Editing History of logic (section)

===Logic in the Middle East===
{{Main|Logic in Islamic philosophy}}
{{See also|Avicennism#Avicennian logic|l1=Avicennian logic}}
[[File:Canon-Avicenna-small.jpg|alt=Arabic text in pink and blue|thumb|A text by [[Avicenna]], founder of [[Avicennism#Avicennian logic|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.<ref>See e.g. [http://www.rep.routledge.com/article/H057 Routledge Encyclopedia of Philosophy Online Version 2.0]  {{webarchive |url=https://web.archive.org/web/20220606082214/https://www.rep.routledge.com/articles/islamic-philosophy;jsessionid=B31B033F077DD5E68E09CC9D35C02105 |date=2022-06-06}}, article 'Islamic philosophy'</ref> [[Al-Farabi]] (Alfarabi) (873–950) was an Aristotelian logician who discussed the topics of [[future contingent]]s, the number and relation of the categories, the relation between [[logic]] and [[grammar]], and non-Aristotelian forms of [[inference]].<ref name="Britannica"/> Al-Farabi also considered the theories of [[conditional syllogism]]s and [[Analogy|analogical inference]], which were part of the [[Stoicism|Stoic]] tradition of logic rather than the Aristotelian.<ref>{{cite journal |issn=0022-362X |volume=61 |issue=22 |pages=724–734 |author-last=Feldman |author-first=Seymour |title=Rescher on Arabic Logic |journal=The Journal of Philosophy |date=1964-11-26 |jstor=2023632 |doi=10.2307/2023632 |publisher=Journal of Philosophy, Inc.}} [726]. {{cite book |publisher=Cambridge University Press |isbn=0-521-27556-3 |author-last1=Long |author-first1=A. A. |author-first2=D. N. |author-last2=Sedley |title=The Hellenistic Philosophers. Vol 1: Translations of the principal sources with philosophical commentary |location=Cambridge |date=1987}}</ref>

[[Maimonides]] (1138-1204) wrote a ''Treatise on Logic'' (Arabic: ''Maqala Fi-Sinat Al-Mantiq''), referring to Al-Farabi as the "second master", the first being Aristotle.

[[Avicenna|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,<ref name="Hasse">{{cite encyclopedia |author-first=Dag Nikolaus |author-last=Hasse |title=Influence of Arabic and Islamic Philosophy on the Latin West |encyclopedia=[[Stanford Encyclopedia of Philosophy]] |date=19 September 2008 |url=http://plato.stanford.edu/entries/arabic-islamic-influence/ |access-date=2009-10-13}}</ref> and also had an important influence on Western medieval writers such as [[Albertus Magnus]].<ref>Richard F. Washell (1973), "Logic, Language, and Albert the Great", ''Journal of the History of Ideas'' '''34''' (3), pp. 445–450 [445].</ref> Avicenna wrote on the [[hypothetical syllogism]]<ref name="Goodman"/> and on the [[propositional calculus]], which were both part of the Stoic logical tradition.<ref>Goodman, Lenn Evan (1992); ''Avicenna'', p. 188, [[Routledge]], {{ISBN|0-415-01929-X}}.</ref> He developed an original "temporally modalized" syllogistic theory, involving [[temporal logic]] and [[modal logic]].<ref name="Britannica">[http://www.britannica.com/ebc/article-65928 History of logic: Arabic logic], ''[[Encyclopædia Britannica]]''.</ref> He also made use of [[inductive reasoning|inductive logic]], such as the [[Mill's Methods|methods of agreement, difference, and concomitant variation]] which are critical to the [[scientific method]].<ref name="Goodman">Goodman, Lenn Evan (2003), ''Islamic Humanism'', p. 155, [[Oxford University Press]], {{ISBN|0-19-513580-6}}.</ref> 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.<ref>Kneale p. 229</ref> 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.<ref>Kneale: p. 266; Ockham: [[Summa Logicae]] i. 14; Avicenna: ''Avicennae Opera'' Venice 1508 f87rb</ref>

