Trivial Pursuits: some thoughts on tools of learning and a new quadrivium

I have been rereading Dorothy Sayers' The Lost Tools of Learning, and thinking about it. Basically, Sayers suggested a modified return to the curriculum of the Trivium: i.e., Grammar, Dialectic, and Rhetoric, so as better to train young children in using these tools of thought to better train the memory, reason, and imagination of these children, and so better prepare them for the life of the mind. That essay is well worth reading, and I think that it could profitably be used as the basis for an education of the young.

I have been thinking, however, that such a training would assist older people who had not obtained a proper education (including university graduates). In consequence, I have been going through my old books and looking to building a curriculum which could help people obtain a remedial education. Rather than simply being concerned with the subject of Grammar, or more particularly, the Grammar of Latin or Greek, however, I would suggest a training in how to assimilate and learn the structure of knowledge of a field of study, including a new language. For dialectic, I would suggest a training in how to use deductive and inductive reasoning. And for rhetoric, in addition to learning how to write or to speak well, I would suggest training how to apply one's imagination to a particular field of study.

One problem that I have seen, however, with the separation of the university into so many subjects, is that there are few who have an ability to understand the sciences, or mathematics, or the arts, or much of anything else. I have long been thinking of a solution, only to find that one has already been made.

Plato, in his Republic suggested the training proper to a philosopher, and began it with a description of the Trivium as stated above: a philosopher should have a grounding in grammar, dialectic, and rhetoric. He thought, however, that there were certain disciplines which helped further to train the mind: arithmetic, geometry, astronomy, and music. He felt that each of these disciplines trained certain aspects of the mind, or soul, and that one who had gone through such training would have the basis for becoming a philosopher, or a lover of wisdom.

The mediaeval universities, founded by people who read Plato and certain neo-platonists, made the Trivium the basis for a primary education, and taught these four subjects as the Quadrivium in their schools.

With the great expansion of knowledge which the Universities brought, however, and the desire to continue such expansion, the secular universities, which changed their focus from the development of the soul of the student to the further inquiry into particular matters, abandoned the Quadrivium, and instead specialized their inquiry into many subjects. While this has greatly enriched the arts and the sciences, it has impoverished most of us, who are unable to contemplate their truths, as few of us have a training in them.

I suggest, however, that one may make a return to the Quadrivium, as a means of obtaining a training of mind and a synthesis of knowledge which would enable an intelligent man or woman to understand and appreciate both the arts and the sciences.

While arithmetic has long been outstripped by developments in modern mathematics, it would be reasonable for a student to have a training in mathematical logic and number theory, and the fields of mathematics which proceed from it: algebra, analytical geometry, calculus, statistics, etc. Such a training would assist one's mind in understanding mathematical reasoning.

Similarly, while modern geometry has progressed far beyond simple two dimensional spatial reasoning and conics, a training in visual thinking, which a modern geometry could facilitate, would also assist as the basis for a study of two and three dimensional arts, such as drawing, painting, sculpture, architecture, etc. Foremost however in such study would be the development of visual thinking.

And while the natural sciences have long gone far beyond the astronomy of Ptolemy, they retain at their base the attempt to create predictive models for their respective subjects, and the application of scientific reasoning in making such models, in physics, chemistry, biology, etc. A training in scientific reasoning, together with a synthetic approach to the formulae (or predictive models) of physics, chemistry, and biology would assist an intelligent mind in more readily understanding what the sciences can teach us.

Finally, while music has progressed far beyond the understanding of monophonic music, nonetheless, a training in understanding melody, harmony, counterpoint, form and analysis, and composition, would greatly assist in developing the hearing mind of the individual.

With such a new Quadrivium, of mathematics, geometrics, natural sciences, and music, there would be an effective synthesis of the arts and sciences, and such an education would assist the individual in a better training of visual, auditory, mathematic, and scientific reasoning.

And while I doubt, as did Sayers, that modern educators would make a use of such either a modern Trivium or Quadrivium, someone in search of a proper education would do worse than to attempt to study such.