LOGIC IN THE ISLAMIC WORLD

Arabic logic, like the rest of medieval Arabic science and philosophy, is entirely Western and has nothing to do with Oriental philosophy. It developed wholly in the wake of the classical Greek tradition as preserved in and transmitted through late Greek Aristotelianism. The present account briefly traces the evolution of Arabic logic from its inception in the late eighth century to its stultification in the sixteenth century, mentioning only the most important trends, figures, and achievements. Information on individual writers can be found in Carl Brockelmann's monumental Geschichte der arabischen Litteratur, cited hereafter as GAL (2 vols.—I, II—Weimar, 1890; Berlin, 1902; 2nd ed., Leiden, 1943–1949; 3 supp. vols.—SI, SII, SIII—Leiden, 1937–1942).

Transmission of Greek Logic to the Arabs

After their conquest of Syria-Iraq the Arabs came into contact with Greek learning as it continued to be nursed by various Christian sects—primarily the Nestorians and the Monophysites, or Jacobites—that had transplanted there (via such centers as Antioch, Edessa, and Nisibis) the Hellenistic scholarship of Alexandria. Thus, the first writers on logic in Arabic were Syrian Christian scholars, and their tradition of logical studies—closely linked to medicine—was transferred to an Arabic-language setting and laid the foundation for the development of Arabic logic.

The Syriac expositors of Aristotelian logic arrived at the following standard arrangement of logical works: Isagoge (by Porphyry), Categories, De Interpretatione, Prior Analytics, Posterior Analytics, Topics, De Sophisticis Elenchis, Rhetoric, and Poetics. These nine works were thought of as dealing with nine distinct branches of logic, each based on its own canonical text. This construction of Aristotelian logic was taken over by the Arabs, resulting in the following organization of the subject matter of logic:

The totality of this organon was referred to as the nine books of logic, or as the eight books with the Poetics (or sometimes Isagoge ) excluded. The first four of these logical treatises were apparently the only ones translated into Syriac prior to 800 and into Arabic prior to 850. They were called the four books of logic, and they constituted the object of logical studies in the basic curriculum of the Syrian academies.

Arabic translations of Aristotle's logical treatises and of several Greek studies and commentaries on them prepared the ground for the first indigenous Arabic writer on logic, the philosopher Abū-Yūsuf Yaʿqūb ibn Isḥāq al-Kindī (c. 805–873; GAL, I, pp. 209–210). His logical writings, however, probably amounted to little more than summaries of the writings of others about the Aristotelian texts.

School of Baghdad

In the late ninth and the tenth centuries Arabic logic was virtually the monopoly of a single school of logicians centered at Baghdad. The founders of this school belonged to a closely knit group of Syrian Christians, including the teachers of Abū Bishr Mattā ibn Yūnus and the teachers of these teachers. Its principal continuators were the pupils of Abū Bishr's pupil Yaḥyā ibn ʿAdī and the pupils of these pupils. Virtually all of these men—with the notable exception of al-Fārābī, a Muslim—were Nestorian Christians.

Abū Bishr Mattā ibn Yūnus (c. 870–c. 940; GAL, I, p. 207) was the first specialist in logical studies to write in Arabic. He produced the first Arabic translations of Posterior Analytics and Poetics and translated several Greek commentaries on Aristotelian works (such as Themistius on Posterior Analytics ). In addition he wrote logical commentaries and treatises of his own, which unfortunately have not survived.

Abū Naṣr al-Fārābī (c. 873–950; GAL, I, pp. 210–213) was perhaps the most important logician of Islam. His commentaries, only a fraction of which survive, covered the entire Aristotelian Organon in great detail. All later Arabic logicians—even those who, like Avicenna, have opposed al-Fārābī's influence—have seen Aristotle through his eyes. Among the points of special interest in the commentaries of al-Fārābī are (1) a strong emphasis on ecthesis (the setting out of terms) as a principle of syllogistic reduction, (2) an increased resort to noncategorical (for instance, hypothetical and disjunctive) types of syllogism, (3) an elaborate treatment of inductive uses of syllogistic reasoning, especially the application of the categorical syllogism in argument by analogy, and (4) a detailed treatment of the problem of future contingency, providing for a reading of Chapter 9 of De Interpretatione that does not deny prior truth status to future contingents (anticipating the position of Peter Abelard).

