In “History and Natural Science” (1894), the neo-Kantian Wilhelm Windelband (1848-1915) proposes a distinction between the study of
the general in the form of the natural law ["nomothetic" sciences] or the particular in the historically determined form ["idiographic" sciences]. They consider in one part the ever-enduring form, in the other part the unique content, determined within itself, of an actual happening. The one comprises sciences of law, the other sciences of events; the former teaches what always is, the latter what once was. (Theory and Psychology 8.1 : 13 [5-22; subscription required], orig. “Geschichte und Naturwissenschaft,” in Praeludien, vol. 2 [Tübingen, 1915] 136-60)
The nomothetic approach to knowledge draws on our tendency to generalize, and is expressed in the natural sciences. It describes the effort to derive laws that explain objective phenomena. (“Nomothetic” f. Gk νομοθετικός, from νομοθέτης nomothetēs “lawgiver,” from νόμος nomos “law” and the root θη- thē- “posit, place, lay down,” thus “legislative [lit. law-giving].”)
For example, nomothetic psychology studies what we share with others, i.e., the quantifiable properties of the cohort.
It is a Platonic (otherworldly, supersensible, Realist) approach, applying ideas to things. Plato the philosopher-king legislates.
It can go wrong, hence the nomothetic fallacy: the belief that naming a problem (or group or phenomenon) effectively solves it (or captures its essence).
The idiographic approach to knowledge draws on our tendency to specify, and is expressed in the social sciences (or humanities). It describes the effort to understand the meaning of contingent, accidental, and often subjective phenomena. (“Idiographic” f. Gk ιδιος-γραφιχος, from ídios “personal, peculiar, particular” + graphikós “written, drawn,” thus “describing the particular.”)
For example, idiographic psychology wants to discover what makes each of us unique, i.e., the distinctive qualities of the individual. Aristotle the scientist discovers.
It is an Aristotelian (worldly, sensory, naturalist) approach, finding ideas in things. (This Platonic/Aristotelian distinction is something of a hasty generalization, of course: with his inductive method, Aristotle is also a generalizer—and the mentor of natural science. But he does start from things rather than ideas.)
See Earl R. Babbie, “Idiographic and Nomothetic Explanation,” The Practice of Social Research, 12th ed. (Cengage Learning, 2009) 21-22.