A Natural Philosopher’s Lament

The divide between the “two cultures” of the sciences and the humanities is a well-known problem in education. The discipline that we need in order to unify them is natural philosophy.

Natural philosophy, founded by the ancient Greeks, is an all-encompassing wonder at and inquiry into the secrets of nature’s order. Today, those who were once called “natural philosophers” are called by the 19th-century neologism “scientists.” This is because, after the scientific revolution, “scientists” and “philosophers”—the hard sciences and the humanities—parted ways.

This has long been recognized as a cultural and educational weakness. Consider, for instance, C. P. Snow’s famous lecture “The Two Cultures” and the debate it instigated and continues to inspire.

If we are ever to overcome this divide, we must recover the philosophy of nature.

An Educational Jeremiad

In his 2002 essay “A Mathematician’s Lament,” which he later expanded into a book, the mathematician and teacher Paul Lockhart argues that modern mathematics curricula cheat their students out of a full mathematical education. His essay begins with imaginary scenarios in which a music teacher is not allowed to let her students listen to, let alone make, any music. Instead, “music” is a system of sheet notation that students must master by rote. In another scenario, an art teacher is prohibited from teaching art history and the principal techniques of drawing or painting; she is limited to “paint-by-numbers.”

The students in these scenarios do not make any music, nor do they actually paint anything. Analogously, today’s students are not allowed to “make” any mathematics. What Lockhart wishes to highlight is that instead of teaching mathematics as a living art, we teach it as a mechanical set of techniques. The last thing that people want to hear, Lockhart argues, “is that math is really about raw creativity and aesthetic sensitivity. Many a graduate student has come to grief when they discover, after a decade of being told they were ‘good at math,’ that in fact they have no real mathematical talent and are just very good at following directions.”

Lockhart’s comparison of mathematics to art leads him to outline a teaching style that emphasizes students’ guided explorations into the world of numbers and shapes. They are allowed to arrive at mathematical truths on their own, and they even construct beginners’ theorems—much like simple recorder compositions or one’s first self-portrait.

To many, Lockhart’s methods seem more like mathematical “unstruction” than instruction. Even sympathetic reviewers conclude that a balance must be struck between instilling a creative and fruitful love of mathematics in students’ souls and ensuring that they have the requisite mathematical qualifications for higher levels of education. Nonetheless, Lockhart’s lament struck a nerve.

If the Mathematician Can Lament, So Can the Natural Philosopher

A similar problem is found in the sciences and the humanities. Lockhart’s lament presupposes something akin to the ancient Greeks’ distinction between arithmētikē, or the theory of number pursued for its own sake, and logistikē, the art of calculation that is good because it is useful. The one is pure, disinterested love of the truth; the other, a skilled application of true ideas.

In the natural sciences, love and skill can be at odds. Curricula that overemphasize technical competence or STEM-readiness train students in the specific techniques of a given field (i.e., various “parts” of science) without educating them to love knowledge as a whole. They turn out to be all skills and no love. They can pace out intricate waltzes, but they will never enjoy the ball. There is a similar danger for those studying the humanities. For individuals, high schools, or colleges that pursue a classical curriculum and seek out Plato or Aristotle for their logic, ethics, and metaphysics classes, the danger is not reductionism but a form of rationalism.

Recovering classical philosophy is a laudable aim. Yet if these classes are not integrated with classes in the contemporary sciences or the history of science, students risk inculcating a vain love of the whole without a familiarity with any of its parts. Such students are trained to love a game of empty concepts. They are empty because students have not been taught to find those concepts instantiated in the complex natural world around them. They will use terms such as “nature,” “final causality,” or “soul,” but will be strangers to the details supporting and diversifying the use of those names. They love being at the ball—at least at first—but later discover that they have two left feet.

In both cases, students run the risk of developing an intellectual hatred of natural science or of philosophy. They may grow disillusioned with Aristotle’s wonder or Feynman’s pleasure of finding things out. Both extremes must and can be avoided when it comes to education in the sciences and humanities.

Why Natural Philosophers Have Cause to Lament

The compartmentalization of scientific knowledge should invigorate our pedagogical concerns.

Philosopher and erstwhile social constructionist Bruno Latour’s book Science in Action begins with an extended reflection on the stages and strategies of scientific research programs. A concept Latour employs is that of the “black box,” found in scientific or engineering diagrams. A black box is a component of a system too complex for the purposes of the diagram, and which is consequently drawn as a black box, with an input and output, summarizing its role in the larger whole.

Analogously, there are black boxes when it comes to “science in action.” These are ideas that are too complex to reconsider or reevaluate, given an end we have in view. For instance, if our research aims to learn more about a specific protein’s role in pancreatic cancer, we will not reconfirm Linus Pauling’s initial discovery of protein structure. We would not rethink the existence of proteins themselves, doubt their distinction from other organic molecules, or try to reconfirm that their constitutive elements (such as carbon) are truly elements. Instead, we would “black box” these pieces of information. The periodic table of the elements is a—most informative—complex of black boxes.

