This lesson is from Bachhuber, Andrew H., S.J. 1957. "Chapter 16: The Definition of Logic by Its Formal Object," An Introduction to Logic. New York: Appleton-Century-Crofts, Inc. Pp. 306-10.
In Chapter 1 we gave a preliminary definition of logic as the science and art of correct thinking. In the present chapter we shall consider logic from another point of view and define it in terms of its formal object.
First we shall treat of the differentiation of the sciences by their formal objects. Then we shall apply to logic what we have said about the sciences in general.
One act of knowledge differs from another act of knowledge because it is knowledge either of a different thing or of a different aspect of the same thing. For instance, our knowledge of a walrus is different from our knowledge of a triangle because a walrus differs from a triangle; and the knowledge a stonecutter has of a stone differs from the knowledge a geologist has of the same stone because each considers a different aspect of the stone.
Sciences differ from one another in the same two ways: either they consider different kinds of things, or they consider different aspects of the same things. Thus, theology differs from anthropology in the first way, because the subject matter of theology is God, whereas the subject matter of anthropology is man. Anatomy differs from biochemistry in the second way: both consider living organisms, but under a different aspect.
The things a science considers—that is, the things as they are in themselves together with all their attributes—constitute its material object. Many sciences can have the same material object (or general subject matter); but each distinct science considers a distinct and special aspect of its material object. This special aspect is called the formal object of the science. Both anatomy and biochemistry, for instance, have the same material object, for both of them investigate living organisms; but they differ in their formal objects, for anatomy investigates the structural make-up of living organisms, whereas biochemistry investigates the chemical changes that take place within them. In their formal objects no two sciences are alike.
Differences in their objects, especially in their formal objects, are the most basic differences among the various sciences. The differences in method, in the nature of the laws they formulate, and in the kind of certainty they attain spring principally from the differences in their formal objects. For this reason the best way to define a particular science is to state its formal object. This, too, is the meaning of the statement that sciences are specified by their objects; for their formal objects place them in their species, making them the kind of science they are.
We shall now state the material object of logic, then the formal object, and then give the actual definition of logic in terms of its formal object.
a. The Material Object
The material object of logic includes all things without exception. It includes all that the human mind can know, all that we can grasp by simple apprehension, judgment, and reasoning. Consequently, the material object of logic includes the material objects of all the other sciences. Logic is similar to metaphysics in this respect, for metaphysics is also a science of all things without exception.
b. The Formal Object
In its formal object logic differs from all the other sciences. Metaphysics, the philosophy of God, the philosophy of human nature, and all the purely speculative sciences study real beings—God, man, the world, and so on—as they exist (or can exist) independently of our thinking of them. They consider beings that human reason does not make but merely discovers and contemplates. Each science, it is true, considers only a particular aspect of things, and no single science investigates beings in all their aspects. Still, these aspects are really in things whether we think of them or not. For instance, Euclidean geometry considers abstract quantity, and quantity really is in things (although not in an abstract way). But logic is different. Logic does not consider things as they are in themselves independently of our thinking of them, but according to a new kind of being they get as a result of being known.
When we know a thing, we confer on it a new kind of being by giving it existence in thought. (For instance, when we know “triangle,” “triangle” somehow exists in us by the mere fact of our knowing it.) In thought, things have many attributes and relationships that they do not have in the real order. They are universal. They can be predicated of one another; they stand towards one another as genus, specific difference, and so on; they can be minor, middle, and major terms in argumentation; and so on and so on. These attributes and relationships that things do not have in the real order but do have as they exist in the mind and that they get as a result of being known constitute the formal object of logic. They are called beings of reason (entia rationis) because they depend on reason for their very existence and cannot exist except in the mind. The logician examines these beings of reason and the various relationships they have towards one another, and draws up the laws of correct thinking in conformity with the requirements of this order of beings that his own mind has established.
In brief, the formal object of logic is not things as they are in themselves and independently of our knowledge of them, but things as reproduced in the mind together with all the attributes and relationships they get as a result of being mentally reproduced. These, together with the principle of contradiction, serve as guide posts to the logician when he formulates the laws of correct thinking.
c. The Definition Itself
In terms of its formal object, logic is defined as the science of the attributes and relationships that things have as they exist in the mind and get as a result of being known. In other words, it is the science of the mental representation of real beings, a science not directly of things but of certain aspects of our knowledge of things, a science of beings of reason. Briefly, logic is the science of second intentions. Logic is the science of beings of reason, or second intentions, in several ways. In the first place, the kind of beings that logic considers is not—at least not directly—real beings but beings of reason. In the second place, the laws that logic formulates constitute an organized body of conclusions about beings of reason (such as subjects and predicates, genus and species, propositions, syllogisms, minor, middle, and major terms, and so on). In the third place, the purpose of logic is to guide the mind in the construction of more beings of reason (syllogisms, for instance). Still, when we apply the laws of logic we are thinking about things—about real things, that is, about things that exist (or can exist). And if our premises give us knowledge of real beings and we reason correctly, our conclusions will also give us knowledge of real beings.
Both of the definitions we have given are too broad if they are taken by themselves. The first definition (“logic is the science and art of correct thinking”) is too broad for two reasons. In the first place, unless we arbitrarily restrict the meaning of “thinking” (as we did in Chapter 1), there are kinds of thinking that do not fall within the scope of logic; for instance, reverie, day-dreaming, and the chance association of ideas. In the second place, logic cannot lay down rules for the validity of material sequence or for the understanding of first principles, and so on. The second definition of logic (“logic is the science of the attributes and relationships that things have as they exist in the mind and get as a result of being known”) is too broad because at least some aspects of these beings of reason fall outside the scope of logic; for instance, their relation¬ ship to real beings. But if we combine both of these definitions into one, we shall have a composite definition that accurately expresses the object and function of logic and clearly delineates its scope. Hence, we give the following definition:
Logic is the science of those beings of reason that the mind must consider in formulating the laws of correct thinking, and the art that applies these laws.
Logic considers beings of reason only insofar as they are the basis of the laws of correct thinking. Logic investigates and formulates the laws of correct thinking only insofar as they are determined by the nature of beings of reason.
Synopsis
Logic is the science which at least indirectly considers all beings (material object). It considers them according to the attributes and relationships they have as they exist in the mind and get as a result of being known (formal object). In accordance with the nature of these beings of reason, guided by the principle of contradiction (first principle), logic investigates and formulates the laws of correct thinking (proximate end or purpose) as a means of attaining truth (ultimate end). As an art, logic also applies these laws.