In Logic Alfarabi follows Aristotle. He has, however, his own original views. His Logic deals with concepts, judgments and reasoning.
According to Alfarabi, a concept is an idea that represents the objective essence or the essential notes of a thing. It is the object of the first mental operation, called conception. "Concepts," says Alfarabi, "are determined by definition; definition declares what a thing is. Through definition concepts are so arranged and systematized that they imply one another until we arrive at the most universal ones, which do not presuppose others, such as Being, Necessary Being, Contingent Being. Such concepts are self-evident. A man's mind may be directed to them and his soul may be cognizant of them, but they cannot be demonstrated to him. Nor can they be explained by deriving them from what is known, since they are already clear in themselves, and that with the highest degree of certitude." 10
For Alfarabi, judgment is the combination of a particular entity with a universal idea. The synthesis of the particular with the universal is never evident of itself. That explains why we must seek a second universal with which the first universal and the particular agree. Once we find a second universal with which the two terms of the judgment agree, both of these will agree too, between themselves, according to the principle which is the supreme law of every syllogism, "Two things which are equal to the same thing, are equal to each other." Thus, for instance, the judgment, "The world is made" is not so clear as to permit the union of the particular "world" with the universal "made". There is a term of mediation for both, and this is the universal "Composed". 11
In Alfarabi's opinion, the process of reasoning by which we start from what is known and well established and proceed to a knowledge of the unknown, is Logic strictly speaking. 12 Philosophy, therefore, is mediation, reasoning and demonstration. Is philosophy only that and nothing else? Certainly not. There is something that cannot be mediated or demonstrated, namely, the First Principles.
The First Principles are those of Contradiction, Causality and of Excluded Middle. Such principles are self-evident, be-cause they have in themselves their own demonstration.
All our concepts could be classified under ten headings, called categories. For, the categories are a complete enumeration of everything that can enter into judgment, either as a subject or predicate. Alfarabi, following Aristotle, enumerates ten: Sub-stance, Quantity, Quality, Relation, Place, Time, Action, Passion, Posture and Having. Such categories, in Alfarabi's view, have been empirically gathered by Aristotle. Observing the things which make the universe, Aristotle found that some of them exist in themselves and are basis of certain accidents or differences. The things existing in themselves he called "substances" and the differences he called "accidents."
Aristotle then asked, "How many kinds of accidents are there?" He noticed that substance is divisible and therefore capable of more or less; thus he named Quantity the first accident-category. Realizing that substance has capacity of acquiring certain characteristics, like, "Peter is good," Paul is a philosopher," Aristotle lost no time in selecting Quality as the second accident-category.
Because substances are inter-related in the sense that the concept of one implies the other, Aristotle lost no time in choosing
[paragraph continues] Relation as the third accident-category. The relation between time and a thing in time led him to name Time in the fourth place. Because of the relation between different objects in space or the relation between place and the thing placed, Aristotle set aside Place as the fifth accident-category. The ability of substance to take various positions helped him select Posture as the sixth accident-category. The physical influence of substance on the production of another substance made him call Action as the seventh accident-category. Since substance is influenced by the efficient cause, he chose Passion as the eighth accident-category. Finally the relation of the thing having and the thing had made him pick Having as the ninth accident-category. 13
In treating the Categories, Alfarabi gave the answer to certain questions that had worried the Logicians of his time. First of all, he believes that not all the ten Categories are absolutely simple. Each is simple when compared with those that are below it. But only four are absolutely simple, namely, Sub-stance, Quality, Quantity and Posture. Action and Passion come from substance and quality; time and place from substance and quantity; Having occurs between two substances; Relation between two of the ten categories. 14
There are degrees in the simplicity of the Categories. For instance, Quantity and Quality depend directly on substance, so much so that to exist both need only a substance. On the contrary, Relation needs several things, perhaps two substances, or a substance and an accident, or two accidents. 15
When asked whether Action and Passion, which are found together, should be classified in the category of Relation, Alfarabi
answers in the negative. For "when we find one thing always with another," he says, "it does not follow that there is a dependence of relation between them." For example, we find respiration only with the lungs, the day only with sunrise, accident only with substance, the spoken word only with the tongue. Now all these things are not to be classified in the dependence of Relation, but rather in that of necessity. Necessity may be essential necessity, as that of the birth of the day upon the rising of the sun; and accidental necessity as that of the departure of Zeid upon the arrival of Amron. Furthermore, there is complete necessity when one thing exists by reason of the other, as father and son; while it is incomplete necessity when the dependence of relation is unilateral, as one and two, the two depends on the one, but the one does not depend on the two. 16
We ask whether the Equal and the Unequal are a property of Quantity, and the Similar and Dissimilar a property of Quality. According to Alfarabi, each of the two terms Equal and Unequal, taken separately, is a property of Quantity, while if both terms are taken together, they are descriptive of Quantity. The same is true of Similar and Dissimilar in reference to Quality. 17
In regard to the theory of Contraries, Alfarabi makes some very profound observations. "Is the contrary the absence (privation) of its contrary? Is white the absence of black?" asks Alfarabi. He answers saying, "It is not. For, white is something and not merely the absence of black. Since the absence of black is a fact in the existence of white, we are led to say that every contrary is the absence of its contrary." 18
People say that the science of the contraries is one. But Alfarabi says that a distinction must be made, for "If we deal with the science of something which happens to have a contrary, then that science is not identical with that of its contrary. The
science of the Just is not that of the Unjust, the knowledge of White is not the knowledge of Black. On the other hand, if we deal with the science of something insofar as it has a contrary, then this science is one with that of its contrary, because in this sense the two contraries are really and truly two relatives." 19
"Opposites and Contraries differ and must be distinguished one from the other," says Alfarabi. "Opposites are two things which cannot exist in the same object at the same time and in the same respect, as the quality of father and son. Opposites are a part of Relatives proper. Contraries are odd and even, affirmation and negation, sight and blindness." 20
Some ask how many things are necessary to the knowledge of the unknown. "Two things are necessary and sufficient," answers Alfarabi. "If there are more than two, this means that they are not necessary to the knowledge of the object under investigation." 21
"Is the proposition, "Man exists" a judgment with or without a predicate?" asks Alfarabi. "If man is considered from the natural and objective viewpoint," he answers, "the judgment is without a predicate because the fact of existence is one with man and cannot be distinguished from him, while the predicate denotes distinction from the thing to which it is referred. From a logical point of view, the judgment has a predicate, because it is made up of two terms which may be either true or false." 22
In Logic too Alfarabi makes some brilliant and original observations, and gives evidence of a great knowledge of the Organon and Isagoge.
1:10 Alfarabi, The Sources of Questions, in Collection, op. cit. n. 1, p. 65.
1:11 Alfarabi, The Sources of Questions, in Collection, op. cit. n. 2, p. 65.
2:12 Id. op. cit. n. 2, p. 66.
3:13 Alfarabi, A Letter in Reply to Certain Questions, in Collection, op. cit. n. 25, pp. 103-105.
3:14 Alfarabi, A Letter in Reply to Certain Questions, in Collection, op. cit. n. 19, pp. 98-99.
3:15 Id. op. cit. n. 13, p. 98.
4:16 Id. op. cit. n. 18, p. 98.
4:17 Id. op. cit. n. 24, p. 102.
4:18 Id. op. cit. n. 17, pp. 97-98.
5:19 Id. op. cit. n. 37, p. 109.
5:20 Id. op. cit. n. 38, pp. 109-110.
5:21 Id. op. cit. n. 29, pp. 106-107.
5:22 Id. op. cit. n. 16, p. 97.