Logic Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.Anti-spam check. Do not fill this in! ==History== {{Main|History of logic}} {{multiple image|perrow= 2|total_width=330 | image1= Aristotle_Altemps_Inv8575.jpg | alt1= Bust of Aristotle | image2= Avicenne_-_Avicenna_-_Ibn_Sina_(980-1037)_CIPB2067.jpg | alt2= Portrait of Avicenna | image3= Guillaume Occam.jpg | alt3= Portrait of William of Ockham | image4= Wismar Marienkirche Bronzebüste Gottlob Frege (01-1).JPG | alt4= Bust showing Gottlob Frege | footer= Top row: [[Aristotle]], who established the canon of western philosophy;{{sfn |Groarke}} and [[Avicenna]], who replaced Aristotelian logic in [[Logic in Islamic philosophy|Islamic discourse]].{{sfn |Lagerlund |2018}} Bottom row: [[William of Ockham]], a major figure of medieval scholarly thought;{{sfn |Spade |Panaccio |2019}} and [[Gottlob Frege]], one of the founders of modern symbolic logic.{{sfnm|1a1=Haaparanta|1y=2009|1pp=[https://books.google.com/books?id=0jXavKsArnIC&pg=PA4 4–6] |1loc=1. Introduction|2a1=Hintikka|2a2=Spade|2loc=Modern logic, Logic since 1900 |3a=Klement |3y=1995a}} }} Logic was developed independently in several cultures during antiquity. One major early contributor was [[Aristotle]], who developed ''term logic'' in his ''[[Organon]]'' and ''[[Prior Analytics]]''.{{sfnm|1a1=Kline|1y=1972|1loc="A major achievement of Aristotle was the founding of the science of logic", p. 53|2a1=Łukasiewicz|2y=1957|2p=7|3a1=Liu|3a2=Guo|3y=2023|3p=15}} He was responsible for the introduction of the [[hypothetical syllogism]]{{sfn| Lear |1980 |page=34}} and temporal modal logic.{{sfnm|1a1=Knuuttila|1y=1980|1p=71|2a1=Fisher|2a2=Gabbay|2a3=Vila|2y=2005|2p=119}} Further innovations include inductive logic{{sfn|Berman|2009|p=133}} as well as the discussion of new logical concepts such as [[terminology|terms]], [[predicable]]s, syllogisms, and propositions. Aristotelian logic was highly regarded in classical and medieval times, both in Europe and the Middle East. It remained in wide use in the West until the early 19th century.{{sfnm|1a1=Frede|2a1=Groarke}} It has now been superseded by later work, though many of its key insights are still present in modern systems of logic.{{sfnm|1a1=Ewald|1y=2019|2a1=Smith|2y=2022|loc=1. Introduction}} [[Avicenna|Ibn Sina]] (Avicenna) was the founder of Avicennian logic, which replaced Aristotelian logic as the dominant system of [[Logic in Islamic philosophy|logic in the Islamic world]].{{sfnm|1a1=Hasse|1y=2008|2a1=Lagerlund|2y=2018}} It influenced Western medieval writers such as [[Albertus Magnus]] and [[William of Ockham]].{{sfnm|1a1=Washell|1y=1973|1pp=445–50|2a1=Kneale|2a2=Kneale|2y=1962|2pp=229, 266}} Ibn Sina wrote on the hypothetical syllogism{{sfn |Goodman |2003 |p=155}} and on the [[propositional calculus]].{{sfn |Goodman |1992 |p=188}} He developed an original "temporally modalized" syllogistic theory, involving temporal logic and modal logic.{{sfn |Hintikka |Spade |loc=[https://www.britannica.com/topic/history-of-logic/Medieval-logic#ref65928 Arabic Logic]}} He also made use of inductive logic, such as [[Mill's Methods|his methods]] of agreement, difference, and concomitant variation, which are critical to the [[scientific method]].{{sfn |Goodman |2003 |p=155}} [[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.{{sfn |Iqbal |2013 |pp=99–115 |loc=The Spirit of Muslim Culture}} During the [[Middle Ages]], many translations and interpretations of Aristotelian logic were made. Of particular influence were the works of [[Boethius]]. Besides translating Aristotle's work into Latin, he also produced textbooks on logic.{{sfnm|1a1=Marenbon|1y=2021|1loc=Introduction; 3. The Logical Text-Books|2a1=Hintikka|2a2=Spade}} Later, the works of Islamic philosophers such as Ibn Sina and [[Averroes|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 ''[[Sum of Logic|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.