Islamic logic

Logic (Arabic: منطق‎), or Islamic logic, played an important role in Islamic philosophy. Islamic law and jurisprudence placed importance on formulating standards of argument, which gave rise to a novel approach to logic in Kalam, as seen in the method of qiyas. This approach, however, was later displaced to some extent by ideas from ancient Greek and Hellenistic philosophy with the rise of the Mu'tazili school, who highly valued Aristotle's Organon. The works of Hellenistic-influenced Islamic philosophers were crucial in the reception of Aristotelian logic in medieval Europe, along with the commentaries on the Organon by Averroes, founder of Averroism. In turn, the Aristotelian tradition was later displaced by Avicennian logic, which in turn was succeeded by Post-Avicennian logic.

Important developments made by Islamic logicians included the development of original systems of logic, notably Avicennian and Post-Avicennian logic, and the development of early theories on temporal logic, modal logic, inductive logic, hypothetical syllogism, propositional calculus, analogical reasoning, and legal logic. Other important developments in early Islamic philosophy include the development of a strict science of citation, the isnad or "backing", and the development of a scientific method of open inquiry to disprove claims, the ijtihad, which could be generally applied to many types of questions.

Another important Islamic contribution to modern logic is algebra (see Islamic mathematics), which led to the development of modern algebraic logic in the 19th century. [4]

History

According to the Routledge Encyclopedia of Philosophy:

"For the Islamic philosophers, logic included not only the study of formal patterns of inference and their validity but also elements of the philosophy of language and even of epistemology and metaphysics. Because of territorial disputes with the Arabic grammarians, Islamic philosophers were very interested in working out the relationship between logic and language, and they devoted much discussion to the question of the subject matter and aims of logic in relation to reasoning and speech. In the area of formal logical analysis, they elaborated upon the theory of terms, propositions and syllogisms as formulated in Aristotle's Categories, De interpretatione and Prior Analytics. In the spirit of Aristotle, they considered the syllogism to be the form to which all rational argumentation could be reduced, and they regarded syllogistic theory as the focal point of logic. Even poetics was considered as a syllogistic art in some fashion by most of the major Islamic Aristotelians."

"Since logic was viewed as an organon or instrument by which to acquire knowledge, logic in the Islamic world also incorporated a general theory of argumentation focused upon epistemological aims. This element of Islamic logic centred upon the theory of demonstration found in Aristotle's Posterior Analytics, since demonstration was considered the ultimate goal sought by logic. Other elements of the theory of argumentation, such as dialectics and rhetoric, were viewed as secondary to demonstration, since it was held that these argument forms produced cognitive states inferior in certitude and stability to demonstration. The philosopher's aim was ultimately to demonstrate necessary and certain truth; the use of dialectical and rhetorical arguments was accounted for as preparatory to demonstration, as defensive of its conclusions, or as aimed at communicating its results to a broader audience."

Logic in Arabic grammar

Some of the earliest known logic in the Islamic world came from the work of Arabic grammarians. Examples include the grammatical works of Ibn Abi Ishaq (d. 735) and Sibawayh (d. 797). The latter's work in particular has been compared in its logical sophistication to the work of Pāṇini, a Sanskrit grammarian of the Indian tradition.

Logic in Islamic law and theology

See also: Qiyas and Kalam

Early forms of analogical reasoning, inductive reasoning and categorical syllogism were introduced in Fiqh (Islamic jurisprudence), Sharia (Islamic law) and Kalam (Islamic theology) from the 7th century with the process of Qiyas, at least a century before Muslims had become aware of Aristotelian logic. The Qiyas process was described by early Islamic legal scholars such as Abū Ḥanīfa (699-765) and Muhammad ibn Idris ash-Shafi`i (767-820). Later during the Islamic Golden Age, there was a logical debate among Islamic philosophers, logicians and theologians over whether the term Qiyas refers to analogical reasoning, inductive reasoning or categorical syllogism. Some Islamic scholars argued that Qiyas refers to inductive reasoning, which Ibn Hazm (994-1064) disagreed with, arguing that Qiyas does not refer to inductive reasoning, but refers to categorical syllogism in a real sense and analogical reasoning in a metaphorical sense. On the other hand, al-Ghazali (1058-1111) (and in modern times, Abu Muhammad Asem al-Maqdisi) argued that Qiyas refers to analogical reasoning in a real sense and categorical syllogism in a metaphorical sense. Other Islamic scholars at the time, however, argued that the term Qiyas refers to both analogical reasoning and categorical syllogism in a real sense.

