The history of logic documents the development of logic as it occurs in various cultures and traditions in history. Logic is the study of the principles of valid demonstration and Inference. While many cultures have employed intricate systems of reasoning, and logical thinking was implicit in Babylonian thought to some extent, logic as an explicit analysis of the methods of reasoning received sustained development originally only in three traditions: those of China, India, and Greece. Babylonia was an Amorite state in lower Mesopotamia (modern southern Iraq) with Babylon as its capital In the History of logic, logic in China plays a particularly interesting role due to its length and relative isolation from the strong current of development The development of Indian logic can be said to date back to the anviksiki of Medhatithi Gautama (c Ancient Greek philosophy focused on the role of Reason and Inquiry. Although exact dates are uncertain, particularly in the case of India, it is possible that logic emerged in all three societies by the 4th century BC. The 4th century BC started the first day of 400 BC and ended the last day of 301 BC. The formally sophisticated treatment of modern logic descends from the Greek tradition, particularly Aristotelian logic, which was further developed by Islamic logicians and then medieval European logicians. The Organon is the name given by Aristotle 's followers the Peripatetics to the standard collection of his six works on Logic. Logic ( Arabic: Mantiq) played an important role in Early Islamic philosophy. The discovery of Indian logic among British scholars from the 18th century also influenced modern logic. The development of Indian logic can be said to date back to the anviksiki of Medhatithi Gautama (c

Contents 1 Logic in Mesopotamia 2 Logic in Greece 3 Logic in India 4 Logic in China 5 Logic in Islamic philosophy 6 Logic in medieval Europe 7 Traditional logic 8 The advent of modern logic 9 See also 10 Notes 11 References 12 External links

Logic in Mesopotamia

In Mesopotamia, Esagil-kin-apli's medical Diagnostic Handbook written in the 11th century BC was based on a logical set of axioms and assumptions, including the modern view that through the examination and inspection of the symptoms of a patient, it is possible to determine the patient's disease, its aetiology and future development, and the chances of the patient's recovery. Mesopotamia (from the Greek meaning "land between the rivers" is an area geographically located between the Tigris and Euphrates rivers largely corresponding In traditional Logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject ^[1]

During the 8th and 7th centuries BC, Babylonian astronomers began employing an internal logic within their predictive planetary systems, which was an important contribution to logic and the philosophy of science. Babylonian astronomy refers to the astronomical theories and methods that were developed in ancient Mesopotamia, the "land between the rivers" Tigris Philosophy of science is the study of assumptions foundations and implications of Science. ^[2] Babylonian thought had a considerable influence on early Greek thought. Babylonia was an Amorite state in lower Mesopotamia (modern southern Iraq) with Babylon as its capital ^[3]

Logic in Greece

In Greece, two main competing logical traditions emerged. Greece (Ελλάδα transliterated: Elláda, historically, Ellás,) officially the Hellenic Republic (Ελληνική Δημοκρατία Stoic logic traced its roots back to Euclid of Megara, a pupil of Socrates, and with its concentration on propositional logic was perhaps closer to modern logic. Stoicism, a school of Hellenistic philosophy, was founded in Athens by Zeno of Citium in the early third century BC Euclid of Megara, a Greek Socratic Philosopher who lived around 400 BC founded the Megarian school of philosophy. SOCRATES is the European Community action programme in the field of Education. This is a technical mathematical article about the area of mathematical logic variously known as "propositional calculus" or "propositional logic" However, the tradition that survived to influence later cultures was the Peripatetic tradition which originated in Aristotle's collection of works known as the Organon or instrument, the first systematic Greek work on logic. The Peripatetics were members of a school of philosophy in Ancient Greece. Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. The Organon is the name given by Aristotle 's followers the Peripatetics to the standard collection of his six works on Logic. Aristotle's examination of the syllogism bears interesting comparison with the Indian schema of inference and the less rigid Chinese discussion. A syllogism, or logical appeal, (συλλογισμός &mdash "conclusion" "inference" (usually the categorical syllogism) is a kind of

Through Latin in Western Europe, and disparate languages more to the East, such as Arabic, Armenian, and Georgian, the Aristotelian tradition was considered to pre-eminently codify the laws of reasoning. Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. Arabic (ar الْعَرَبيّة (informally ar عَرَبيْ) in terms of the number of speakers is the largest living member of the Semitic language The Armenian language (hy հայերեն լեզու hajɛɹɛn lɛzu —, conventional short form) is an Indo-European language spoken by the Armenian Georgian (ka ქართული ენა kartuli ena) is the Official language of Georgia, a country in the Caucasus. It was only in the 19th century that this viewpoint changed. The 19th century of the Common Era began on January 1, 1801 and ended on December 31, 1900, according to the Gregorian calendar