[[Fakhr al-Din al-Razi]] (b. 1149) criticised Aristotle's "[[Syllogism|first figure]]" and formulated an early system of inductive logic, foreshadowing the system of inductive logic developed by [[John Stuart Mill]] (1806–1873).<ref name="Iqbal">[[Muhammad Iqbal]], ''[[The Reconstruction of Religious Thought in Islam]]'', "The Spirit of Muslim Culture" ([[cf.]] [http://www.allamaiqbal.com/works/prose/english/reconstruction] and [http://www.witness-pioneer.org/vil/Books/MI_RRTI/chapter_05.htm])</ref> Al-Razi's work was seen by later Islamic scholars as marking a new direction for Islamic logic, towards a [[Logic in Islamic philosophy#Post-Avicennian logic|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 [[concept]]ions and [[Grammar of Assent|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.<ref name="Stanford"/>

The [[Illuminationist philosophy|Illuminationist school]] was founded by [[Shahab al-Din Suhrawardi]] (1155–1191), who developed the idea of "decisive necessity", which refers to the reduction of all modalities (necessity, [[Logical possibility|possibility]], [[Contingency (philosophy)|contingency]] and [[Epistemic possibility|impossibility]]) to the single mode of necessity.<ref>Lotfollah Nabavi, [http://public.ut.ac.ir/html/fac/lit/articles.html Sohrevardi's Theory of Decisive Necessity and kripke's QSS System] {{webarchive|url=https://web.archive.org/web/20080126100838/http://public.ut.ac.ir/html/fac/lit/articles.html |date=2008-01-26 }}, ''Journal of Faculty of Literature and Human Sciences''.</ref> [[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'').<ref name="Roubi">Abu Shadi Al-Roubi (1982), "Ibn Al-Nafis as a philosopher", ''Symposium on Ibn al-Nafis'', Second International Conference on Islamic Medicine: Islamic Medical Organization, Kuwait ([[cf.]] [http://www.islamset.com/isc/nafis/drroubi.html Ibn al-Nafis As a Philosopher] {{webarchive |url=https://web.archive.org/web/20080206072116/http://www.islamset.com/isc/nafis/drroubi.html |date=2008-02-06}}, ''Encyclopedia of Islamic World'').</ref> [[Ibn Taymiyyah]] (1263–1328), wrote the ''Ar-Radd 'ala al-Mantiqiyyin'', where he argued against the usefulness, though not the validity, of the [[syllogism]]<ref>See pp.&nbsp;253–254 of {{cite book |publisher=Cambridge University Press |isbn=978-0-521-52069-0 |pages=247–265 |editor1=Peter Adamson |editor2=Richard C. Taylor |author-last=Street |author-first=Tony |title=The Cambridge Companion to Arabic Philosophy |chapter=Logic |date=2005}}</ref> and in favour of [[inductive reasoning]].<ref name="Iqbal"/> Ibn Taymiyyah also argued against the certainty of [[syllogism|syllogistic arguments]] and in favour of [[analogy]]; his argument is that concepts founded on [[inductive reasoning|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.<ref>{{cite journal |author=Ruth Mas |title=Qiyas: A Study in Islamic Logic |journal=Folia Orientalia |volume=34 |pages=113–128 |date=1998 |url=http://www.colorado.edu/ReligiousStudies/faculty/mas/LOGIC.pdf |issn=0015-5675}}</ref><ref name="Sowa">{{cite conference |author1=John F. Sowa |author2=Arun K. Majumdar |title=Analogical reasoning |book-title=Conceptual Structures for Knowledge Creation and Communication, Proceedings of ICCS 2003 |publisher=Springer-Verlag |date=2003 |location=Berlin |url=http://www.jfsowa.com/pubs/analog.htm |author-link1=John F. Sowa}}, pp. 16–36</ref> This model of analogy has been used in the recent work of [[John F. Sowa]].<ref name="Sowa"/>

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.<ref>[[Nicholas Rescher]] and Arnold vander Nat, "The Arabic Theory of Temporal Modal Syllogistic", in George Fadlo Hourani (1975), ''Essays on Islamic Philosophy and Science'', pp. 189–221, [[State University of New York Press]], {{ISBN|0-87395-224-3}}.</ref> 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.<ref name="Stanford">{{cite encyclopedia |author=Tony Street |title=Arabic and Islamic Philosophy of Language and Logic |encyclopedia=[[Stanford Encyclopedia of Philosophy]] |date=23 July 2008 |url=http://plato.stanford.edu/entries/arabic-islamic-language |access-date=2008-12-05}}</ref>