Aquinas: The Construction of the Sciences

The Philosophical System of Thomas Aquinas, by Maurice de Wulf, edited and adapted for the web by Jonathan Dolhenty

XVI. The Construction of the Sciences

A. Logic as a teaching method, and as a branch of philosophy

Thomas asks whether logic is an art or a science, and comes to the conclusion that it is both.

The thirteenth century, in fact, considered logic as an art and retained the practice of exercises in logic. At the universities of Paris and Oxford, students were trained in the analysis of syllogisms, the refutation of sophisms, and the discussion of arguments for an against a given thesis. This kind of logic, which the early Middle Ages placed among the seven liberal arts under the name of Dialectica, is not strictly speaking a branch of philosophy.

But, side by side with this instrumental logic destined to discipline the mind, as athletic exercises train the muscles, the philosophers of the thirteenth century recognize and cultivate a philosophical logic which consists in a study of the architecture of human knowledge or of the methods adopted by the mind in the construction of the sciences, whether particular or philosophical. In this meaning of the term, logic itself is a science. It takes as its subject matter the whole content of knowledge, in order to study the laws which govern its coordination, synthesis, and systematization; and just as knowledge reaches an objective reality, logic too, in the final analysis leads us to truth and to certitude. We may say that in the realm of their logic, the Schoolmen not only followed but also completed Aristotle.

B. Judgment

The most elementary construction of knowledge is the judgment, or the perception that a content of representation (for instance, ‘white’) applies or does not apply to another (for instance, ‘snow’). It consists in the union or disunion of the two contents of representation (II, D).

Science has to do with only one kind judgment, the necessary and universal judgment, known as a ‘law.’ Scientia non est de particularibus. — Science has nothing to do with particular cases, or mere ‘atomic propositions.’ The logical law, or judgment, may be dependent upon, or independent of experience. Accordingly, it is included in one of the two classes of judgments which we have called above judgments of the existential and of the ideal order (IV, B).

Let us consider each of these classes in more detail.

(a) With judgments of the ideal order, we are confronted with the process of pure deduction. An understanding and a comprehension of the subject and the predicate are sufficient in making the necessity of their connection evident, — just as in order to affirm the principle of contradiction it is enough to understand the meaning of being and non-being.

Mathematical judgments are of this sort; and the only difference between these and the directing principles of knowledge is that the latter are the foundation of all affirmation, whereas mathematical judgments relate only to a special field, namely quantity.

Moreover, the judgments of ideal order with which mathematics is concerned belongs to the same two types which we already discussed in connection with the directing principles. Thus mathematics comprehends

  • Judgments in which the subject considered in its essential elements includes the predicate, as for instance, 2 + 2 = 4.
  • Judgments in which the predicate is not included in the subject, although a comparison of the content of both is sufficient to make the necessity of their connection evident. That every number is either odd or even, remarks Thomas Aquinas, is a judgment belonging to that second type. The content of odd or even is not comprehended in the notion of number, but from the mere comparison of both it appears that being odd or even is a necessary property of every number.

(b) With the judgments of the existential order, we are confronted with the process of induction. A comprehension of the meaning of chlorine and oxygen is not sufficient to reveal the law governing their combination. Observation and experiences are needed in order to discover how they react to one another; and the law is obtained by applying to observation and experience such directing principles as those of sufficient reason and causality. For, these two principles justify us in concluding that the convergence and constancy of observed phenomena (as for instance the boiling of water under the action of heat) can only be explained by reference to a tendency on the part of the substance to act in a particular way, a tendency which is stable, and rests upon the nature of the thing in question (thus it is of thenature of water to boil at 100 degrees C.). The Schoolmen did not study the methods of experiment with care and detail. This was only to be expected, seeing that the experimental sciences were in an undeveloped state in those times. But we already find among them — notably John Duns Scotus, who flourished a few years after Thomas — a keen analysis of the methods of induction, or the ways by which we may pass from the observation of particular cases to the law which governs all.

C. Reasoning

A process of reasoning is itself a system of judgments, since it consists in passing from judgments already known to another less known or not known at all. The syllogism, which is the simplest expression of reasoning, consists of three judgments. It starts out from the enunciation of a law, or of a necessary relation, based upon the nature of things (for instance, “it is of the nature of a spiritual being to be simple, i.e., without parts”), and proceeds to show that this law applies to all or certain beings seen to be comprised under the extension of the law (for instance, “the human soul, belonging as it does to the category of spiritual beings, is endowed with simplicity”). The law, which is the foundation of the syllogism, belongs to either class of judgments, as it is dependent upon or independent of experience. The result of a syllogism is a new judgment, so that the judgment is the unit of logical construction, with which all knowledge begins and ends.

