Treatise on the Art of Logic

Introduction

In the name of God, the merciful and the compassionate! An eminent person, one of the masters of the juridical sciences and the possessors of clarity and eloquence in the Arabic language, has asked a man who studied the art of logic to explain to him the meanings of the numerous terms frequently occurring in the art of logic, to interpret to him the technical language commonly adopted by the masters of this art, and to endeavor to do this with extreme brevity and not to indulge in details of meaning, lest the discourse become too long. For his intention, may his glory be everlasting, was not to learn the art I am about to outline to him—since the introductions placed before one who desires to learn it are many—but only to know those technical terms in most of their meanings, and nothing else.

I begin then to present the desired discussion. [ . . . ]

Chapter 6

A little reflection will make it evident that from any two distinct propositions nothing else will ever result, as when we say, “Every man is an animal,” and “Every fire is hot,” and “Every snow is cold.” Even if the number of the distinct propositions is indefinitely increased, nothing will result from their combination. But if they are connected in some form, so that another proposition follows from them, then the combination of these two propositions is called a syllogism; and each one of the two propositions is called a premise; and the third proposition which results from the union of these two propositions is called a conclusion and also a consequent. For example, when we say “Every man is an animal,” and “Every animal is sentient,” it necessarily results from this combination that “Every man is sentient,” which is the conclusion.

Observe this example and you will find that the syllogism consists of three parts; for every proposition has, as explained, two parts: a predicate and a subject; and there is also one part which the two propositions have in common. Hence there are three parts: the part common to both propositions, which we call the middle term, and the two distinct parts which we call extremes and whose union constitutes the conclusion. Observe also the parts of the conclusion. The predicate in the conclusion is what is called in the syllogism the first and major term, and that premise of the syllogism which contains the first term is called the major premise; the subject of the conclusion is what is called the last and minor term of the syllogism, and the premise of the syllogism which contains the minor term is what we call the minor premise.

Let us return to our example so as to clarify further the meaning of the terms. The syllogism which we used as an example was “Every man is an animal,” and “Every animal is sentient,” the conclusion of this syllogism being “Every man is sentient.” The parts of this syllogism are three: “man,” “animal,” and “sentient”; its middle term is “animal” and the extremes are “man” and “sentient”; the minor premise is our expression “Every man is an animal,” and the major premise is our expression “Every animal is sentient.” This is the explanation of the meaning of these most important terms which one must know in the art of logic. [ . . . ]

Chapter 8

The propositions which are known to be true and require no proof for their truthfulness are of four kinds: perceptions, as when we know that this is black, this is white, this is sweet, and this is hot; first ideas, as when we know that the whole is greater than the part, that two is an even number, and that things equal to the very same thing equal each other; conventions, as when we know that uncovering the privy parts is ugly, that compensating a benefactor generously is beautiful; and traditions, i.e., whatever is received from a chosen person or from a chosen assembly. For we demand proof for the trustworthiness of a transmitter of a tradition only generally and not for every word that he utters. He is met with nothing short of complete acceptance; for his general reliability has already been demonstrated.

Now as to perceptions and ideas, there is no difference among those of the human species that possess normal senses and intuitions, nor is there any contention for superiority among them with reference to their truthfulness. But as to conventions, there is difference and rivalry for superiority, since there are propositions that have become known among one people and not among another; and whenever a precept is known among many peoples its acceptability is stronger. Similarly, in the case of traditions, a tradition among one group may be lacking in another. Now, that which is obtained from whatever is perceived by means of a healthy sense is undoubtedly true. The same applies to ideas, first and second; by second ideas I mean such as geometric theorems and astronomic calculations, which are all true, because they may all be demonstrated by premises, most of which come close to the first ideas. In like manner, all the results of experience, e.g., that scammony is a cathartic and gall-nut causes constipation, are also true. Whatever becomes known through one of these three truthful channels the logicians call apodictic.

After these preliminaries, you must know that every syllogism both of whose premises are apodictic, we call a demonstrative syllogism; and the making of these syllogisms and a knowledge of their conditions constitute what we call the art of demonstration. [ . . . ] Furthermore, when we say concerning a child when he is born that he is a writer, it means that he is a writer by remote potentiality; and when we say concerning a lad before he begins to study that he is a potential writer, this potentiality is nearer than the first; and when we say it concerning him during his studying, the potentiality is nearer than those preceding; and when we say it concerning one who has been engaged in writing but who is at present asleep, the potentiality is still nearer; and when we say it concerning him when he is awake and has before him ink, pen, and parchment, it is indeed a very near potentiality. But we do not call him a writer in actuality, except at the time that he writes. It is the same with all other such cases.