Yaḥyā ibn ʿAdī (893–974; GAL, I, p. 207), who studied logic and philosophy with both Abū Bishr and al-Fārābī, not only translated Greek works from Syriac into Arabic but also taught virtually half of the Arabic logicians of the tenth century. He wrote various independent works (including a commentary on Prior Analytics that devoted special attention to modal syllogisms), almost none of which have survived.

The three principal achievements of this school of Baghdad are (1) completion of the series of Arabic translations of Greek logical works, (2) the masterly commentaries of al-Fārābī (and possibly others) on the logical treatises of Aristotle, and (3) the elaborate study of certain extra-Aristotelian topics by Abū Bishr Mattā and al-Fārābī (for instance, theory of "conditional," or hypothetical and disjunctive, syllogisms along lines already found in Boethius, and the syllogistic reduction of inductive modes of argument).

Avicenna and His Influence

Despite the demise of the school of Baghdad around 1050, the ultimate survival of logical studies in Islam was assured by the fact that logic had, through the mediation of medicine, become an integral constituent of the Arabic medicophilosophical tradition as taken over from the Syrian Christians. From a quantitative standpoint the eleventh century was a low ebb in the history of Arabic logic. Yet this period produced perhaps the most creative logician of Islam, the great Persian scholar Abū ibn Sīnā, known as Avicenna (980–1037; GAL, I, pp. 452–458).

Avicenna made a daring innovation. Although greatly indebted to the school of Baghdad, he had nothing but contempt for it because it regarded logic as the study of the Aristotelian texts. Avicenna disapproved of this orientation toward the text rather than the subject. For him, and for the tradition he dominated, a logic book was no longer a commentary on Aristotle but an independent, self-sufficient treatise or handbook that covered the ground after its own fashion. Avicenna's masterpiece is a series of treatises in his monumental Kitāb al-shifāʾ dealing with the nine parts of the Arabic logical organon.

An example of Avicenna's originality is the following: In Aristotle and in the Stoics one finds a temporal construction of the modality of necessity that construes "All X 's are necessarily Y 's" as "At any time t all X 's-at-t are Y 's-at-t." This construction works well for, say, "All men are necessarily animals" but clearly not for "All men necessarily die." Avicenna distinguished between such cases as:

(1) At every time during its existence every X is a Y ("All men are necessarily animals").

(2) At most times during its existence every X is a Y ("All men are necessarily breathing beings").

(3) At some time during its existence every X is a Y ("All men are necessarily dying beings").

He then constructed a detailed theory of syllogistic inference from temporally modalized propositions of this sort.

Avicenna styled his own work in logic (and philosophy) as Eastern, in deliberate contrast with the Western approach of the school of Baghdad. This Eastern logic espoused by Avicenna differs from that of, say, al-Fārābī not so much in matters of substance as in emphasis and in willingness to depart from Aristotelian precedent. Thus, Avicenna imported into his logic a certain amount of material derived probably from Galen (including an at least grudging recognition of the fourth figure of the categorical syllogism) and certainly from the Stoics (for example, quantification of the predicate of categorical propositions, elaboration of quality and quantity for "conditional" propositions, and a treatment of singular propositions in the manner of the Stoics).

Avicenna's call to study logic from independent treatises rather than via the Aristotelian texts met with complete success in Eastern Islam. Only in Muslim Spain did the tradition of Aristotelian studies of the school of Baghdad manage—for a time—to survive.

Logicians of Andalusia

During the late eleventh and the twelfth centuries Andalusia (Muslim Spain) was the principal center of logical studies in Islam. Muḥammad ibn ʿAbdūn (c. 930–c. 995; Heinrich Suter, Die Mathematiker und Astronomen der Araber und ihre Werke, Leipzig, 1900–1902, no. 161; not in GAL ), a Spanish Muslim who studied medicine and philosophy in Baghdad, was instrumental in transplanting to Córdoba the teachings of the school of Baghdad in Aristotelian logic. In the medicological tradition of Andalusia these teachings stayed alive for more than two and a half centuries, surviving well past their extinction in Eastern Islam.

