Also known as reduction function, it is a law (or set of laws) connecting the predicates of the reduced theory (the theory to be reduced) with the predicates of the reducing theory (the theory to which the first is reduced). First introduced by Ernest Nagel (1901-1985) as a means of integrating different levels of organization in a supratheoretic system and thus a step toward achieving the unity of science (i.e., a Theory of Everything). He held that one theory could be reduced to another if it was possible to logically derive the first from the second, together with bridge laws. One claim for a bridge law that has been made is self-organization, something that is evident at all levels of organization. Under restricted circumstances, Nagel’s approach has been shown to work, as in the case of reducing the theory of optics to the theory of electromagnetic radiation (viz., light waves are electromagnetic waves). In other instances it has not as, for example, with regard to attempts at reducing classical thermodynamics to statistical mechanics, because the latter does not contain any non-statistical features that relate to temperature. Attempts to find bridge laws between psychology and neuroscience has so far not been achieved in a convincing manner, except perhaps with the concept self-organization. All told, today there is very little adherence to searching for bridge laws, except perhaps within restricted domains of physics. One alternative proposed is to start with analogies and then to see if they can be worked up to the status of bridge laws. Certainly, analogies offer a better departure point for establishing interdisciplinarity than do bridge laws.
See Analogy (as trope), Classical thermodynamics, Deductive-nomological (D-N) model, Interdisciplinarity, Laws, Levels of analysis, Levels of organization, Neuroscience, Psychology, Reductionism, Self-organization, Theory of Everything (ToE)