Multiple realizability is a key issue in debates over the nature of mind and reduction in the sciences. The subject consists of two parts: multiplicity and realizability. "Multiplicity" designates variability in the mechanism and materials from which a particular type of thing can be made. "Realizability" designates a specific relation that exists when there is the stated variability.

Realizability

Apart from the broad folk notion of realization meaning that a thing is made real, philosophers apply several technical notions of realization to paradigm cases such as computational states realized by engineering states, minds realized by brains, and persons realized by their bodies. The technical notions fall into three broad traditions: mathematical, logico-semantic, and metaphysical.

The mathematical tradition equates realization with a form of mapping between objects. Generally speaking, x (mathematically) realizes y because elements of y map onto elements of x. The notion is useful for...