Abūʾl-Ṣalt (1068–1134; GAL, I, pp. 486–487) wrote an influential logic compendium that follows al-Fārābī closely; like most other Spanish Arab logicians, he seems to have had special interest in modal syllogisms. The detailed study of the writings of Aristotle was revitalized by Ibn Bājja (or Avempace; c. 1090–1138; GAL, I, p. 460), who wrote an important series (extant but unpublished) of discussions of Aristotle's works based on the commentaries of al-Fārābī.

Ibn Rushd (or Averroes; c. 1126–c. 1198; GAL, I, pp. 461–462) was unquestionably the most important of the Arabic logicians of Spain. His elaborate commentaries on the treatises of Aristotle's logical Organon rival (and conceivably surpass) those of al-Fārābī in their detailed understanding of Aristotle's logic. Averroes stands, as he considered himself to stand, heir to the masters of the school of Baghdad and successor to the heritage of al-Fārābī.

Among the points of special interest in the Aristotelian commentaries of Averroes are (1) certain historical data—for instance, regarding Galen's origination of the fourth syllogistic figure—taken from the last writings of al-Fārābī, (2) anti-Avicennist polemics that afford us a view of the points of dispute between Avicenna and his opponents, (3) the detailed account of the Aristotelian theory of modal syllogisms, and (4) in general, his effort to systematize as unified doctrine the teachings of the Aristotelian Organon.

After Averroes the logical tradition of Muslim Spain entered a period of decline. Arabic logic became extinct in Spain because there—in contrast to Eastern Islam, where logic achieved a modus vivendi with religious orthodoxy—popular and theological hostility toward logic and philosophy as an integral part of "alien learning" continued unabated.

Quarrel of the Eastern and Western Schools

Avicenna's criticisms of the school of Baghdad and his shift away from Aristotelian orthodoxy were not received with universal acceptance. A Western school arose to oppose Avicenna's innovations. Its principal exponents were the prolific Persian scholar Fakhr al-Dīn al-Rāzī (1148–1209; GAL, I, pp. 506–508) and his followers al-Khūnajī (1194–1249; GAL, I, p. 463) and al-Urmawī (1198–1283; GAL, I, p. 467). These logicians not only offered detailed criticisms of Avicenna's departures from Aristotle but also wrote handbooks of logic that became standard textbooks both during the lifetime of their school and later.

Opposed to these Westerners, the school of the Easterners, which supported Avicenna, continued to be active throughout the thirteenth century. Its leading exponent was the eminent and versatile Persian scholar Kamāl al-Dīn ibn Yūnus (1156–1242; GAL, SI, p. 859). His position was supported by his pupils al-Abharī (1200–1264; GAL, I, pp. 464–465) and Naṣīr al-Dīn al-Ṭūsī (1201–1274; GAL, I, pp. 508–512), as well as by the pupils of the last-named scholar, especially the logician al-Qazwīnī al-Kātibī (c. 1220–c. 1280; GAL, I, pp. 466–467). These logicians produced polemical treatises to attack the theses of the Westerners, as well as textbooks and handbooks to facilitate the teaching of logic according to their conceptions.

Amid this disputation and textbook writing the logical treatises of Aristotle were completely lost sight of. In effect, Avicenna carried the field before him; in Eastern Islam, Aristotle's logical writings were utterly abandoned. Ibn Khaldūn (1332–1406) could lament, "The books and methods of the ancients are avoided, as if they had never been, although they are full of the results and useful aspects of logic." The handbooks of the two thirteenth-century schools provided a basis for all future study in Islam, completely replacing the works of Aristotle. But very little produced at this stage has any significance for logic as a science rather than as a field of instruction.

Final Period

The period 1300–1500 may be characterized as the final period of Arabic logic, when its ossification became complete. It was a time not of creative logicians but of teachers of logic writing expository commentaries and supercommentaries on the thirteenth-century handbooks, now basic to all Arabic instruction in logic.

