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| title | chunk | source | category | tags | date_saved | instance |
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| History of logic | 1/13 | https://en.wikipedia.org/wiki/History_of_logic | reference | science, encyclopedia | 2026-05-05T03:59:53.898187+00:00 | kb-cron |
The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic (or term logic) as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. The Stoics, especially Chrysippus, began the development of predicate logic. Christian and Islamic philosophers such as Boethius (died 524), Avicenna (died 1037), Thomas Aquinas (died 1274) and William of Ockham (died 1347) further developed Aristotle's logic in the Middle Ages, reaching a high point in the mid-fourteenth century, with Jean Buridan. The period between the fourteenth century and the beginning of the nineteenth century saw largely decline and neglect, and at least one historian of logic regards this time as barren. Empirical methods ruled the day, as evidenced by Sir Francis Bacon's Novum Organon of 1620. Logic revived in the mid-nineteenth century, at the beginning of a revolutionary period when the subject developed into a rigorous and formal discipline which took as its exemplar the exact method of proof used in mathematics, a hearkening back to the Greek tradition. The development of the modern "symbolic" or "mathematical" logic during this period by the likes of Boole, Frege, Russell, and Peano is the most significant in the two-thousand-year history of logic, and is arguably one of the most important and remarkable events in human intellectual history. Progress in mathematical logic in the first few decades of the twentieth century, particularly arising from the work of Gödel and Tarski, had a significant impact on analytic philosophy and philosophical logic, particularly from the 1950s onwards, in subjects such as modal logic, temporal logic, deontic logic, and relevance logic.
== Logic in India ==
=== Hindu logic ===
==== Origin ==== The Nasadiya Sukta of the Rigveda (RV 10.129) contains ontological speculation in terms of various logical divisions that were later recast formally as the four circles of catuskoti: "A", "not A", "A and 'not A'", and "not A and not not A".
Logic began independently in ancient India and continued to develop to early modern times without any known influence from Greek logic.
==== Before Gautama ==== Though the origins in India of public debate (pariṣad), one form of rational inquiry, are not clear, we know that public debates were common in preclassical India, for they are frequently alluded to in various Upaniṣads and in the early Buddhist literature. Public debate is not the only form of public deliberations in preclassical India. Assemblies (pariṣad or sabhā) of various sorts, comprising relevant experts, were regularly convened to deliberate on a variety of matters, including administrative, legal and religious matters.
==== Dattatreya ==== A philosopher named Dattatreya is stated in the Bhagavata Purana to have taught Anviksiki to Aiarka, Prahlada and others. It appears from the Markandeya purana that the Anviksiki-vidya expounded by him consisted of a mere disquisition on soul in accordance with the yoga philosophy. Dattatreya expounded the philosophical side of Anviksiki and not its logical aspect.
==== Medhatithi Gautama ==== While the teachers mentioned before dealt with some particular topics of Anviksiki, the credit of founding the Anviksiki in its special sense of a science is to be attributed to Medhatithi Gautama (c. 6th century BC). Guatama founded the anviksiki school of logic. The Mahabharata (12.173.45), around the 5th century BC, refers to the anviksiki and tarka schools of logic.
==== Panini ==== Pāṇini (c. 5th century BC) developed a form of logic (to which Boolean logic has some similarities) for his formulation of Sanskrit grammar. Logic is described by Chanakya (c. 350–283 BC) in his Arthashastra as an independent field of inquiry.
==== Nyaya-Vaisheshika ==== Two of the six Indian schools of thought deal with logic: Nyaya and Vaisheshika. The Nyāya Sūtras of Aksapada Gautama (c. 2nd century AD) 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.
=== Jain logic ===
Jains made its own unique contribution to this mainstream development of logic by also occupying itself with the basic epistemological issues, namely, with those concerning the nature of knowledge, how knowledge is derived, and in what way knowledge can be said to be reliable. The Jains have doctrines of relativity used for logic and reasoning:
Anekāntavāda – the theory of relative pluralism or manifoldness; Syādvāda – the theory of conditioned predication and; Nayavāda – The theory of partial standpoints. These concepts in Jain philosophy made important contributions to the thought, especially in the areas of skepticism and relativity. [4]
=== Buddhist logic ===
==== Nagarjuna ==== Nagarjuna (c. 150–250 AD), the founder of the Madhyamaka ("Middle Way") developed an analysis known as the catuṣkoṭi (Sanskrit), a "four-cornered" system of argumentation that involves the systematic examination and rejection of each of the four possibilities of a proposition, P:
P; that is, being. not P; that is, not being. P and not P; that is, being and not being. not (P or not P); that is, neither being nor not being.Under propositional logic, De Morgan's laws would imply that the fourth case is equivalent to the third case, and would be therefore superfluous, with only 3 actual cases to consider.