Logic in India

Main article: Indian logic

Two of the six Indian schools of thought deal with logic: Nyaya and Vaisheshika. The development of Indian logic can be said to date back to the anviksiki of Medhatithi Gautama (c Nyāya ( Sanskrit ni-āyá, literally "recursion" used in the sense of " Syllogism, inference" is the name given to one of the six orthodox Vaisheshika, or Vaiśeṣika, (Sanskrit वैशॆषिक) is one of the six Hindu schools of Philosophy (orthodox Vedic systems The Nyaya Sutras of Aksapada Gautama constitute the core texts of the Nyaya school, one of the six orthodox schools of Hindu philosophy. The Nyāya Sūtras is an ancient Indian text on of Philosophy composed by Akṣapāda Gautama (also Gotama; c The Nyāya Sūtras is an ancient Indian text on of Philosophy composed by Akṣapāda Gautama (also Gotama; c A Hindu ( Devanagari: हिन्दू is an adherent of the philosophies and scriptures of Hinduism, a set of religious, Philosophical This realist school developed a rigid five-member schema of inference involving an initial premise, a reason, an example, an application and a conclusion. Contemporary philosophical realism is the belief in a Reality that is completely Ontologically independent of our conceptual schemes linguistic practices beliefs Inference is the act or process of deriving a Conclusion based solely on what one already knows The idealist Buddhist philosophy became the chief opponent to the Naiyayikas. In Western civilization, Idealism is the philosophy which maintains that the Ultimate nature of reality is ideal or based upon ideas values essences The so-called Buddhist philosophy deals extensively with problems in Metaphysics, phenomenology, Ethics, and Epistemology. Nagarjuna, the founder of the Madhyamika "Middle Way" developed an analysis known as the "catuskoti" or tetralemma. Acharya Nāgārjuna ( Telugu: నాగార్జున (c 150 - 250 CE) was an Indian philosopher the founder of the Madhyamaka Madhyamaka ( Sanskrit: मध्यमक Madhyamaka,, Pinyin: Zhōngguānzōng; also known as Śunyavada) is a Buddhist The tetralemma ( catuskoti) is a figure that features prominently in Indian traditional logic This four-cornered argumentation systematically examined and rejected the affirmation of a proposition, its denial, the joint affirmation and denial, and finally, the rejection of its affirmation and denial. But it was with Dignaga and his successor Dharmakirti that Buddhist logic reached its height. Dignāga ( fl 5th century) was an Indian scholar and one of the Buddhist founders of Indian logic. Dharmakirti ( ca 7th century was an Indian scholar and one of the Buddhist founders of Indian philosophical logic. Their analysis centered on the definition of necessary logical entailment, "vyapti", also known as invariable concomitance or pervasion. To this end a doctrine known as "apoha" or differentiation was developed. This involved what might be called inclusion and exclusion of defining properties. The difficulties involved in this enterprise, in part, stimulated the neo-scholastic school of Navya-Nyāya, which developed a formal analysis of inference in the 16th century. The Navya-Nyāya or Neo-Logical darśana (view system or school of Indian Philosophy was founded in the 13th century CE

Logic in China

Main article: Logic in China

In China, a contemporary of Confucius, Mozi, "Master Mo", is credited with founding the Mohist school, whose canons dealt with issues relating to valid inference and the conditions of correct conclusions. In the History of logic, logic in China plays a particularly interesting role due to its length and relative isolation from the strong current of development Confucius ( lit " Master Kung " September 28, 551 BC - 479 BC) was a Chinese thinker and social philosopher Mozi ( Lat as Micius, ca 470 BCE&ndashca 391 BCE was a Philosopher who lived in China during the Hundred Schools of Thought Mohism or Moism ( was a Chinese philosophy developed by the followers of Mozi (also referred to as Mo Di 470 &ndashc In particular, one of the schools that grew out of Mohism, the Logicians, are credited by some scholars for their early investigation of formal logic. The Logicians or School of Names (名家 Míngjiā; "School of names" was a Chinese philosophical school that grew out of Mohism Mathematical logic is a subfield of Logic and Mathematics with close connections to Computer science and Philosophical logic. Unfortunately, due to the harsh rule of Legalism in the subsequent Qin Dynasty, this line of investigation disappeared in China until the introduction of Indian philosophy by Buddhists. In Chinese history, Legalism ( was one of the four main philosophic schools during the Spring and Autumn Period and the Warring States Period (the other Not to be confused with the Qing Dynasty, the last dynasty of China Buddhism is a family of beliefs and practices