The progress of science is littered with black boxes—established elements of knowledge—which thousands of people have helped build over thousands of years. If we see further than those before us, it is because we stand on the shoulders of giant mountains of dormant results. To un-box a single box is to recapitulate the exquisite knowledge needed to make that box. To un-box a sufficient number of boxes is to rethink one’s entire scientific discipline. Finally, to educate a student in a modern scientific discipline, a teacher must choose for the student the number of black boxes introduced, partially opened, left closed, or simply ignored.

Therein lurks the problem of compartmentalization. The complexity of the black boxes on which each discipline relies can make it easy to lose sight of the broader, pointillist portrait the sciences paint of nature. A thriving inquiry into nature requires the desire and skill not just to build the black boxes, but to understand why they are needed and how they all fit together. Consequently, it is easy to doubt that a person could actually achieve unified knowledge of nature.

A Dualism in Our Knowledge

The division of labor between science and art grew up with modernity; it is enshrined in the German distinction between the Naturwissenschaften (the natural sciences) and the Geisteswissenschaften (the humanities). If we are to overcome it, we must do more than simply strengthen a dual regime of “Pure STEM and Mere Humanities.”

Why is the compartmentalization of the sciences and their separation from the humanities so bad? Isn’t it the necessary condition for the advanced stage of science “we” have reached? Well, if all knowledge is divided into two parts, who stands outside the division and knows each side? And what sort of knowledge is that? Is there not, therefore, a third type?

Let us call this knowledge that unifies each side—if it exists—philosophia.

In Plato’s Phaedo, Socrates describes his first attempts to discover the causes of things, especially the cause of goodness and order in nature. He recalls how the philosophers he used to read would make much about a “Mind” that guided all the workings of nature, but they never satisfactorily explained themselves. Frustrated, Socrates began to employ a “second-best method,” a “second sailing.” Instead of looking directly at things themselves (which he compares to staring directly at the sun), Socrates turns to find the truth of things as reflected in human speech (like glancing at the sun indirectly in a reflection). He turns away from physics and begins Socratic philosophy. He “[busied] himself about ethical matters and [neglected] the world of nature as a whole,” recalls Aristotle (Metaphysics, I.6).

However, letting such a dualism stand was not part of the original ideal of knowledge. The goal was to find a harmony between the truths discovered by both methods. The heights of philosophical conversation about the good—think of Socrates and the zenith of Plato’s Republic, the image of the Sun—were meant to be joined with the final results of natural inquiry—imagine Aristotle observing life in the lagoon of Lesvos and contemplating its ultimate causes. While both ethics and metaphysics play a role in this unification, one does not begin with ethics and metaphysics when pursuing philosophia. One needs an introduction.

Let us name the needed discipline that introduces us to the unity of human experience and the natural order “natural philosophy.”

Why Education Needs Natural Philosophy

We need natural philosophy because it provides a coherent, if introductory, overview of things. It leads us to nature whole and entire, before we head off into the details of the sciences or humanities.

To see this, consider that the mind requires that, before we begin any particular natural science, we possess two prior types of knowledge: sense knowledge and intellectual knowledge.

The need for the first type of knowledge is fairly clear. Whether it’s physics, chemistry, or biology, the student requires a familiarity with the empirical objects of his study. If we take seriously Goethe’s idea that the experiment serves as mediator between the knowing human subject and the natural object, then we realize that a broad familiarity with nature through personal experience is superior to mere laboratory demonstrations. Students of natural philosophy should imitate the attentiveness of Aristotle or J. Henri Fabre. This more immediate knowledge of nature underlies both science and the humanities; this is clear from Wordsworths “Tables Turned.”

By the need for intellectual knowledge, I do not mean the theories or mathematical laws one finds in introductory science textbooks. As Werner Heisenberg recognized, ordinary language is prior to the technical language of science. We use a common language to describe those features of the natural world that—far from being nature’s secrets—are easily knowable. These ideas are the soil or elements out of which the natural sciences grow. As such, they are present throughout the lifespan of the natural sciences and provide them with a unified philosophical basis.

Natural philosophy helps us to organize and systematically deepen both types of knowledge about nature, before we proceed to study the more specific natural sciences. Its vocabulary, developed from our most fundamental experiences and ideas about nature, is later enriched and strengthened through the details discovered about nature.

Which Natural Philosophy?

Who has succeeded in discovering such a natural philosophy? Do we turn to Hegel? Kant? A combination of what the best scientists propose? Heraclitus redivivus? Whose proposal successfully fills the role of the discipline that introduces us to the unity of human experience and the natural order? Since proposing a candidate and defending it against all comers is too large task a task for this essay, I must make do with an analogy.

There already exists a tradition of natural philosophy, originating with Aristotle and his medieval commentators. Just as a Thomistic natural law theory still defends the fundamental knowledge about which a wide-ranging tradition of jurisprudence and constitutional law has developed, so also this Aristotelian-Thomistic natural philosophy would defend knowledge that is fundamental to the modern sciences. The complexities of the modern sciences and the claims of rival versions of natural philosophy can be addressed by this tradition. Aristotle may yet have his revenge.

If it is needed, then how, exactly, should an Aristotelian-Thomistic natural philosophy shape high-school, undergraduate, and graduate education? That is a longer conversation, for another day.

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