The Liberal Arts are first in the order of learning. The objects of these seven arts are constructed within the intellect, not outside, as are the objects of the technical arts. The carpenter’s house, the health of the doctor’s patient, and the republic fashioned by the statesman all exist apart from the mind; the objects of the liberal arts do not. The principles proper to these arts are formally studied in tutorials.
Three of these arts — grammar, rhetoric, and logic (the trivium) — concern themselves with the ways in which we naturally order our thoughts and express that order in speech. Hence these arts are concerned with words and the various forms of verbal expression such as sentences and their grammatical parts, the various forms of logical argument, and so forth.
The four remaining liberal arts (the quadrivium: arithmetic, geometry, astronomy, and music) are all mathematical and concern themselves not with the tools of thought itself, but with things which come first in the order of contemplative learning. Mathematics — etymologically the “learnable things” — has long been understood as essential to the early part of a philosophical education
As they discover the beautiful intelligibility of mathematical beings, students are also led to cultivate intellectual discipline, a sense of wonder, and a character predisposed to the love of order and beauty.
Syntax, or the relations of grammar, are the mental constructs closest to words themselves. Latin is the means through which the rules for this art become explicit. It is a highly inflected language, illustrative of the nature of grammar. Often one comes to understand his own tongue best through the study of a foreign language; by comparison and contrast, moreover, he sees what is common between them and essential to language itself. A knowledge of Latin for the study of theology, philosophy, and the classics is itself worthwhile.
The art of grammar is a means of signifying concepts and the relations of reason. The ultimate work of reason is to produce proofs or arguments, and these are of two kinds: those calculated to persuade and those meant for philosophic or scientific demonstration.
The art of rhetoric treats the first, and logic or dialectic the second. “Rhetoric,” says Aristotle, “is a counterpart of dialectic.” These are coordinate but contrasting arts and are naturally and profitably studied together. The Logic Tutorial lasts through the freshman year and, together with grammar in the Language Tutorial, completes the trivium.
Since language and logic extend to all subject matters, they represent the necessary and universal instruments of all science. In this way the trivium, logic especially, stands as the first and introductory part of the philosophy sequence.
The four remaining liberal arts (the quadrivium) are mathematical in character. Two — geometry and arithmetic – are pure mathematics, while in astronomy and music one discovers the mathematical beauty and order of the cosmos and the human soul. In astronomy students witness the role of artfulness in human contemplation as they examine the great astronomers’ application of geometry to the heavenly motions. In music, likewise, students discover and contemplate the wonderful, moving patterns of numbers and ratios in both the soul and in physical sounds themselves.
The Mathematics Tutorial, which includes the study of pure mathematics (beginning with the Elements of Euclid) and the study of astronomy (beginning with the Almagest of Ptolemy), follows the developments of these parts of the quadrivium up to modern times. The writings of Copernicus, Einstein, Descartes, Lobachevski, and other such masters make up the sources. Here one sees the “modern mind” evolve. (See Why We Study Mathematics, by Dr. Brian T. Kelly.)
The remaining part of the quadrivium is studied separately. The philosophers of antiquity recognized the hearing and making of great music — especially vocal music — as a necessary part of the acquisition of good character and an important preparation for a well grounded study of ethics. The theoretical study of music follows this preparation; through it one discovers the inner mathematical structure of music and what may be called its audible syntax, and music’s power to manifest beauty and move the heart is explained. Like the arts of the trivium, music also has its own special notation, which must be learned as well. Because of music’s kinship with moral philosophy, these are studied together in the junior year.
Philosophy begins with what is best known and most known to us, namely, the sensible world. This is the subject of the second-year tutorial. Texts of primary significance include the writings of the pre-Socratic philosophers, the Physics and the treatise On the Soul by Aristotle. The questions in these texts are reconsidered as they appear in the study of mathematical physics in the Mathematics Tutorial, and as they arise in the various experimental science laboratory discussions
Moral philosophy, which follows, concerns human action. This study depends upon natural philosophy and, like it, deals with objects we directly experience — but they are less intelligible, because of their contingent character. For this reason it requires more experience. Aristotle’s Ethics and Politics are of particular interest. The contrasts of modern moral and political thought are carefully studied.
Metaphysics or natural theology, which also depends upon natural philosophy, treats of divine things and is studied in the senior year. These are the richest objects of the intellect, but the most difficult for us to know. Supernatural reality is demonstrated through natural philosophy and is understood by analogy to natural things. Though these divine things are remote from us, they are the most worthy of our efforts to know them.
