Important developments made by Muslim logicians included the first forms of non-Aristotelian logic, notably Avicennian logic, and the introduction of temporal modal logic and inductive 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.
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."
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, before the Arabic translations of Aristotle's works. 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.[1]
Ibn Hazm (994-1064) wrote the Scope of Logic, in which he stressed on the importance of sense perception as a source of knowledge.[2] 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.[3]
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.[4]
Al-Ghazali (Algazel) (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.[5] Despite the logical sophistication of al-Ghazali, the rise of the Ash'ari school from the 12th century slowly suffocated original work on logic in western Islamic regions such as the Maghreb and al-Andalus, but logic continued to be studied in eastern Islamic regions such as the Levant, Egypt and Persia.
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.[6] 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).[7]
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.[5]
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.[5] 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.[6]
Though al-Farabi (Alfarabi) (873–950) was mainly an Aristotelian logician, he introduced a number of non-Aristotelian elements of logic. 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. He is credited for categorizing logic into two separate groups, the first being "idea" and the second being "proof".[5]
Al-Farabi also introduced the theories of conditional syllogism and analogical inference, which were not part of the Aristotelian tradition.[8] 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.[9]
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,[10] though Aristotelian logic later became more popular in Europe due to the strong influence of Averroism.
Avicenna developed an early theory on hypothetical syllogism, which formed the basis of his early risk factor analysis.[11] He also developed an early theory on propositional calculus, which was an area of logic not covered in the Aristotelian tradition.[12] The first criticisms on Aristotelian logic were also written by Avicenna, who developed an original theory on temporal modal syllogism.[5] He also contributed inventively to the development of inductive logic, being the first to describe the methods of agreement, difference and concomitant variation which are critical to inductive logic and the scientific method.[11]
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).[2] 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.[13] 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).[6] Another systematic refutation of Greek logic was written by Ibn Taymiyyah (1263-1328), who wrote the ar-Radd 'ala al-Mantiqiyyin (Refutation of Greek Logicians), in which he gave a proof for induction being the only true form of argument, which had an important influence on the development of the scientific method of observation and experimentation.[2] The Sharh al-takmil fi'l-mantiq written by Muhammad ibn Fayd Allah ibn Muhammad Amin al-Sharwani in the 15th century was the last major Arabic work on logic.[14]
In 1965, 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.