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Arabic Logic up to Avicenna
Abstract
This volume, the first dedicated and comprehensive companion to medieval logic, covers both the Latin and the Arabic traditions and shows that they were in fact sister traditions, which both arose against the background of a Hellenistic heritage and which influenced one another over the centuries. A series of chapters by both established and younger scholars covers the whole period including early and late developments, and offers new insights into this extremely rich period in the history of logic. The volume is divided into two parts, 'Periods and traditions' and 'Themes', allowing readers to engage with the subject from both historical and more systematic perspectives. It will be a must-read for students and scholars of medieval philosophy, the history of logic, and the history of ideas.
Could formal logic be a naturalist field of study? This paper analyses how medieval logicians committed to Aristotelian naturalism thought about the metaphysical grounding of logic. As they assumed, it is at least sometimes a fact that a conclusion follows from some premises; here it is questioned how they thought this fact, or logical validity, to be grounded. The early medieval Arabic tradition (e.g. Ibn Sinā) thought in a way comparable to Immanuel Kant’s position that logic is a formal study of intellectual structures, but given their metaphysical realism concerning universals, such intellectual structures may be taken to be natural parts of Aristotelian metaphysics. On the other hand, the early medieval Latin tradition (e.g. Abelard) thought in a way comparable to Bernard Bolzano that the subject matter logic studies is not the intellectual realm, but essentially linguistic facts, taking language to be a natural phenomenon. Robert Kilwardby endeavoured to combine these traditions, but turns out to have taken a stance much closer to Kant, and to have given little importance to linguistic facts in his account of how syllogistic validity and thereby validity in general is grounded. At the same time, Kilwardby’s work enhanced the conception of the formality of logic, although he thought that only the syllogistic form is a properly logical form. Analysis of John Buridan’s logic shows that he had a generalized conception of logical form that was tightly knit with linguistic form as it is found in mental language, which he took to be a metaphysically natural domain. Unlike Kant and Bolzano, both Kilwardby and Buridan can be viewed as naturalists as concerns the study of formal logic, inasmuch as they thought that logical validity is grounded in facts that their Aristotelian metaphysics would consider natural.
Ibn Ḥazm of Córdoba’s (994–1064) defence of logic has lasting consequences for the logic of norms. His book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples is a demonstration of how Aristotelian logic may be applied in the religious sciences, especially law. Among other things, he thoroughly investigates deontic notions and their modal counterparts, assuring him a place among the fathers of the logic of norms. The basic units of Islamic deontic logic qualify the performance of actions as subject to either reward, or sanction, or neither; and they might therefore be called, indulging in terminological anachronism, heteronomous imperatives. With remarkable insight, Ibn Ḥazm pairs these with the natural modalities of necessity, possibility, and impossibility. Employing some features of Martin-Löf’s Constructive Type Theory (CTT) to shape the logic of heteronomous imperatives thus emerging from Ibn Ḥazm’s insights, the authors formulate a new approach to the logical analysis of deontic categories.KeywordsArabic logicHeteronomous imperativeIbn ḤazmDeontic logicIslamic jurisprudence
Felsefe ve mantık, Hıristiyan düşünce geleneğinden farklı olarak, İslâm kültüründe güçlü bir irade sonucu ve herhangi bir sınırlamaya tabi olmadan gelişmiştir. Tarihin gördüğü en büyük entelektüel atılım olarak Eski Yunan, Süryani, Pers, Yahudi ve Hind düşüncesinin önemli kültürel içerikleri, çeviri hareketleri çerçevesinde, Arapçaya aktarılmıştır. Bu bağlamda bazı kültürel unsurlar, söz gelimi kelâm, felsefî düşüncenin kabulü ve anlaşılmasında etkili de olmuştur. Çevirilere konu olan içerik başlangıçta, tıp, astronomi, kimya ve matematik gibi alanlarla ilgili olsa da bunlarla bağlantılı felsefe ve mantık unsurları da sürece eklenmiştir. Aristoteles’in derin etkisi mantığın, Meşşâî biçimiyle İslâm kültüründe yaygınlaşmasını sağlamış ve bu bağlamda felsefeciler ile bazı kelâmcılar arasında güçlenmesinin yolunu açmıştır. Bu süreçte içeriğin özellikle kısıtlanmadan aktarılması, özgür bir entelektüel ortamın bulunması, Müslüman düşünürlerin bunlara erişimini kolaylaştırmış, onların özgün katkılar sunmalarını sağlamıştır. Bu bağlamda mantık, zamanla, kelâm, dil ve fıkıh gibi disiplinlerle etkileşim halinde olmuştur. Özellikle Fârâbî’nin (öl. 339/950) tasarladığı biçimiyle mantık, İslâm entelektüel geleneğinde özgün bir alan haline gelmiştir. Fârâbî, tıpkı Aristoteles gibi, mantığı doğruluğun bir ölçütü olarak kurgulamak istemiş, onu diğer bilimler için kullanılabilir kılma adına, kavramlar ve yargılar düzleminde ortaya koymuştur. Güçlü mantık kurgusu, sadece felsefe değil diğer İslâmî ilimler için de sağlam bir temelin oluşmasına katkı sağlamıştır. Bu anlamda İslâm felsefesinin ve mantığının anlaşılması, Fârâbî düşüncesini daha yakından ve farklı bağlamlarda incelemeyi gerektirmektedir. Çalışmamızda felsefe ve mantığın İslâm öncesi kökenlerini kısaca ele alacağız ve bu düzlemde genel olarak Fârâbî’nin söz konusu geleneğe katkılarını Tanrı, bilimlerin tasnifi, mantığın felsefî boyutu gibi temel bazı konular çerçevesinde incelemeye gayret edeceğiz.
