In reality, the two are quite different from each other.
The two terms are sometimes used dismissively, to imply that certain curricula lack rigor or real-world practicality; but note carefully that the Liberal Arts Department in the School of the Art Institute of Chicago offers the following courses: Marine Biology, Mathematical Thinking, and The Physics of Motion.
The Liberal Arts Department at Henry Ford College offers Criminal Justice and Introduction to Homeland Security. The College of Liberal Arts at Temple University includes the Department of Economics and the Neuroscience Program.
The College of Liberal Arts at the University of Minnesota offers full programs in Mathematics, Chemistry, and Physics.
These examples show that the term “Liberal Arts” refers, in its true meaning, to academic disciplines including all the natural sciences and mathematics. What is the logic of this definition? The history of the phrase, as given in the Oxford English Dictionary (2009 edition), explains that it was “originally the seven subjects of the trivium (grammar, rhetoric, and logic) and quadrivium (arithmetic, geometry, music, and astronomy) considered collectively.”
To modern readers, grouping rhetoric in the same category as geometry, and grouping music in the same category as astronomy, might seem odd. But in the medieval educational systems, these content areas were seen to have a common thread: they were considered to be “free” topics, because they were not “in the service of” some vocational or professional training: they were unapplied. Because they were “free,” they were called the “liberal” arts — they enjoyed liberty.
Even today, many post-secondary educational institutions distinguish between “pure” mathematics and “applied” mathematics. Likewise, Biology is one of the Liberal Arts, but Medicine is professional training; Physics is one of the Liberal Arts, but Mechanical Engineering is professional training.
The Liberal Arts are, therefore, investigations into different areas of knowledge — investigations with the goal of gaining knowledge. This is in contrast to being trained for specific tasks: engineering, healthcare, legal work, business.
Under the heading of “Liberal Arts,” one finds learning about nearly any conceivable topic, learning for the sake of learning: education, not training.
What is meant by “the Humanities”?
The word itself gives a clue: the academic disciplines grouped together under the label have this in common — they all involve the experience of being human. They are experiential and therefore empirical. Music, painting, sculpture, and architecture studied by means of sense data: using one or more of the five senses.
History is a collection of individual or shared experiences of human beings in the past. Literature is the experience of writing and the experience of reading, and the study of those experiences.
By contrast, mathematics, e.g., is an a priori investigation, and has no need of specific sense data.
The Oxford English Dictionary explains what people are discussing when they’re discussing the Humanities:
The branch of learning concerned with human culture; the academic subjects collectively comprising this branch of learning, as history, literature, ancient and modern languages, law, philosophy, art, and music.The humanities are typically distinguished from the social sciences in having a significant historical element, in the use of interpretation of texts and artefacts rather than experimental and quantitative methods, and in having an idiographic rather than nomothetic character.
The contrast to the social sciences is helpful: the Humanities tend to deal with concrete and specific examples — texts and artifacts. The social sciences look for patterns and trends which can possibly be formulated as laws — charts and graphs, percentages and equations. The Humanities might study, e.g., the American Revolution, the French Revolution, and the Russian Revolution. The social sciences might study a generic description of the social dynamics which are associated with revolutions.
‘The Humanities’ is sometimes used in second sense, which is slightly narrower, according to the OED:
Literary learning or scholarship; secular letters as opposed to theology; esp. the study of ancient Latin and Greek language, literature, and intellectual culture (as grammar, rhetoric, history, and philosophy); classical scholarship.
It is clear that the Humanities and the Liberal Arts are two different and distinct groups of topics.
Thus the true definitions of the phrases. But common speech rarely honors precise exposition, and thus the current confusion and sloppy usage.
The definition in the OED notes that “in later use more generally,” the Liberal Arts are assumed to be “arts subjects as opposed to science and technology.” It goes on to note that this usage is “now chiefly North American.”
By analyzing how such words are defined and grouped, readers can develop an intellectual apparatus which can organize educational institutions.