A
philosophical term of art, introduced by
Herbert J. Feigl in order to argue against
epiphenomenalism, the doctrine (whose most notable modern practitioner, perhaps, is the eminent philosopher of mind
John Searle, though he might deny it and call his views '
Biological Naturalism') which holds that the mental (or, in plain English, "the mind"), though real, is an
epiphenomenon, a sort of metaphysical excretion, a secondary phenomenon, which is exuded by the complex physical apparati constituting thinking brains.
Epiphenomenalism was, itself, a backtracking from Cartesian substance dualism, which holds that there are two kinds of substances, mental and physical, which interact causally. This has very few adherents in modern philosophy.
'Nomological' means lawlike - in this case, causal laws, not legal ones, are intended - and Feigl points out that in (at least naive) epiphenomenalism, where the mind is caused by physical events but doesn't 'cause them back', the normal two-way attribute of causality is violated, hence mental events, which are caused by, but do not themselves cause, physical ones, must be possessed of the capacity to engage in a strange one-way causality, which is unlike any causality known to physicists.
This lead Feigl to formulate an early and influential version of the Mind-Brain Identity Theory, holding that the physical brain and the mental mind were simply one and the same thing, in preference to the problems of dealing with the mind as a nomological dangler.