Ibn Hazm (994-1064) wrote the Scope of Logic, in which he stressed on the importance of sense perception as a source of knowledge. He wrote that the "first sources of all human knowledge are the soundly used senses and the intuitions of reason, combined with a correct understanding of a language." He also criticized some of the more traditionalist theologians who were opposed to the use of logic and argued that the first generations of Muslims did not rely on logic. His response was that the early Muslims had witnessed the revelation directly, whereas the Muslims of his time have been exposed to contrasting beliefs, hence the use of logic is necessary in order to preserve the true teachings of Islam. Ibn Hazm's Fisal (Detailed Critical Examination) also stressed the importance of sense perception as he realized that human reason can be flawed, and thus criticized some of the more rationalist theologians who placed too much emphasis on reason. While he recognized the importance of reason, since the Qur'an itself invites reflection, he argued that this reflection refers mainly to sense data, since the principles of reason are themselves derived entirely from sense experience. He concludes that reason is not a faculty for independent research or discovery, but that that sense perception should be used in its place, an idea which forms the basis of empiricism.

Al-Ghazali (1058–1111) had an important influence on the use of logic in theology, as he was the first to apply the Avicennian system of temporal modal logic to Islamic theology. He also established the application of three types of logical systems in Islamic Sharia law: reasoning by analogy, deductive logic, and inductive logic. In cases that have multiple legal precedents, he recommended the use of inductive logic, stating that the "larger the number of pieces of textual evidence is, the stronger our knowledge becomes." His followers, Fakhr al-Din al-Razi (1149-1209) and Ibn Taymiyyah (1263-1328), also applied inductive logic to Islamic Sharia law. Ibn Taymiyyah in particular argued against the certainty of syllogistic arguments and in favour of analogy.

Ibn al-Nafis (1213-1288) wrote two major works dealing with logic in Islamic theology. Theologus Autodidactus was a fictional story dealing with many Islamic topics. Through its story, Ibn al-Nafis attempted to establish that the human mind is capable of deducing the natural, philosophical and religious truths of Islam through logical thinking. In A Short Account of the Methodology of Hadith, he demonstrated the use of logic in the classification of the hadiths into four categories: decidedly true (maclūm al-sidq), probably true (yuz annu bihi'l-sidq), probably false (yuz annu bihi'l-kadhb) and decidedly false (maclūm al-kadhb).

Aristotelian logic

Most early Muslim logicians during the 8th and 9th centuries produced commentaries on Aristotelian logic. The first original Arabic writings on logic were produced by al-Kindi (Alkindus) (805–873), who produced a summary on earlier logic up to his time.

Ibn Rushd (Averroes) (1126–1198) was the last major logician from al-Andalus, who wrote the most elaborate commentaries on Aristotelian logic. He was also the last major Aristotelian logician from the Islamic world. Though his commentaries on Aristotelian logic and metaphysics had little influence in the Islamic world, his commentaries had a strong influence on medieval Europe after the Latin translations of the 12th century.

The last major logician to write a commentary on Aristotelian logic was Ibn al-Nafis (1213-1288), though he himself was not an Aristotelian logician. He wrote the Al-Wurayqat (The Little Papers), a commentary on Aristotle's Organon and Rhetoric.

Farabian logic

Al-Farabi (Alfarabi) (873–950) is considered the father of logic in the Islamic philosophical tradition. Though he was mainly an Aristotelian logician, he included a number of non-Aristotelian elements in his works. He discussed the topics of future contingents, the number and relation of the categories, the relation between logic and grammar, and non-Aristotelian forms of inference.

Al-Farabi also considered the theories of conditional syllogisms and analogical inference, which were part of the Stoic tradition of logic rather than the Aristotelian. Another addition al-Farabi made to the Aristotelian tradition was his introduction of the concept of poetic syllogism in a commentary on Aristotle's Poetics.

Avicenna
Avicennism
The Canon of Medicine
The Book of Healing
Hayy ibn Yaqdhan
Criticism of Avicennian philosophy
Unani medicine

File:Canon-Avicenna-small.jpg

A text by Avicenna, founder of Avicennian logic.