Logic in Islamic philosophy

Main article: Logic in Islamic philosophy

For a time after Muhammad's death, Islamic law placed importance on formulating standards of argument, which gave rise to a novel approach to logic in Kalam, but this approach was later displaced by ideas from Greek philosophy and Hellenistic philosophy with the rise of the Mu'tazili philosophers, who highly valued Aristotle's Organon. Logic ( Arabic: Mantiq) played an important role in Early Islamic philosophy. IMPORTANT PLEASE READ ##### For all questions relating to the addition of (pbuh peace be upon him or other honorifics Sharia ( Arabic: ar شريعة) is the body of Islamic Religious law. Kalām (علم الكلام is the Islamic philosophy of seeking Islamic theological principles through Dialectic. Ancient Greek philosophy focused on the role of Reason and Inquiry. Hellenistic philosophy is the period of Western philosophy that was developed in the Hellenistic civilization following Aristotle and ending with Neoplatonism Muʿtazilah ( Arabic المعتزلة al-mu`tazilah) is a theological school of thought within Sunni Islam. Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. The Organon is the name given by Aristotle 's followers the Peripatetics to the standard collection of his six works on Logic. The works of Hellenistic-influenced Islamic philosophers were crucial in the reception of Aristotelian logic in medieval Europe, along with the commentaries on the Organon by Averroes. Abū 'l-Walīd Muḥammad ibn Aḥmad ibn Rushd (Arabicأبو الوليد محمد بن احمد بن رشد better known just as Ibn Rushd (ابن رشد and in European The works of al-Farabi, Avicenna, al-Ghazali and other Muslim logicians who often criticized and corrected Aristotelian logic and introduced their own forms of logic, also played a central role in the subsequent development of medieval European logic. TemplateInfobox Muslim scholars --> Abū Nasr Muhammad ibn al-Farakh al-Fārābi ( Nastaliq:) or Abū Nasr al-Fārābi TemplateInfobox Muslim scholars --> ( Persian /ابو علی الحسین ابن عبدالله ابن سینا (born Abū Ḥāmid Muḥammad ibn Muḥammad al-Ghazālī (1058-1111 ( ابو حامد محمد ابن محمد الغزالی or امام محمد غزالی was born and died

Islamic logic not only included the study of formal patterns of inference and their validity but also elements of the philosophy of language and elements of epistemology and metaphysics. Inference is the act or process of deriving a Conclusion based solely on what one already knows Epistemology (from Greek επιστήμη - episteme, "knowledge" + λόγος, " Logos " or theory of knowledge Metaphysics is the branch of Philosophy investigating principles of reality transcending those of any particular science Due to disputes with Arabic grammarians, Islamic philosophers were very interested in working out the relationship between logic and language, and they devoted much discussion to the question of the subject matter and aims of logic in relation to reasoning and speech. In the area of formal logical analysis, they elaborated upon the theory of terms, propositions and syllogisms. They considered the syllogism to be the form to which all rational argumentation could be reduced, and they regarded syllogistic theory as the focal point of logic. Even poetics was considered as a syllogistic art in some fashion by many major Islamic logicians.

Important developments made by Muslim logicians included the development of "Avicennian logic" as a replacement of Aristotelian logic. Logic ( Arabic: Mantiq) played an important role in Early Islamic philosophy. Avicenna's system of logic was responsible for the introduction of hypothetical syllogism,^[4] temporal modal logic,^[5][6] and inductive logic. TemplateInfobox Muslim scholars --> ( Persian /ابو علی الحسین ابن عبدالله ابن سینا (born In Logic, a hypothetical syllogism has two uses In Propositional logic it expresses a rule of inference while in the History of logic, it is a short-hand In Logic, the term temporal logic is used to describe any system of rules and symbolism for representing and reasoning about propositions qualified in terms of Time A modal logic is any system of formal logic that attempts to deal with modalities. Induction or inductive reasoning, sometimes called inductive logic, is the process of Reasoning in which the premises of an argument are believed ^[7][8] Other important developments in Islamic philosophy include the development of a strict science of citation, the isnad or "backing", and the development of a scientific method of open inquiry to disprove claims, the ijtihad, which could be generally applied to many types of questions. Scientific Citation is the Process by which Conclusions of previous Scientists are used to justify experimental Procedures Apparatus A Hadith was originally just an Arabic story As the stories began to be used formally it became common to provide their chain of transmitters (or sanad سند plural Scientific method refers to bodies of Techniques for investigating phenomena Ijtihad (Arabic اجتهاد is a technical term of Islamic law that describes the process of making a legal decision by independent interpretation of the legal sources From the 12th century, despite the logical sophistication of al-Ghazali, the rise of the Asharite school in the late Middle Ages slowly limited original work on logic in the Islamic world, though it did continue into the 15th century. Abū Ḥāmid Muḥammad ibn Muḥammad al-Ghazālī (1058-1111 ( ابو حامد محمد ابن محمد الغزالی or امام محمد غزالی was born and died The Ash'ari theology ( Arabic الأشاعرة al-asha`irah) is a school of early Muslim speculative theology founded by the theologian Abu al-Hasan

