Reduction, problems of

Reduction is a procedure whereby a given domain of items (for example, objects, properties, concepts, laws, facts, theories, languages, and so on) is shown to be either absorbable into, or dispensable in favour of, another domain. When this happens, the one domain is said to be ‘reduced’ to the other. For example, it has been claimed that numbers can be reduced to sets (and hence number theory to set theory), that chemical properties like solubility in water or valence have been reduced to properties of molecules and atoms, and that laws of optics are reducible to principles of electromagnetic theory. When one speaks of ‘reductionism’, one has in mind a specific claim to the effect that a particular domain (for example, the mental) is reducible to another (for example, the biological, the computational). The expression is sometimes used to refer to a global thesis to the effect that all the special sciences, for example chemistry, biology, psychology, are reducible ultimately to fundamental physics. Such a view is also known as the doctrine of the ‘unity of science’.