Underlying this development was the effort of al-Tustarī (c. 1270–c. 1330; GAL, SI, p. 816) and his disciple al-Taḥtānī (c. 1290–1365; GAL, II, pp. 209–210) to effect an arbitration between the Eastern and Western schools. As a result, later Arabic logicians were free to draw on both sectors of the tradition and to use the handbooks of both schools for the teaching of logic. The flood of glosses and supercommentaries on commentaries on the thirteenth-century logic handbooks marks the final, disintegrative phase of the evolution of logic in Islam.

Contributions of Arabic Logic

Some of the original contributions made by the Arabic logicians to logic as a science are (1) al-Fārābī's syllogistic theory of inductive argumentation, (2) al-Fārābī's doctrine of future contingency, (3) Avicenna's theory of "conditional" propositions, (4) Avicenna's temporal construction of modal propositions, and (5) Averroes's careful reconstruction of Aristotle's theory of modal syllogistic. Many of the prominent "innovations" of medieval Latin logic are in effect borrowings or elaborations of borrowings of Arabic ideas (for example, the distinction between the various modes of suppositio and the distinction between modality de dicto and de re ).

However, in speaking of the "original contributions" of Arabic logic two qualifications are necessary. In the first place, our knowledge of late Greek logic is so incomplete that any "original" item of Arabic work could turn out to be a mere elaboration of a Greek innovation. Second, an emphasis on originality in discussing Arabic logic is somewhat misplaced in that all the Arabic logicians—even Avicenna, the most original of them all—viewed their logical work as the reconstruction of a Greek teaching rather than as an enterprise of innovation.

See also al-Fārābī; al-Kindī, Abū-Yūsuf Yaʿqūb ibn Isḥāq; Aristotelianism; Aristotle; Averroes; Avicenna; Boethius, Anicius Manlius Severinus; Ibn Bājja; Naṣīr al-Dīn al-Ṭūsī; Porphyry.

Bibliography

arabic logic

A complete bibliography of Arabic logic can be found in Nicholas Rescher, The Development of Arabic Logic (Pittsburgh: University of Pittsburgh Press, 1964). On the transmission of Greek logic to the Arabs, see Max Meyerhof, "Von Alexandrien nach Baghdad," in Sitzungsberichte der Preussischen Akademie der Wissenschaften, Philosophisch-historische Klasse 23 (1930): 389–429. The conflict between logic and Islamic religion is detailed in Ignaz Goldziher, "Stellung der alten islamischen Orthodoxie zu den antiken Wissenschaften," in Abhandlungen der Königlichen Preussischen Akademie der Wissenschaften, Philosophisch-historische Klasse, Jahrgang 1915 (Berlin, 1916). For the Arabs' familiarity with Aristotle's logical works, see R. Walzer, "Aristū" (Aristotle), in Encyclopedia of Islam (London, 1960), Vol. I; and Ibrahim Madkour, L'organon d'Aristote dans le monde arabe (Paris: Vrin, 1934).

Some representative Arabic logical texts accessible in European languages are D. M. Dunlop, translations of several logical opuscula of al-Fārābī in Islamic Quarterly, 2 (1955)–5 (1959); Nicholas Rescher, Al-Fārābī's Short Commentary on Aristotle's "Prior Analytics" (Pittsburgh, 1963); A. M. Goichon, Avicenne: Livre de directives et remarques (Paris, 1951); Mohammad Achena and Henri Massé, Avicenne: Le livre de science, Vol. I (Paris, 1955); Aristotelis Opera cum Averrois Commentariis (Venice, 1550 and later; 1562–1574 ed. reprinted photographically, Frankfurt: Minerva, 1962).

Substantive study of the contributions of Arabic logicians has only begun. In addition to Prantl, Geschichte der Logik im Abendlande, Vol. II, above, consult T. J. de Boer, "Mantiḳ," in Encyclopedia of Islam, 1st ed.; and Nicholas Rescher, Studies in the History of Arabic Logic (Pittsburgh: University of Pittsburgh Press, 1963).

Nicholas Rescher (1967)