{{sfnm|1a1=Hintikka|1a2=Spade|2a1=Hasse|2y=2008|3a1=Spade|3a2=Panaccio|3y=2019}} In Chinese philosophy, the [[School of Names]] and [[Mohism]] were particularly influential. The School of Names focused on the use of language and on paradoxes. For example, [[Gongsun Long]] proposed the [[white horse paradox]], which defends the thesis that a white horse is not a horse. The school of Mohism also acknowledged the importance of language for logic and tried to relate the ideas in these fields to the realm of ethics.{{sfnm|1a1=Willman|1y=2022|2a1=Rošker|2y=2015|2pp=301–309}} In India, the study of logic was primarily pursued by the schools of [[Nyaya]], [[Buddhism]], and [[Jainism]]. It was not treated as a separate academic discipline and discussions of its topics usually happened in the context of epistemology and theories of dialogue or argumentation.{{sfn |Sarukkai |Chakraborty |2022 |pp=117–8}} In Nyaya, inference is understood as a source of knowledge ([[pramāṇa]]). It follows the perception of an object and tries to arrive at conclusions, for example, about the cause of this object.{{sfnm |1a1=Dasti|1loc=Lead section; 1b. Inference |2a1=Mills|2y=2018|2p=[https://books.google.com/books?id=sGhqDwAAQBAJ&pg=PA121 121]}} A similar emphasis on the relation to epistemology is also found in Buddhist and Jainist schools of logic, where inference is used to expand the knowledge gained through other sources.{{sfnm|1a1=Emmanuel|1y=2015|1pp=320–2|2a1=Vidyabhusana|2y=1988|2p=221}} Some of the later theories of Nyaya, belonging to the [[Navya-Nyāya]] school, resemble modern forms of logic, such as Gottlob Frege's distinction between [[sense and reference]] and his definition of number.{{sfn |Chakrabarti |1976 |pp=554–563}} The syllogistic logic developed by Aristotle predominated in the West until the mid-19th century, when interest in the foundations of mathematics stimulated the development of modern symbolic logic.{{sfnm|1a1=Groarke|2a1=Haaparanta|2y=2009|2pp=[https://books.google.com/books?id=0jXavKsArnIC&pg=PA3 3–5]|2loc=1. Introduction}} Many see Gottlob Frege's ''[[Begriffsschrift]]'' as the birthplace of modern logic. [[Gottfried Wilhelm Leibniz]]'s idea of a [[characteristica universalis|universal formal language]] is often considered a forerunner. Other pioneers were [[George Boole]], who invented [[Boolean algebra]] as a mathematical system of logic, and [[Charles Peirce]], who developed the [[logic of relatives]]. Alfred North Whitehead and Bertrand Russell, in turn, condensed many of these insights in their work ''[[Principia Mathematica]]''. Modern logic introduced novel concepts, such as [[Function (mathematics)|functions]], quantifiers, and relational predicates. A hallmark of modern symbolic logic is its use of formal language to precisely codify its insights. In this regard, it departs from earlier logicians, who relied mainly on natural language.{{sfnm|1a1=Haaparanta|1y=2009|1pp=[https://books.google.com/books?id=0jXavKsArnIC&pg=PA4 4–6] |loc=1. Introduction|2a1=Hintikka|2a2=Spade|2loc=Modern logic, Logic since 1900}} Of particular influence was the development of first-order logic, which is usually treated as the standard system of modern logic.{{sfn |Ewald |2019}} Its analytical generality allowed the formalization of mathematics and drove the investigation of [[set theory]]. It also made Alfred Tarski's approach to [[model theory]] possible and provided the foundation of modern mathematical logic.{{sfnm|1a1=Ewald|1y=2019|2a1=Schreiner|2y=2021|2p=22}} Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see Christianpedia:Copyrights for details). Do not submit copyrighted work without permission! Cancel Editing help (opens in new window) Discuss this page