Avicennian logic

Dimitri Gutas and the Stanford Encyclopedia of Philosophy consider the period between the 11th and 14th centuries to be the "Golden Age" of Arabic and Islamic philosophy, initiated by Al-Ghazali's successful integration of logic into the Madrasah curriculum and the subsequent rise of Avicennism.

Ibn Sina (Avicenna) (980–1037) developed his own system of logic known as "Avicennian logic" as an alternative to Aristotelian logic. After the Latin translations of the 12th century, Avicennian logic also influenced early medieval European logicians such as Albertus Magnus and John Duns Scotus, though Aristotelian logic later became more dominant in Europe due to the strong influence of Averroism.

The first criticisms of Aristotelian logic were written by Avicenna, who produced independent treatises on logic rather than commentaries. He criticized the logical school of Baghdad for their devotion to Aristotle at the time. He investigated the theory of definition and classification and the quantification of the predicates of categorical propositions, and developed an original theory on temporal modal syllogism. Its premises included modifiers such as "at all times", "at most times", and "at some time".

He wrote on the hypothetical syllogism and on the propositional calculus, which were both part of the Stoic logical tradition. He developed an original theory of “temporally modalized” syllogistic and made use of inductive logic, such as the methods of agreement, difference and concomitant variation which are critical to the scientific method.

One of Avicenna's ideas had a particularly important influence on Western logicians such as William of Ockham. Avicenna's word for a meaning or notion (ma'na), was translated by the scholastic logicians as the Latin intentio. In medieval logic and epistemology, this is a sign in the mind that naturally represents a thing. This was crucial to the development of Ockham's conceptualism. A universal term (e.g. "man") does not signify a thing existing in reality, but rather a sign in the mind (intentio in intellectu) which represents many things in reality. Ockham cites Avicenna's commentary on Metaphysics V in support of this view.

Post-Avicennian logic

See also: Avicennian logic

The Islamic theologian Fakhr al-Din al-Razi (b. 1149) criticised Aristotle's "first figure" and formulated an early system of inductive logic, foreshadowing the system of inductive logic developed by John Stuart Mill (1806-1873). Al-Razi also applied inductive logic to Islamic Sharia law and Fiqh jurisprudence. Al-Razi's work was seen by later Islamic scholars as marking a new direction for Islamic logic, towards a Post-Avicennian logic. This was further elaborated by his student Afdaladdîn al-Khûnajî (d. 1249), who developed a form of logic revolving around the subject matter of conceptions and assents. In response to this tradition, Nasir al-Din al-Tusi (1201-1274) began a tradition of Neo-Avicennian logic which remained faithful to Avicenna's work and existed as an alternative to the more dominant Post-Avicennian school over the following centuries. Al-Tusi's work included the following commentary on Avicenna's theory of absolute propositions:

"What spurred him to this was that in the assertoric syllogistic Aristotle and others sometimes used contradictories of absolute propositions on the assumption that they are absolute; and that was why so many decided that absolutes did contradict absolutes. When Avicenna had shown this to be wrong, he wanted to give a way of construing those examples from Aristotle."

Systematic refutations of Greek logic were written by the Illuminationist school, founded by Shahab al-Din Suhrawardi (1155-1191), who developed the idea of "decisive necessity", which refers to the reduction of all modalities (necessity, possibility, contingency and impossibility) to the single mode of necessity. Ibn al-Nafis (1213-1288) wrote a book on Avicennian logic, which was a commentary of Avicenna's Al-Isharat (The Signs) and Al-Hidayah (The Guidance).

Najm al-Dīn al-Qazwīnī al-Kātibī (d. 1276), a student of al-Tusi, was the author of a work on logic, Al-Risāla al-Shamsiyya (Logic for Shams al-Dīn), that was commonly used as the first major text on logic in Sunni madrasahs, right down until the 20th century and is "perhaps the most studied logic textbook of all time." Al-Qazwīnī's logic was largely inspired by the Avicenna's formal system of temporal modal logic, but is more elaborate and departs from it in several ways. While Avicenna considered ten modalities and examined six of them, Al-Qazwlni considers many more modalized propositions and examines thirteen which he considers 'customary to investigate'.