Employing Constructive Type Theory (CTT), we provide a logical analysis of Ibn Sīnā’s descriptional propositions. Compared to its rivals, our analysis is more faithful to the grammatical subject-predicate structure of propositions and can better reflect the morphological features of the verbs (and descriptions) that extend time to intervals (or spans of times). We also study briefly the logical structure of some fallacious inferences that are discussed by Ibn Sīnā. The CTT-framework makes the fallacious nature of these inferences apparent.
In logic, Quṭb al-Dīn al-Razī was broadly an orthodox Avicennan. However, in his enormously infuential commentary on al-Urmawī’s logic handbook Maṭāliʿ al-anwār, he explicitly criticizes Avicenna and advances a novel analysis of atomic propositions. As a later addition that only survives in two manuscripts shows, Quṭb al-Dīn was troubled by traditional accounts of the syntax and semantics of atomic propositions. For him, the main problem was a confused understanding of the copula. In atomic propositions of the form “A is B,” the copula is the word that indicates that B is predicated of A (“is” in English, “esti” in Greek, but not usually expressed in Arabic). Avicenna had maintained, for lack of an Arabic equivalent to Aristotle’s “esti,” that the Arabic pronoun “huwa” should be used to form complete atomic propositions (e.g., “Jīm huwa bā’”). Quṭb al-Dīn considers this to be mistaken on several levels. To straighten out the mistake, he disam- biguates the predicative nexus of a proposition from its judgment, formulates a unified notion of unsaturatedness for predicates, and gives an account of the judgment-nexus. An upshot of this novel analysis is a re-interpretation of the Aristotelian distinction between secundum adiacens and tertium adiacens propositions.
As reported by Cristina d’Ancona in her article “Greek Sources in Arabic and Islamic Philosophy” ([64]), the translations of the Greek corpus started “before the rise of Islam” ([64], Sect. 1) in Syria, by translations from Greek to Syriac, in the fourth and the fifth centuries (AD) and were made by some “theological schools of Edessa and Nisibi” ([1], Sect. 1).
The Arabic logicians include the study of the hypothetical syllogisms in their counterparts of the Prior Analytics, that is, in the treatises called al-Qiyās. In al-Fārābī’s frame, they are also evoked in al-Maqūlāt (the counterpart of the Categories).
Arabic logic started with the translations of the Aristotelian and Greek texts. These translations were first made in Syria from Greek to Syriac, then Arabic during the Umayyad Empire for some treatises, but the most important amount of translations was made during the Abbasid Empire [Baghdad, 750–1258 AD], starting from the reign of Abu Jaafar al-Manṣūr [754–775 AD], then Hārūn al Rashīd [786–809 AD] and al-Ma’mūn [813–833 AD] who founded an academy devoted to translation called “Beit al-Ḥikma” (literally: “the House of Wisdom”) [830 AD] (see [127], 140).
This paper analyzes a classification of different types of demonstration introduced by Alfarabi (d. 950 CE) in his Kitāb al-Burhān (Book of Demonstration). Alfarabi identifies eight combinations of demonstrative syllogisms, grouped in function of the different types of per se relations expressed by their premises and conclusions, where terms are definitionally connected with one another. The list contains a total of thirty-nine moods illustrated by a rich array of examples drawn from various scientific disciplines, including arithmetic, geometry, and natural philosophy. The combinations and moods are discussed extensively by Averroes (d. 1198 CE) in the section of his Epitome of the Organon devoted to the Posterior Analytics and in his Quaesita on logic. Alfarabi’s classification also possibly inspired a simplified taxonomical effort in Avicenna’s (d. 1037 CE) Kitāb al-Burhān. © 2018
Ibn Sīnā (11th century, greater Persia) proposed an analysis of arguments by reductio ad absurdum. His analysis contains, perhaps for the first time, a workable method for handling the making and discharging of assumptions in a formal proof. We translate the relevant text of Ibn Sīnā and put his analysis into the context of his general approach to logic.
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