The Division and Methods of the Sciences

Overview

About a hundred and ten pages, drawn from a much larger work, Aquinas’s early commentary on Boethius’s short treatise De Trinitate, written probably between 1257 and 1259, while Aquinas was a young master teaching in Paris. The full commentary addresses Boethius’s brief and difficult text on the Trinity question by question, but two of those questions, the fifth and sixth, stand apart from the rest in subject matter, turning not to Trinitarian theology directly but to a foundational question in epistemology and the philosophy of science: how is human knowledge properly divided into distinct disciplines, and what method suits each one? These two questions circulate independently under the title The Division and Methods of the Sciences because they form a coherent, self-contained treatise on their own.

The occasion for this digression is a line in Boethius’s own text, where Boethius briefly mentions the threefold division of theoretical or speculative philosophy into natural science, mathematics and theology. Aquinas takes this passing remark as an opportunity to work out, at far greater length and with far more precision than Boethius himself provided, exactly why the sciences divide the way they do and what grounds that division.

Coming early in Aquinas’s career, before the great synthetic works like the Summa Theologiae, this text shows him working out, carefully and from first principles, the epistemological architecture that his later and more famous writing would simply presuppose.

The argument

Question five: how the theoretical sciences divide. Aquinas begins from Aristotle’s basic distinction between practical knowledge, oriented toward action, and speculative or theoretical knowledge, oriented purely toward understanding for its own sake. His concern in this question is with the internal division of theoretical knowledge specifically: why are there three theoretical sciences, natural philosophy, mathematics and metaphysics, rather than one, or five, or some other number?

His answer rests on a theory of abstraction, a technical but genuinely elegant piece of analysis. Any object of theoretical knowledge can be considered in relation to matter, physical stuff, and motion, change, in three possible ways.

Natural philosophy, physics in the broad Aristotelian sense, considers things that depend on matter and motion both for their actual existence and for being properly understood at all. A natural thing, a living body, a physical element, cannot even be correctly defined without reference to the matter it is made of, because being made of that kind of matter is part of what the thing essentially is.

Mathematics considers things that depend on matter for their actual existence, since numbers and shapes as instantiated in the world exist only in material things, but that do not depend on matter for being understood, since the mathematician can define and reason about a triangle or a number without any reference to what particular material the triangle happens to be drawn in or the number happens to be counting. This is the technical sense in which mathematical objects are said to abstract from matter while remaining tied to it in existence.

Metaphysics, which Aquinas, following the tradition, also calls divine science or first philosophy, considers things that depend on matter for their being neither in the natural nor in the mathematical way, extending to what can exist entirely apart from matter, being as such, substance as such, and ultimately God, considered not as an object of faith but insofar as reason itself can arrive at knowledge of a first, immaterial cause of all things.

Aquinas is careful to argue that this threefold division tracks genuinely distinct sciences rather than one science studied from three different angles or under three different names. His principle is that a science is properly individuated by its formal object, meaning the specific aspect or mode under which it considers its subject matter, not simply by the material things it happens to discuss, which is why, for instance, natural philosophy and mathematics can both, in some sense, discuss the same physical body, the one considering it as a changeable material thing, the other considering only its quantifiable, measurable aspect, and yet remain genuinely different sciences because they consider that body under formally different aspects.

Question six: the proper method of each science. Having established the division, Aquinas turns to how each of these sciences ought to proceed, and whether the human mind, employing reason on its own, can attain direct vision of God in this present life.

He distinguishes reason, the discursive movement of the mind from one thing already known to another not yet known, from intellect, the more immediate, non-discursive grasp of a truth all at once. Different sciences, he argues, rely on these two capacities to different degrees and require different combinations of imagination, sense-derived images, and abstract reasoning depending on how far their object stands from matter.

The question’s most pointed and consequential article asks directly whether the human mind, in this life, through the exercise of natural reason alone, can see the divine essence, God’s own inner nature, directly. Aquinas answers no, and grounds the denial in a specific claim about how human cognition actually works in its present embodied condition: because the human intellect, joined as it is to a body, naturally and necessarily operates by turning to phantasms, images derived ultimately from sense experience, it cannot in this life attain the kind of direct, non-mediated vision of a purely immaterial reality that seeing the divine essence would require. Whatever knowledge of God natural reason can achieve in this life is achieved indirectly, by reasoning from effects, the created world, back to their first cause, never by direct intellectual vision of that cause itself. Direct vision of the divine essence, the beatific vision, is reserved, on Aquinas’s broader theological view, for the next life, and requires a supernatural elevation of the intellect’s ordinary natural capacity.

This conclusion sets a firm and consequential boundary around what unaided natural philosophy and metaphysics, however rigorously pursued, can actually deliver, and it is one of the clearest statements anywhere in Aquinas of the systematic limit he places on natural reason relative to what revealed theology, resting on faith rather than demonstration, can offer instead.

How to read it

Read question five first and slowly, working through the threefold division of natural philosophy, mathematics and metaphysics with a concrete example in hand for each, a living animal for natural philosophy, a triangle for mathematics, being or God for metaphysics, and testing Aquinas’s abstraction theory against each example as you go.

Notice that Aquinas’s criterion for what makes sciences genuinely distinct is not simply what they talk about but the formal aspect under which they consider it. This is a recurring and important move in scholastic thought generally, and seeing it worked out clearly here, in one of its clearest and most compact statements, makes it easier to recognize when it appears elsewhere in Aquinas’s writing.

Read question six for the argument about the limits of natural reason regarding direct knowledge of God, and pay attention to exactly why Aquinas thinks the human intellect’s dependence on sense-derived images rules out direct vision of a purely immaterial reality in this life. The argument is more specific and more carefully grounded than a general claim that God is simply too great for the human mind to grasp.

Read this text alongside Aquinas’s commentary on the Posterior Analytics if you want the fuller picture of his theory of scientific knowledge. That commentary addresses what makes reasoning within any given science genuinely demonstrative and certain; this text addresses how the sciences themselves come to be distinguished from one another in the first place, and together they give a much more complete account of Aquinas’s epistemology than either provides alone.

Keep the occasion in mind: this is technically a digression within a commentary on Boethius’s treatise on the Trinity, written by a young Aquinas working out foundational questions before turning to the specifically theological material the commentary was ostensibly about. Reading it as free-standing epistemology, which is how it is almost always read now, loses nothing important, but it is worth knowing the text did not start out as an independent treatise.

Questions it raises

• Is Aquinas’s theory of abstraction, that sciences divide by their degree of independence from matter, still a useful way of distinguishing disciplines, or has the growth of modern interdisciplinary and applied science made the division harder to sustain?
• Does individuating sciences by their formal object, rather than by their subject matter, successfully explain why two disciplines that study the same physical things can nonetheless be genuinely different sciences?
• What follows for metaphysics if its central claim, that reason can arrive at knowledge of an immaterial first cause, is correct but direct vision of that cause remains permanently unavailable to natural reason?
• Is Aquinas’s argument that the intellect’s dependence on sense images rules out direct vision of God in this life a good argument, or does it merely restate the conclusion as a premise?
• If metaphysics considers what does not depend on matter at all, how does Aquinas avoid metaphysics collapsing entirely into theology, given that God is its ultimate object?
• What would change in this account of the division of the sciences if it had to accommodate disciplines, like biology or psychology as currently practiced, that did not exist in anything like their modern form when Aquinas was writing?