Editing History of logic (section)

==Medieval logic==

===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>

===Logic in medieval Europe===
[[File:Britoquestionsonoldlogic.jpg|alt=Top left corner of early printed text, with an illuminated S, beginning "Sicut dicit philosophus"|thumb|[[Radulphus Brito|Brito's]] questions on the ''Old Logic'']]

"Medieval logic" (also known as "Scholastic logic") generally means the form of Aristotelian logic developed in [[Middle Ages|medieval Europe]] throughout roughly the period 1200–1600.<ref name="Boehner p. xiv"/> 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 (historiography)|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.<ref name="Kneale198">Kneale p. 198</ref> Until the twelfth century, the only works of Aristotle available in the West were the ''Categories'', ''On Interpretation'', and Boethius's translation of the [[Isagoge]] of [[Porphyry (philosopher)|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,<ref>Stephen Dumont, article "Peter Abelard" in Gracia and Noone p. 492</ref> 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.<ref>Kneale, pp. 202–203</ref> The proof for the [[principle of explosion]], also known as the principle of Pseudo-Scotus, the law according to which any proposition can be proven from a contradiction (including its negation), was first given by the 12th century French logician [[William of Soissons]].

By the early thirteenth century, the remaining works of Aristotle's ''Organon'', including the ''[[Prior Analytics]]'', ''[[Posterior Analytics]]'', and the ''[[Sophistical Refutations]]'' (collectively known as the ''[[Logica Nova]]'' or "New Logic"), had been recovered in the West.<ref>See e.g. Kneale p. 225</ref> Logical work until then was mostly paraphrasis or commentary on the work of Aristotle.<ref>Boehner p. 1</ref> 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:<ref>Boehner pp. 19–76</ref>

* The theory of [[Supposition theory|supposition]]. Supposition theory deals with the way that predicates (''e.g.,'' 'man') range over a domain of individuals (''e.g.,'' all men).<ref>Boehner p. 29</ref> In the proposition 'every man is an animal', does the term 'man' range over or 'supposit for' men existing just in the present, or does the range include past and future men? Can a term supposit for a non-existing individual? Some medievalists have argued that this idea is a precursor of modern [[first-order logic]].<ref>Boehner p. 30</ref> "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".<ref>Ebbesen 1981</ref>
* The theory of [[Syncategorematic term|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 [[Logical consequence|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'').<ref>Boehner pp. 54–55</ref> 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 conditional|material implication]] and [[logical implication]] respectively. Similar accounts are given by [[Jean Buridan]] and [[Albert of Saxony (philosopher)|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).