Logic in medieval Europe

"Medieval logic" (also known as "Scholastic logic") generally means the form of Aristotelian logic developed in medieval Europe throughout the period c 1200–1600. The Organon is the name given by Aristotle 's followers the Peripatetics to the standard collection of his six works on Logic. This began after the Latin translations of the 12th century, when Arabic texts on Aristotelian logic and Avicennian logic were translated into Latin. The Renaissance of the 12th century saw a major search by European scholars for new learning which led them to the Arabic fringes of Europe especially to Islamic Logic ( Arabic: Mantiq) played an important role in Early Islamic philosophy. While Avicennian logic had an influence on early medieval European logicians such as Albertus Magnus,^[9] the Aristotelian tradition became more dominant due to the strong influence of Averroism. Averroism is the term applied to either of two philosophical trends among scholastics in the late 13th century, the first of which was based on the

After the initial translation phase, the tradition of Medieval logic was developed through textbooks such as that by Peter of Spain (fl. Peter of Spain or in Latin, Petrus Hispanus ( 13th century) is the Mediaeval author of Tractatus, a standard textbook on Logic 13th century), whose exact identity is unknown, who was the author of a standard textbook on logic, the Tractatus, which was well known in Europe for many centuries.

The tradition reached its high point in the fourteenth century, with the works of William of Ockham (c. William of Ockham (also Occam, Hockham, or any of several other spellings ˈɒkəm (c 1287–1347) and Jean Buridan. Jean Buridan (in Latin, Johannes Buridanus; ca 1295 &ndash 1358 was a French Priest who sowed the seeds of the Copernican revolution

One feature of the development of Aristotelian logic through what is known as Supposition Theory, a study of the semantics of the terms of the proposition. Supposition theory was a branch of Medieval logic that was probably aimed at giving accounts of issues similar to modern accounts of Reference, Plurality

The last great works in this tradition are the Logic of John Poinsot (1589–1644, known as John of St Thomas), and the Metaphysical Disputations of Francisco Suarez (1548–1617). John of St Thomas, (family name John Poinsot) Theologian, born at Lisbon, 9 June, 1589; died at Fraga, Spain Francisco Suárez ( 5 January 1548, Granada, Spain - 25 September 1617, Lisbon, Portugal) was a

Traditional logic

"Traditional Logic" generally means the textbook tradition that begins with Antoine Arnauld and Pierre Nicole's Logic, or the Art of Thinking, better known as the Port-Royal Logic. Antoine Arnauld, ( February 6, 1612 - August 6, 1694) &mdash le Grand as contemporaries called him to distinguish him from his Pierre Nicole ( 1625 - November 16, 1695) was one of the most distinguished of the French Jansenists Born in Chartres Port-Royal Logic, or Logique de Port-Royal, is the common name of La logique ou l'art de penser, an important textbook on logic first published anonymously Published in 1662, it was the most influential work on logic in England until Mill's System of Logic in 1825. The book presents a loosely Cartesian doctrine (that the proposition is a combining of ideas rather than terms, for example) within a framework that is broadly derived from Aristotelian and medieval term logic. Between 1664 and 1700 there were eight editions, and the book had considerable influence after that. It was frequently reprinted in English up to the end of the nineteenth century.

The account of propositions that Locke gives in the Essay is essentially that of Port-Royal: "Verbal propositions, which are words, [are] the signs of our ideas, put together or separated in affirmative or negative sentences. In Logic and Philosophy, proposition refers to either (a the content or Meaning of a meaningful Declarative sentence So that proposition consists in the putting together or separating these signs, according as the things which they stand for agree or disagree. " (Locke, An Essay Concerning Human Understanding, IV. 5. 6)

Works in this tradition include Isaac Watts' Logick: Or, the Right Use of Reason (1725), Richard Whately's Logic (1826), and John Stuart Mill's A System of Logic (1843), which was one of the last great works in the tradition. Isaac Watts ( July 17, 1674 – November 25, 1748) is recognised as the "Father of English Hymnody" as he was the first prolific and Richard Whately ( 1 February 1787 – 8 October 1863) was an English Logician and theological writer who also John Stuart Mill (20 May 1806 &ndash 8 May 1873 British Philosopher, political economist, civil servant and Member of Parliament, was an influential

