Top row: Aristotle, who established the canon of western philosophy;[108] and Avicenna, who replaced
Aristotelian logic in Islamic discourse.[180] Bottom row: William of Ockham, a major figure of medieval
scholarly thought;[181] and Gottlob Frege, one of the founders of modern symbolic logic.[182]
Ibn Sina (Avicenna) was the founder of Avicennian logic, which replaced Aristotelian logic as the
dominant system of logic in the Islamic world.[189] It influenced Western medieval writers such as
Albertus Magnus and William of Ockham.[190] Ibn Sina wrote on the hypothetical syllogism[191] and on
the propositional calculus.[192] He developed an original "temporally modalized" syllogistic theory,
involving temporal logic and modal logic.[193] He also made use of inductive logic, such as his methods
of agreement, difference, and concomitant variation, which are critical to the scientific method.[191] Fakhr
al-Din al-Razi was another influential Muslim logician. He criticized Aristotelian syllogistics and
formulated an early system of inductive logic, foreshadowing the system of inductive logic developed by
John Stuart Mill.[194]
During the Middle Ages, many translations and interpretations of Aristotelian logic were made. The
works of Boethius were particularly influential. Besides translating Aristotle's work into Latin, he also
produced textbooks on logic.[195] Later, the works of Islamic philosophers such as Ibn Sina and Ibn
Rushd (Averroes) were drawn on. This expanded the range of ancient works available to medieval
Christian scholars since more Greek work was available to Muslim scholars that had been preserved in
Latin commentaries. In 1323, William of Ockham's influential Summa Logicae was released. It is a
comprehensive treatise on logic that discusses many basic concepts of logic and provides a systematic
exposition of types of propositions and their truth conditions.[196]