D. Scientific systematization and its methods

1. First principles of each science.

Isolated reasonings could not make a science. In their turn they are connected together like the links of a chain: each finds its justification in a previous inference. But there must be a beginning to the process, — there must be something from which the whole chain may hang. An infinite regression would render all knowledge impossible.

There are therefore at the base of each and every science certain indemonstrable judgments, known as the first principles of the science in question. They formulate certain very simple and evident relationships, and are derived from the subject matter of the science. Their enunciation may or may not presuppose observation, according to the nature of the subject matter of the science. Thus that 1 + 1 = 2 is a principle of arithmetic; that the group life is for the sake of the individual members is a principle of social science. These principles, which do not admit of further definition or demonstration, constitute the limits and boundaries of each science. They consist generally of ‘definitions,’ inasmuch as they make clear what is the object studied by each particular science. We see, then, that besides the governing principles of all knowledge which are common to every science, like the principle of contradiction, each science has its own fundamental principles [1].

2. Material and formal object of each science.

The numerous reasonings which go to make up a science, together with its definitions and the first principles which constitute its basis, for one coherent whole, a unified system. The unity which runs through the whole, and is more or less evident according to the importance of each section, depends on the ‘formal object’ of the science. What does this mean?

The Schoolmen point out that in every science there is room to distinguish between the things themselves which are studied — the raw material of the science, its ‘material object’ — and the point of view, or aspect from which these materials are considered (‘formal object’). For example, the human body is the material studied by physiology, but this only considers it from one point of view, namely, that of the functions exercised by its organs. This point of view is grasped as a result of abstraction, so that abstraction (II, C) is the generative process which underlies all science.

Every reasoning or principle must express in some way the formal object of the science in question. Thus in physiology, every doctrine ought to be concerned with the functional role of organs. It is the ‘formal object’ which gives each science its distinctive character, and makes it what it is, — hence the designation of formal object [2]. Whence it follows, that two sciences may possess the same subject matter, may have the same ‘raw material,’ but unless they are to be identical, each must study this material from a distinct and separate point of view. Thus anatomy also studies the human body, but from the point of view of its structure. If it were to concern itself with functions, it would trespass upon and identify itself with physiology, and one or the other would have to disappear.

Thomas applies this theory of the specification of sciences to philosophy and theology, which have to some extent the same material object, but of which the formal points of view are quite distinct. “A difference in the point of view from which the mind contemplates the object entails a diversity in the branches of knowledge (diversa ratio cognoscibilis diversitatem scientiarum inducit). The astronomer and the physicist both may prove the same conclusion, — that the earth, for instance, is round: the astronomer by means of mathematics (i.e., abstracting from matter), but the physicist by means of matter itself. Hence there is no reason why those things which may be learned from philosophical science, so far as they can be known by natural reason, may not also be taught us by another science so far as they fall within revelation. Hence theology included in Sacred Doctrine differs in kind from that theology which is part of philosophy” [3].

This justifies what we said at the beginning, that scholastic Philosophy is quite different from scholastic Theology, despite the relation between them, of which there will be made a brief mention toward the end of this work.

On these notions of the formal and material object, the scholastics rest their classification of the sciences whether particular or general, i.e., philosophical, and their division of philosophy (XVIII).



  1. Scheme of scientific judgments. If we bear in mind that there are two types of judgments, namely judgments of the ideal and of the existential order (IV, B), and that the first type includes two classes, we may establish the following scheme of judgments which are involved in any science.

A. Axioms, relating to all being, and common to all the sciences: these are judgments of the ideal order, especially of the second class.

B. Judgments proper to certain sciences.

  • 1. Deductive sciences: judgments of the ideal order (both classes). They are either (a) the fundamental principles of the science in question; immediate and self-evident judgments (example, 1 = 1). (b) mediate, or calling for demonstration, e.g., the complicated theorems of geometry.
  • 2. Experimental sciences: judgments of the existential order. (a) immediate or self-evident, e.g., “I think, therefore I exist.” (b) mediate, e.g., “water boils at 100 degrees C.”
  1. In formal, we find the determination, which belongs to the forma.

3. Summa Theol., Ia, q. 1, art. 1.

The late Dr. Jonathan Dolhenty was the Founder and President of The Center for Applied Philosophy and the Radical Academy, and is Honorary Philosophy Editor at The Moral Liberal. The Moral Liberal has adopted these projects beginning with a republishing and preserving of all of Dr. Dolhenty’s work.