By Jean Oesterle
We might begin our answer to this question by observing that everyone naturally desires to know. This self-evident statement simply that a human being is so constituted that he cannot help wanting to know. A human being is a knowing being.
But what kind of knowing? We know in various ways. For example, I know that a dinner is cooking by smelling it. I know that a man is in a chair by looking at him. I know what New York looks like by remembering my visit there a year ago. In a more complex way than in any of the preceding examples, I know that sooner or later I shall die; even more, I know that every man dies and why every man must die.
What kind of knowing do we mean, then, when we say that everyone naturally desires to know? In the sense that every human being is so constituted that he cannot help wanting to know, every kind of knowing is included. But if we take the statement to mean the kind of knowing with which a human being is distinctively concerned, then the statement applies properly to the last kind of knowing. The last kind of knowing is reasoned knowledge.
What do we mean by reasoned knowing? It is that kind of knowing by which we find out why this or that is so. Thus, if someone asks me why every man must die—why every man is mortal—I have to give him some reason for accepting the statement as true. In brief, I have to prove it. This kind of knowing is distinctively human knowing for we do not go about proving to horses or cows or even apes that they too must dies, although it is just as true that they die as it is that human beings die.
All human beings, then, in varying degrees want to know why things are so. An evident sign of this is that even as children we frequently ask for the why of things. We are insatiably curious. This universal wonder of human beings is never entirely smothered, although we often disregard its promptings. As the ancient Greeks declared, wonder is the starting point of knowledge, Wonder is the starting point in the sense that we wonder what can be the explanation of cause of the things that we are continually observing. IT is only when we do not know the cause of a thing that our wonder ceases about that thing, for only by knowing the cause is our wonder fully satisfied.
Now logic is nothing else than the art that guides us in coming to know something previously unknown to us. Logic, then, is an instrument for helping us to find out why things are as they are. An axe is an instrument for cutting down a tree. A sharp axe is an efficient instrument for cutting down a tree. The power of thinking is an instrument for knowing the why and wherefore of things, but thinking sharpened by skill in logic is an efficient instrument for scientific knowing. We thus have at least a preliminary answer to what logic is and why we should study it. If every human being wants to know, in some degree, and if logic is an indispensable means of obtaining knowledge more easily, more surely, and more efficiently, then the study of logic is of use to every human being.
Let us now investigate in greater detail what logic is about and how we reason in a logical way. Suppose that you were walking down a street on a wintry day after a heavy snowfall. The sun is out and shining brightly. You notice the shining of the sun in particular because your eyes are bothered by the reflection of the sun on the snow. The thought might occur to you how much the snow reflects the light of the sun. This thought, in turn, might call your attention to the whiteness of the snow. You would recognize at once that the whiteness of the snow was the reason for the bright reflection of the snow in your eyes.
In this very ordinary example, you have informally gone through a reasoning process. You started with the statement Snow reflects light. You proceeded almost immediately to give the reason why snow reflects light, namely, snow is white. The first statement follows from the second statement, and the two statements can be put down in the following order:
Snow is white.
Therefore, snow reflects light.
The word “therefore” indicates that the second statement follows as a conclusion from the first. Now if you analyze these two statements, you will notice that there is a third statement implicitly contained in them, a statement containing the words “white” and “light.” This third statement would reason: white reflects light. You would then have three statements, appearing in the following order:
White reflects light.
Snow is white.
Therefore, snow reflects light.
This full argument is called a syllogism. It is a movement of our power of reasoning that grasps the truth of a conclusion by seeing the truth and connection of the two propositions leading to the conclusion. Logic guides us in knowing how to construct an argument like this, a kind of knowing, as we shall see, that is demonstrative knowledge. But to know what a syllogism is, and how to construct a syllogism, we have to know the parts of a syllogism, just as we have to know the different parts of a house in order to build a house.
The most immediate parts of a syllogism are the propositions of which it is composed. Logic will help us to understand what propositions are, and what their relation is to each other, so that from them we can make good arguments, or syllogism, and thus demonstrate what we know.
There are, however, other parts of a syllogism besides propositions. Words, which signify concepts, also make up a syllogism; for instance, “snow”, “light,” and “white” were parts of the syllogism given above. Words, in fact, are parts of propositions as well as parts of syllogisms. The words “snow” and “white” were parts of the proposition Snow is white. “Snow” and “white” are also parts of the syllogism given above, but they are parts of a syllogism differently from the way in which they are parts of a proposition, as we shall see later.
The syllogism given above was chosen deliberately to bring out the need of knowing the parts of a proposition before knowing the whole proposition; it also brings out the need of knowing the parts of a syllogism before knowing the whole syllogism. Clearly we have to know what various words mean before we put them into propositions and we have to know whether propositions are true before we can construct a sound argument out of them. Thus, in the given syllogism we have to know what “snow” means and what “white” means—we have to be able to define the words—before we can determine whether the proposition is true or not. And then, before we can give a full syllogism, we must further know the structure of a proposition, and how to determine when a proposition is true. Finally, in giving the full syllogism, we have to know how to relate propositions to each other and infer a conclusion from them.
We can now see the extent of an elementary course in Logic. There are three main topics to be considered: 1) definition 2) proposition and 3) syllogism. Each of these belongs to a different act of the human intellect.
Definition is known by the act of simple apprehension. The act of simple apprehension is the way in which we grasp a simple object, such as man or dog or horse. This is the first act of the human intellect, and we express these simple notions by definitions. We must know such simple objects first before we can combine simple objects into the complex structure of a proposition. In short, we must know the definitions of dog and animal before we can combine them into the proposition every dog is an animal.
The proposition (also called an enunciation) is known by the intellectual act of composition and division of terms, in which truth or falsity appears. If we combine or compose two terms, as in every dog is an animal, we have an affirmative proposition. If we divide or deny two terms of each other, as in no horses are dogs, we have a negative proposition.
The syllogism is known by the act of reasoning, in which we proceed from one thing to another. More specifically, by knowing two propositions as true and as related in a certain way to each other, we reason to a third proposition concluding from them. Thus, by knowing every mammal is an animal and Every cow is a mammal, we arrive at the reasoning knowledge Every cow is an animal. Let us recall here that we originally spoke of logic as the art that guides us in coming to know the unknown. There are , actually, only two kinds of unknown objects: a simple object, such as man, and a complex object, such as man is artistic. Let us relate the two kinds of unknown objects to the three acts of the intellect listed above.
As we have seen, a simple object is made known by the first act of the intellect, which we called simple apprehension. The principal means of knowing a simple object is by defining it. A sign that we know the simple object man is the definition that we give of man. Since the purpose of the first act of the intellect is to arrive at definitions, this act is guided by the part of logic that we call the art of defining.
A complex object is made known by means of argumentation. But argumentation requires two additional acts of the intellect: the act of composition or division and the act of reasoning. Hence, the second act of the intellect combines the simple objects that have been made known by the first act of the intellect in definition; it divides them by denying one of the other. If such a combination or division is not self-evident, then it must be manifested by argumentation, and because of this, a third act of the intellect is necessary. The third act is the reasoning process by which we proceed from propositions made known by the second act of the intellect to a conclusion following from these propositions.
From this discussion we can now give a definition of logic: Logic is the art that directs the three acts of the intellect.