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Logic in the Middle East Main article: Logic in Islamic philosophy See also: Avicennian logic Arabic text in pink and blue A text by Avicenna, founder of Avicennian logic The works of Al-Kindi, Al-Farabi, Avicenna, Al-Ghazali, Averroes and other Muslim logicians were based on Aristotelian logic and were important in communicating the ideas of the ancient world to the medieval West.[43] Al-Farabi (Alfarabi) (873–950) was an Aristotelian logician who 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.[44] 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.[45] Ibn Sina (Avicenna) (980–1037) was the founder of Avicennian logic, which replaced Aristotelian logic as the dominant system of logic in the Islamic world,[46] and also had an important influence on Western medieval writers such as Albertus Magnus.[47] Avicenna wrote on the hypothetical syllogism[48] and on the propositional calculus, which were both part of the Stoic logical tradition.[49] He developed an original theory of "temporally modalized" syllogistic[44] and made use of inductive logic, such as the methods of agreement, difference and concomitant variation which are critical to the scientific method.[48] 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.[50] 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.[51] 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).[52] 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.[53] 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.[54] 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).[55] Ibn Taymiyyah (1263–1328), wrote the Ar-Radd 'ala al-Mantiqiyyin, where he argued against the usefulness, though not the validity, of the syllogism[56] and in favour of inductive reasoning.[52] Ibn Taymiyyah also 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.[57][58] This model of analogy has been used in the recent work of John F. Sowa.[58] 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.[59] However, "thousands upon thousands of pages" on logic were written between the 14th and 19th centuries, though only a fraction of the texts written during this period have been studied by historians, hence little is known about the original work on Islamic logic produced during this later period.[53] Logic in medieval Europe Main article: Term logic Top left corner of early printed text, with an illuminated S, beginning "Sicut dicit philosophus" Brito's questions on the Old Logic "Medieval logic" (also known as "Scholastic logic") generally means the form of Aristotelian logic developed in medieval Europe throughout the period c 1200–1600.[60] For centuries after Stoic logic had been formulated, it was the dominant system of logic in the classical world. When the study of logic resumed after the Dark Ages, the main source was the work of the Christian philosopher Boethius, who was familiar with some of Aristotle's logic, but almost none of the work of the Stoics.[61] Until the twelfth century the only works of Aristotle available in the West were the Categories, On Interpretation and Boethius' translation of the Isagoge of Porphyry (a commentary on the Categories). These works were known as the "Old Logic" (Logica Vetus or Ars Vetus). An important work in this tradition was the Logica Ingredientibus of Peter Abelard (1079–1142). His direct influence was small,[62] but his influence through pupils such as John of Salisbury was great, and his method of applying rigorous logical analysis to theology shaped the way that theological criticism developed in the period that followed.[63] By the early thirteenth century the remaining works of Aristotle's Organon (including the Prior Analytics, Posterior Analytics and the Sophistical Refutations) had been recovered in the West and was revived by Saint Thomas Aquinas.[64] Logical work until then was mostly paraphrasis or commentary on the work of Aristotle.[65] The period from the middle of the thirteenth to the middle of the fourteenth century was one of significant developments in logic, particularly in three areas which were original, with little foundation in the Aristotelian tradition that came before. These were:[66] The theory of supposition. Supposition theory deals with the way that predicates (e.g. 'man') range over a domain of individuals (e.g. all men).[67] In the proposition 'every man is an animal', does the term 'man' range over or 'supposit for' men existing in the present? Or does the range include past and future men? Can a term supposit for non-existing individuals? Some medievalists have argued that this idea was a precursor of modern first order logic.[68] "The theory of supposition with the associated theories of copulatio (sign-capacity of adjectival terms), ampliatio (widening of referential domain), and distributio constitute one of the most original achievements of Western medieval logic".[69] The theory of syncategoremata. Syncategoremata are terms which are necessary for logic, but which, unlike categorematic terms, do not signify on their own behalf, but 'co-signify' with other words. Examples of syncategoremata are 'and', 'not', 'every', 'if', and so on. The theory of consequences. A consequence is a hypothetical, conditional proposition: two propositions joined by the terms 'if ... then'. For example 'if a man runs, then God exists' (Si homo currit, Deus est).[70] A fully developed theory of consequences is given in Book III of William of Ockham's work Summa Logicae. There, Ockham distinguishes between 'material' and 'formal' consequences, which are roughly equivalent to the modern material implication and logical implication respectively. Similar accounts are given by Jean Buridan and Albert of Saxony. The last great works in this tradition are the Logic of John Poinsot (1589–1644, known as John of St Thomas), the Metaphysical Disputations of Francisco Suarez (1548–1617), and the Logica Demonstrativa of Giovanni Girolamo Saccheri (1667–1733). |
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