Editing History of logic (section)

==Logic in India==
{{Main|Indian logic}}

=== Hindu logic ===

==== Origin ====
The [[Nasadiya Sukta]] of the ''[[Rigveda]]'' ([[Mandala 10|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".
{{Rquote|right|"Who really knows? <br/>Who will here proclaim it? <br/>Whence was it produced? Whence is this creation? <br/>The gods came afterwards, with the creation of this universe. <br/>Who then knows whence it has arisen?"|[[Nasadiya Sukta]], concerns the [[origin of the universe]], [[Rig Veda]], ''10:129-6'' <ref name="Kramer1986">{{cite book |author-first=Kenneth |author-last=Kramer |title=World Scriptures: An Introduction to Comparative Religions |url=https://books.google.com/books?id=RzUAu-43W5oC&pg=PA34 |date=January 1986 |publisher=Paulist Press |isbn=978-0-8091-2781-8 |pages=34–}}</ref><ref name="Christian2011">{{cite book |author-first=David |author-last=Christian |title=Maps of Time: An Introduction to Big History |url=https://books.google.com/books?id=7RdVmDjwTtQC&pg=PA18|date=1 September 2011 |publisher=University of California Press |isbn=978-0-520-95067-2 |pages=18–}}</ref><ref name="Singh2008">{{cite book |author-first=Upinder |author-last=Singh |title=A History of Ancient and Early Medieval India: From the Stone Age to the 12th Century |url=https://books.google.com/books?id=H3lUIIYxWkEC&pg=PA206 |date=2008 |publisher=Pearson Education India |isbn=978-81-317-1120-0 |pages=206–}}</ref>}}
Logic began independently in [[ancient India]] and continued to develop to early modern times without any known influence from Greek logic.<ref>Bochenski p. 446</ref>

==== 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 ''[[Upanishads|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.{{Citation needed|date=January 2025}}

==== 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|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.<ref>{{cite book |author-last=Vidyabhusana |author-first=S. C. |url=http://archive.org/details/in.ernet.dli.2015.213362 |title=History Of Indian Logic. |date=1921 |pages=11}}</ref><ref>{{cite book |author-first=Satis Chandra Vidya |author-last=Bhusana |url=http://archive.org/details/in.ernet.dli.2015.489008 |title=A History Of Indian Logic |date=1921}}</ref>

==== 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 [[Indian logic|Medhatithi Gautama]] (c. 6th century BC). Guatama founded the ''[[anviksiki]]'' school of logic.<ref>S. C. Vidyabhusana (1971). ''A History of Indian Logic: Ancient, Mediaeval, and Modern Schools'', pp. 17–21.</ref> The ''[[Mahabharata]]'' (12.173.45), around the 5th century BC, refers to the ''anviksiki'' and ''tarka'' schools of logic.

==== Panini ====
{{IAST|[[Pāṇini]]}} (c. 5th century BC) developed a form of logic (to which [[Boolean logic]] has some similarities) for his formulation of [[Vyakarana|Sanskrit grammar]]. Logic is described by [[Chanakya]] (c. 350–283 BC) in his ''[[Arthashastra]]'' as an independent field of inquiry.<ref>R. P. Kangle (1986). ''The Kautiliya Arthashastra'' (1.2.11). Motilal Banarsidass.</ref>

==== 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 [[Philosophical realism|realist]] school developed a rigid five-member schema of [[inference]] involving an initial premise, a reason, an example, an application, and a conclusion.<ref>Bochenski p. 417 and ''passim''</ref> The [[Idealism|idealist]] [[Buddhist philosophy]] became the chief opponent to the Naiyayikas.

=== Jain logic ===
[[File:उमास्वामी आचार्यजी.jpg|thumb|Umaswati (2nd century AD), author of first Jain work in Sanskrit, [[Tattvartha Sutra|Tattvārthasūtra]], expounding the [[Jain philosophy]] in a most systematized form acceptable to all sects of Jainism.]]
[[Jainism|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 [[Relativism|relativity]] used for logic and reasoning:

* [[Anekantavada|Anekāntavāda]] – the theory of relative pluralism or manifoldness;
* [[Syadvada|Syādvāda]] – the theory of conditioned predication and;
* [[Anekantavada#Nayav%C4%81da|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. [http://www.jainworld.com/jainbooks/firstep-2/indianjaina-1-2.htm]<ref>{{cite journal |author-last=Ganeri |author-first=Jonardon |title=Jaina Logic and the Philosophical Basis of Pluralism |url=https://www.academia.edu/2146233 |journal=History and Philosophy of Logic |date=2002 |language=en |volume=23 |issue=4 |pages=267–281 |doi=10.1080/0144534021000051505 |s2cid=170089234 |issn=0144-5340}}</ref>

=== 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&nbsp;''P''; that is, not being.
# [[File:Eight Patriarchs of the Shingon Sect of Buddhism Nagarjuna Cropped.jpg|thumb|Painting of Nāgārjuna from the ''Shingon Hassozō'', a series of scrolls authored by the [[Shingon]] school of Buddhism. Japan, [[Kamakura period]] (13th–14th century)]]''P'' and not&nbsp;''P''; that is, being and not being.
# not (''P'' or not&nbsp;''P''); that is, neither being nor not being.{{Paragraph break}}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.

=== Dignaga ===
However, [[Dignāga]] (c 480–540 AD) is sometimes said to have developed a formal syllogism,<ref>Bochenski pp. 431–437</ref> and it was through him and his successor, [[Dharmakirti]], that [[Buddhist logic]] reached its height; it is contested whether their analysis actually constitutes a formal syllogistic system. In particular, their analysis centered on the definition of an inference-warranting relation, "[[vyapti]]", also known as invariable concomitance or pervasion.<ref name="Matilal">{{cite book |author-last=Matilal |author-first=Bimal Krishna |title=The Character of Logic in India |date=1998 |publisher=State University of New York Press |location=Albany, New York, USA |isbn=9780791437407 |pages=12, 18}}</ref> To this end, a doctrine known as "apoha" or differentiation was developed.<ref>Bochenksi p. 441</ref> This involved what might be called inclusion and exclusion of defining properties.

Dignāga's famous "wheel of reason" (''[[Hetucakra]]'') is a method of indicating when one thing (such as smoke) can be taken as an invariable sign of another thing (like fire), but the inference is often inductive and based on past observation. Matilal remarks that Dignāga's analysis is much like John Stuart Mill's Joint Method of Agreement and Difference, which is inductive.<ref>Matilal, 17</ref>