St. Thomas points out that “almost all of philosophy is directed toward the knowledge of God, and that is why metaphysics, which deals with divine things, is the last part of philosophy to be learned.” Philosophy brings us naturally to sacred theology, which elevates and illuminates our minds with regard to the Supreme Being. Philosophy also supplies naturally knowable truths that serve as principles by which revealed truth may be more fully understood — it is the handmaiden to theology. The intellectual aspirations that liberal education pursues carry the believer naturally to sacred theology and find their fulfillment in that subject. Sacred Scripture occupies the first year, the Fathers of the Church are studied in the second, and the last two years focus on the principal doctrines and mysteries of the faith — studied chiefly through the writings of St. Thomas Aquinas.
Two kinds of experience form the basis for natural science. One is the spontaneous, inescapable experience common to all men, which produces a certain, but somewhat indistinct and general, knowledge of nature. It is here that natural science begins. The Treatises on natural philosophy view nature in the light of this experience. But most of the differences among natural things require a more particular experience.
Experimentation seeks such experience. It submits objects to close observation, alters them in order to turn up distinguishing characteristics, and measures their response to its questioning. Such experimentation, if it is scientific and not merely random, occurs in a context of a theory about the natural world, or else grows out of questions which arise from some view of the world already possessed.
Mathematics has also played a role in theories about the natural world since the time of Ptolemy and Archimedes. In the modern era, experimental science has striven to be as mathematical as possible. This is understandable, since mathematics gives a kind of intelligibility to the world, and the human mind, while capable of grasping certain general truths about nature without such theories, is unable to understand the finer details on the basis of observation alone. The mathematical approach to nature is seriously limited, however, in that it does not attain the natural as such.
Accordingly, the mathematical approach to science (whether modern or ancient) must be balanced with studies which concern the proper principles of natural things. In part, this balance is achieved through the philosophy tutorials. General inquiries of this sort are also appropriately carried out within the Science Tutorial, as the students are led to reflect on particular theories. In the first year, therefore, experimental biology is approached through natural history — that is, through the observation of living things as they are actually living and functioning in their natural environment. Knowledge of the living gives us our primary insight into the sphere of the non-living. After a brief consideration of the theory of measurement, chemistry is taken up next, leading to the classical atomic theory. In subsequent years, rational mechanics, optics, electromagnetism, and relativity theory are studied. Texts by such scientists as Linnaeus, Lavoisier, Galilee, Newton, Huygens, Faraday, and Maxwell are supplemented by laboratory sessions. The Science Tutorial is coordinated with the progress of the Philosophy and Mathematics Tutorials.
A variety of topics make up the Seminar. There are many works of literature that contribute to the intellectual life, not in purely intellectual terms, but by an appeal to the imagination or by moving the affections. At the same time, these works often present or imply important “world views” in a way that is often more accessible to the young than are works of pure philosophy. There are other works worthy of study. History, as well as fiction, supplies the student with valuable experience not available to him in his own life. Many philosophical and theological works of primary historical importance are also included in the reading program. Writings such as these make up the materials used in Seminar discussions. In these discussions the students are largely responsible for conducting the discourse along relevant lines. Evening scheduling permits discussions to continue beyond the usual class period if need be.
The Seminar is also coordinated with other parts of the curriculum. For example, the works of poetry read for the Seminar are discussed in relation to grammar, rhetoric, and logic, since poetry, too, is a mode of discourse and type of argument. Other readings are related to logic and philosophy. The histories used in the Seminar give rise to questions about the nature of historical knowledge. Similar questions may be asked about the social sciences, instances of which are also read in the Seminar. The philosophical and theological poetry or literature read is, of course, pertinent to the Philosophy and Theology Tutorials
History and Social Science
The uniform curriculum of Thomas Aquinas College does not include distinct parts devoted to history and the social sciences. When one considers that these subjects are often prominent in contemporary humanities programs, this fact may be puzzling. No college can claim to complete a student’s education, nor should it claim to teach all things. It ought to assert that it will teach him what is first and fundamental. Histories by such writers as Herodotus, Thucydides, Plutarch, Gibbon, and Tocqueville are read. However, the discussions they provoke are not limited merely to an interest in historical fact. These discussions, for example, may involve an analysis of the assumptions used by the writer in establishing and evaluating historical events. The value of reading history will always depend upon the quality of the reader’s general understanding of reality. History itself will not make a well-ordered mind, but the cultivated intellect will profit greatly from the study of history.