History of logic

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The history of logic documents the development of logic as it occurs in various cultures and traditions in history. 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. 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 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 discovery of Indian logic among British scholars from the 18th century also influenced modern logic.

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[edit] 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.[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.[2] Babylonian thought had a considerable influence on early Greek thought.[3]

[edit] Logic in Greece

In Greece, two main competing logical traditions emerged. 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. 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. Aristotle's examination of the syllogism bears interesting comparison with the Indian schema of inference and the less rigid Chinese discussion.

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. It was only in the 19th century that this viewpoint changed.

[edit] Logic in India

Main article: Indian logic

Two of the six Indian schools of thought deal with logic: Nyaya and Vaisheshika. The Nyaya Sutras of Aksapada Gautama constitute the core texts of the Nyaya school, one of the six orthodox schools of Hindu philosophy. This realist school developed a rigid five-member schema of inference involving an initial premise, a reason, an example, an application and a conclusion. The idealist Buddhist philosophy became the chief opponent to the Naiyayikas. Nagarjuna, the founder of the Madhyamika "Middle Way" developed an analysis known as the "catuskoti" or tetralemma. 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. 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.

[edit] 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 particular, one of the schools that grew out of Mohism, the Logicians, are credited by some scholars for their early investigation of formal 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.

[edit] 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. 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. 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.

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. 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. Avicenna's system of logic was responsible for the introduction of hypothetical syllogism,[4] temporal modal logic,[5][6] and inductive logic.[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. 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.

[edit] 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. This began after the Latin translations of the 12th century, when Arabic texts on Aristotelian logic and Avicennian logic were translated into Latin. 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.

After the initial translation phase, the tradition of Medieval logic was developed through textbooks such as that by Peter of Spain (fl. 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. 1287–1347) and Jean Buridan.

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.

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).

[edit] 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. 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. 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.

[edit] 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". 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. 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".

In 1889 Giuseppe Peano published the first version of the logical axiomatization of arithmetic. Five of the nine axioms he came up with are now known as the Peano axioms. One of these axioms was a formalized statement of the principle of mathematical induction.

[edit] See also

[edit] Notes

  1. ^ H. F. J. Horstmanshoff, Marten Stol, Cornelis Tilburg (2004), Magic and Rationality in Ancient Near Eastern and Graeco-Roman Medicine, p. 99, Brill Publishers, ISBN 9004136665.
  2. ^ D. Brown (2000), Mesopotamian Planetary Astronomy-Astrology , Styx Publications, ISBN 9056930362.
  3. ^ Giorgio Buccellati (1981), "Wisdom and Not: The Case of Mesopotamia", Journal of the American Oriental Society 101 (1), p. 35-47 [43].
  4. ^ Lenn Evan Goodman (2003), Islamic Humanism, p. 155, Oxford University Press, ISBN 0195135806.
  5. ^ History of logic: Arabic logic, Encyclopædia Britannica.
  6. ^ Dr. Lotfollah Nabavi, Sohrevardi's Theory of Decisive Necessity and kripke's QSS System, Journal of Faculty of Literature and Human Sciences.
  7. ^ Science and Muslim Scientists, Islam Herald.
  8. ^ Wael B. Hallaq (1993), Ibn Taymiyya Against the Greek Logicians, p. 48. Oxford University Press, ISBN 0198240430.
  9. ^ Richard F. Washell (1973), "Logic, Language, and Albert the Great", Journal of the History of Ideas 34 (3), p. 445-450 [445].

[edit] References

  • Alonzo Church, 1936-8. "A bibliography of symbolic logic". Journal of Symbolic Logic 1: 121-218; 3:178-212.
  • Dov Gabbay and John Woods, eds, 2004. 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. 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.

[edit] External links

Logic Portal