The advent of modern logic

Historically, Descartes, may have been the first philosopher to have had the idea of using algebra, especially its techniques for solving for unknown quantities in equations, as a vehicle for scientific exploration. The idea of a calculus of reasoning was also cultivated by Gottfried Wilhelm Leibniz. Leibniz was the first to formulate the notion of a broadly applicable system of mathematical logic. However, the relevant documents were not published until 1901 or remain unpublished to the present day, and the current understanding of the power of Leibniz's discoveries did not emerge until the 1980s. See Lenzen's chapter in Gabbay and Woods (2004).

Gottlob Frege in his 1879 Begriffsschrift extended formal logic beyond propositional logic to include constructors such as "all", "some". Friedrich Ludwig Gottlob Frege ( 8 November 1848, Wismar, Grand Duchy of Mecklenburg-Schwerin  &ndash 26 July 1925 Begriffsschrift is the title of a short book on Logic by Gottlob Frege, published in 1879, and is also the name of the Formal system He showed how to introduce variables and quantifiers to reveal the logical structure of sentences, which may have been obscured by their grammatical structure. For instance, "All humans are mortal" becomes "All things x are such that, if x is a human then x is mortal. " Frege's peculiar two dimensional notation led to his work being ignored for many years.

In a masterly 1885 article read by Peano, Ernst Schröder, and others, Charles Peirce introduced the term "second-order logic" and provided us with much of our modern logical notation, including prefixed symbols for universal and existential quantification. Giuseppe Peano ( August 27, 1858 &ndash April 20, 1932) was an Italian Mathematician, whose work was of exceptional For the actor see Ernst Schröder (actor. Ernst Schröder ( 25 November, 1841 Mannheim Germany – Charles Sanders Peirce (pronounced purse) (September 10 1839 &ndash April 19 1914 was an American Logician mathematician, philosopher In Logic and Mathematics second-order logic is an extension of First-order logic, which itself is an extension of Propositional logic. Logicians in the late 19th and early 20th centuries were thus more familiar with the Peirce-Schröder system of logic, although Frege is generally recognized today as being the "Father of modern logic". The 19th century of the Common Era began on January 1, 1801 and ended on December 31, 1900, according to the Gregorian calendar The twentieth century of the Common Era began on

In 1889 Giuseppe Peano published the first version of the logical axiomatization of arithmetic. Year 1889 ( MDCCCLXXXIX) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar (or a Common Giuseppe Peano ( August 27, 1858 &ndash April 20, 1932) was an Italian Mathematician, whose work was of exceptional Five of the nine axioms he came up with are now known as the Peano axioms. In Mathematical logic, the Peano axioms, also known as the Dedekind-Peano axioms or the Peano postulates, are a set of Axioms for the Natural One of these axioms was a formalized statement of the principle of mathematical induction. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Mathematical induction is a method of Mathematical proof typically used to establish that a given statement is true of all Natural numbers It is done by proving that

See also

• Term Logic
• Ernst Schröder
• Charles Peirce

Notes

References

• Alonzo Church, 1936-8. Alonzo Church ( June 14, 1903 – August 11, 1995) was an American Mathematician and logician "A bibliography of symbolic logic". Journal of Symbolic Logic 1: 121-218; 3:178-212.
• Dov Gabbay and John Woods, eds, 2004. Dov M Gabbay is Augustus De Morgan Professor of Logic at the Group of Logic, Language and Computation, Department of Handbook of the History of Logic. Vol. 1: Greek, Indian and Arabic logic; Vol. 3: The Rise of Modern Logic I: Leibniz to Frege. Elsevier, ISBN 0-444-51611-5.
• Ivor Grattan-Guinness, 2000. Ivor Grattan-Guinness (Born 23 June 1941 Bakewell, England is a Historian of mathematics and Logic. The Search for Mathematical Roots 1870-1940. Princeton University Press.
• Kneale, William and Martha, 1962. The development of logic. Oxford University Press, ISBN 0-19-824773-7.

External links

• History of logic and his relation to ontology: an annotated bibliography
• Overview of Indian and Greek Development of Logic and Language
• Petrus Hispanus (Stanford Encyclopedia of Philosophy)
• Paul Spade's "Thoughts Words and Things"
• John of St Thomas
• Joyce's Principles of Logic (Traditional Logic Primer)
• Article on Logic in Britannica 1911 - a good summary of developments in logic before Frege-Russell

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