys 1997, Bedau and Humphreys 2008). Different accounts have attempted to articulate the idea of a whole being different from or more than the mere sum of its parts (see the entry on  emergent properties).  Emergence has been described beyond logical relations, synchronically as an ontological property and diachronically as a material process of fusion, in which the powers of the separate constituents lose their separate existence and effects (Humphreys 1997). This concept has been widely applied in discussions of complexity (see below). Unlike the earliest antireductionist models of complexity in terms of holism and cybernetic properties, more recent approaches track the role of constituent parts (Simon 1996). Weak emergence has been opposed to nominal and strong forms of emergence. The nominal kind simply represents that some macro-properties cannot be properties of micro-constituents. The strong form is based on supervenience and irreducibility, with a role for the occurrence of autonomous downwards causation upon any constituents (see below). Weak emergence is linked to processes stemming from the states and powers of constituents, with a reductive notion of downwards causation of the system as a resultant of constituents’ effects; yet the connection is not a matter of Nagelian formal derivation, but of implementation through, for instance, computational aggregation and iteration. Weak emergence, then, can be defined in terms of simulation: a macro-property, state or fact is weakly emergent if and only if it can be derived from its macro-constituents only by simulation (Bedau 2008) (see entry on  simulations in science).  