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I constantly see evidence that people are confused about phrases like “the liberal arts,” the “arts & sciences,” and “the humanities.” Although some of my definitions may be controversial, I thought a lexicon might be helpful:
The liberal arts encompass the natural sciences, the social sciences, and the humanities. These disciplines are meant to be valuable irrespective of their utility as preparation for careers. The root meaning is that they are appropriate for a gentleman or -lady. In the middle ages, it was common to list seven liberal arts, often the following: music (which was really music theory), arithmetic, geometry, astronomy, grammar, logic, and rhetoric. The last three were about language, whereas the first four were about nature. Philosophy and theology were sometimes substituted or added to the list, and philosophy has subsequently given rise to a range of liberal arts, from anthropology to zoology.
The phrase arts & sciences seems to be synonymous with liberal arts but avoids the modern implication that the “arts” exclude the sciences.
The humanities involve the interpretation of human culture. Interpretation generally takes the form of insightful description, whether organized over time (as narrative) or across space, but the humanities also encompass theorizing about human culture and applying such theories. By this definition, the humanities encompass the study of literature, music, and the arts. They also include portions of history (cultural history and historical narrative), anthropology (qualitative cultural anthropology/ethnography), political science (normative political theory), and philosophy (history of philosophy and some approaches to ethics and political philosophy). Many would disagree, but I believe that the rigorous moral assessment of human phenomena is intrinsic to the humanities, whereas science claims to separate facts from values.
The social sciences investigate the human world in ways analogous to the natural sciences, meaning that they generally seek to classify, model, and/or explain human phenomena. So a historian who tells the story of Boston’s development is a humanist, but a historian who tries to model the causes of urban growth is a social scientist. The social sciences can be primarily qualitative, quantitative, or theoretical. The line between the humanities and social sciences cuts through departments; the criterion is whether the research is analogous to natural science.
The behavioral sciences do not seem to me sharply distinguishable from the social sciences, but they put human mental states (such as choices and responses) at the center, as opposed to social systems and processes. They tend to employ the elaborate toolkit of empirical psychology rather than other methods.
The arts (in the context of a university) involve the actual production of cultural products, from ceramics and paintings to dance performances and music.
The natural sciences investigate nature, sometimes including human beings as natural species. They thus encompass not only mathematics, physics, chemistry, biology, and their offshoots but also some forms psychology, anthropology, and philosophy.
Engineering, computer science and related fields do not investigate nature but rather aim to change nature through deliberate interventions.
The professional disciplines aim to understand and teach the techniques, ethics, and underlying principles applicable to particular socially constructed professions, ranging from those that are strictly licensed (e.g., medicine and law) to those that are more loosely and informally defined (business, journalism).