Another systematic refutation of Greek logic was written by Ibn Taymiyyah (1263-1328), the Ar-Radd 'ala al-Mantiqiyyin (Refutation of Greek Logicians), where he argued against the usefulness, though not the validity, of the syllogism and in favour of inductive reasoning, providing a logical proof for induction being a superior form of argument, which had an important influence on the development of the scientific method of observation and experimentation. He also applied inductive logic to Islamic Sharia law and Fiqh jurisprudence. The "fundamental idea underlying Ibn Thymiyya's theory of logic in general, and legal logic in particular, is that the knowledge of the external world results from the observation of particular things." This could be seen as an anticipation of Mill's theory in the 19th century. Later, Ibn Taymiyyah argued against the certainty of syllogistic arguments and in favour of analogy. His argument is that concepts founded on induction are themselves not certain but only probable, and thus a syllogism based on such concepts is no more certain than an argument based on analogy. He further claimed that induction itself is founded on a process of analogy. His model of analogical reasoning was based on that of juridical arguments. This model of analogy has been used in the work of John F. Sowa.

In the 14th century, the Islamic sociologist and historiographer Ibn Khaldun discussed the Post-Avicennian tradition in his Muqaddimah (1377). He wrote the following on how Islamic logic had changed substantially since the 12th century:

"Treatment of [the subject as newly conceived] has become lengthy and wide-ranging—the first to do this was Fakhraddîn ar-Râzî (d. 1210) and, after him, Afdaladdîn al-Khûnajî (d. 1249), on whom Eastern scholars rely even now… The books and ways of the ancients have been abandoned, as though they had never been."

The Sharh al-takmil fi'l-mantiq written by Muhammad ibn Fayd Allah ibn Muhammad Amin al-Sharwani in the 15th century is the last major Arabic work on logic that has been studied. However, there have been "thousands and thousands of pages" devoted to logical subjects throughout the period from the 14th century through to the 19th century. Only a fraction of the texts written during this period have been studied, hence little is known about the original work on Islamic logic produced during this later period.

On the influence of Islamic mathematics on modern logic, Hermann Weyl wrote: "Occidental mathematics has in past centuries broken away from the Greek view and followed a course which seems to have originated in India and which has been transmitted, with additions, to us by the Arabs; in it the concept of number appears as logically prior to the concepts of geometry." (Weyl, 1929)

Fuzzy logic

In 1965, the Iranian Azeri mathematician Lotfi Asker Zadeh founded fuzzy set theory as an extension of the classical notion of set and he founded the field of Fuzzy Mathematics.

Later in 1973, Zadeh founded the field of Fuzzy logic. This was the first major contribution to logic from the Islamic world after more than five centuries.

The Japanese were the first to utilize fuzzy logic for practical applications. The first notable application was on the high-speed train in Sendai, in which fuzzy logic was able to improve the economy, comfort, and precision of the ride. It has also been used in recognition of hand written symbols in Sony pocket computers, Canon auto-focus technology, Omron auto-aiming cameras, earthquake prediction and modeling at the Institute of Seismology Bureau of Metrology in Japan, etc.

Major figures in Islamic logic

• Ibn Abi Ishaq (d. 735)
• Abū Ḥanīfa (699-765)
• Sibawayh (c. 760-797)
• Muhammad ibn Idris ash-Shafi`i (767-820)
• Al-Kindi (Alkindus) (805–873)
• Al-Farabi (Alfarabi) (873–950)
• Ibn Sina (Avicenna) (980–1037)
• Ibn Hazm (994-1064)
• Al-Ghazali (Algazel) (1058–1111)
• Ibn Rushd (Averroes) (1126–1198)
• Fakhr al-Din al-Razi (1149-1210)
• Shahab al-Din Suhrawardi (Sohrevardi) (1155-1191)
• Afdaladdîn al-Khûnajî (d. 1249)
• Nasir al-Din al-Tusi (1201-1274)
• Najm al-Dīn al-Qazwīnī al-Kātibī (d. 1276)
• Ibn al-Nafis (1213-1288)
• Ibn Taymiyyah (1263-1328)
• Muhammad ibn Fayd Allah ibn Muhammad Amin al-Sharwani (15th century)

See also

• Avicennism
• Islamic mathematics
• Islamic philosophy
  • Early Islamic philosophy
• Logic
  • History of logic
• Mill's Methods

External links

• Logic in Islamic philosophy, Routledge Encyclopedia of Philosophy. Routledge, 1998. (Alternatively, see Logic in Islamic philosophy)
• Ancient Islamic (Arabic and Persian) Logic and Ontology, at Raul Corazzon's Theory and History of Ontology.