View source for Jaina seven-valued logic

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{{use Indian English|date=April 2017}}
{{Jain philosophy}}
'''Jaina seven-valued logic''' is a system of [[argumentation]] developed by [[Jainism|Jaina]] [[philosopher]]s and thinkers in ancient India to support and substantiate their theory of [[Pluralism (philosophy)|pluralism]]. This argumentation system has  seven distinct  semantic [[Predicate (grammar)|predicate]]s which may be thought of as seven different [[truth value]]s. Traditionally, in the Jaina and other Indian literature dealing with topics in [[Jain philosophy]], this system of argumentation is referred to as ''Saptabhangivada'' or ''[[Syadvada]]''.  The earliest reference to ''Syadvada'' occurs is the writings of [[Bhadrabahu]] (c. 433–357 BCE). There is mention of ''Syadvada'' in the ''Nyayavatara'' of Siddhasena Divakara (about 480–550 CE). Samantabhadra (about 600 CE) gave a full exposition of the seven parts of ''Syadvada'' or ''Saptabhanginyaya'' in his ''Aptamimamsa''. The ''Syadvadamanjari'' of Mallisena (1292 CE) is a separate treatise on the same theory. There are, of course, still later works and  a large number of  modern commentaries.<ref name=PCM>{{cite web|last1=P.C. Mahalanobis|title=The Indian-Jaina Dialectic of Syadvad in Relation to Probability (I)|url=http://www.jainworld.com/jainbooks/firstep-2/indianjaina-1-1.htm|website=Jain World|accessdate=28 November 2016|archive-url=https://web.archive.org/web/20051123035659/http://www.jainworld.com/jainbooks/firstep-2/indianjaina-1-1.htm|archive-date=23 November 2005|url-status=dead}} (Dialectica 8, 1954, 95–111)</ref> The interpretation of Saptabhangivada as a [[Many-valued logic|seven-valued logic]] was attempted by [[Harvard University]] philosophy professor George Bosworth Burch (1902–1973) in a paper published in International Philosophical Quarterly in the year 1964.<ref>{{cite journal|last1=George Bosworth Burch|title=Seven-Valued Logic in Jain Philosophy|journal=International Philosophical Quarterly|date=February 1964|volume=4|issue=1|pages=68–93|doi=10.5840/ipq19644140}}</ref> [[Prasanta Chandra Mahalanobis|P. C. Mahalanobis]], an Indian applied statistician, has given a [[probability|probabilistic]] interpretation of the ''Saptabhangivada''.<ref name=PCM/><ref>{{cite web|last1=P.C. Mahalanobis|title=The Indian-Jaina Dialectic of Syadvad in Relation to Probability (II)|url=https://jainworld.com/library/jain-books/books-on-line/jainworld-books-in-indian-languages/first-steps-to-jainism-part-2/the-indian-jaina-dialectic-of-syadvad-part-2/|website=Jain World|accessdate=28 November 2016}} (Dialectica 8, 1954, 95–111)</ref>

==The seven predicates==
The ''Saptabhangivada'', the seven predicate theory may be summarized  as follows:<ref name=Ganeri>{{cite journal|last1=Jonardon Ganeri|title=Jaina Logic and the Philosophical Basis of Pluralism|journal=History and Philosophy of Logic|date=2002|volume=23|issue=4 |pages=267–281|url=https://www.academia.edu/2146233|accessdate=28 November 2016|doi=10.1080/0144534021000051505|s2cid=170089234 }}</ref>

The seven predicate theory consists in the use of seven claims about sentences, each preceded by "arguably" or "conditionally" ({{transliteration|sa|syat}}), concerning a single object and its particular properties, composed of assertions and denials, either simultaneously or successively, and without contradiction. These seven claims are the following.

# Arguably, it (that is, some object) exists ({{transliteration|sa|syad asty eva}}). 
# Arguably, it does not exist ({{transliteration|sa|syan nasty eva}}). 
# Arguably, it exists; arguably, it doesn't exist ({{transliteration|sa|syad asty eva syan nasty eva}}). 
# Arguably, it is non-assertible ({{transliteration|sa|syad avaktavyam eva}}). 
# Arguably, it exists; arguably, it is non-assertible ({{transliteration|sa|syad asty eva syad avaktavyam eva}}). 
# Arguably, it doesn't exist; arguably, it is non-assertible ({{transliteration|sa|syan nasty eva syad avaktavyam eva}}). 
# Arguably, it exists; arguably, it doesn't exist; arguably it is non-assertible ({{transliteration|sa|syad asty eva syan nasty eva syad avaktavyam eva}}).

There are three basic truth values, namely, true (t), false (f) and unassertible (u). These are combined to produce four more truth values, namely, tf, tu, fu, and tfu ([[Three-valued logic]]). Though, superficially, it appears that there are only three distinct truth values a deeper analysis of the Jaina system reveals that the seven truth values are indeed distinct. This is a consequence of the conditionalising operator "arguably" denoted in Sanskrit by the word {{transliteration|sa|syat}}. This Sanskrit word has the literal meaning of "perhaps it is", and it is used to mean "from a certain standpoint" or "within a particular philosophical perspective".

In this discussion the term "standpoint" has been used in a technical sense. Consider a situation in which a globally inconsistent set of propositions, the totality of philosophical discourse, is divided into sub-sets, each of which is internally consistent. Any proposition might be supported by others from within the same sub-set. At the same time, the negation of that proposition might occur in a distinct, though possibly overlapping subset, and be supported by other propositions within it. Each such consistent sub-set of a globally inconsistent discourse, is what the Jainas call a "standpoint" (naya). A standpoint corresponds to a particular philosophical perspective.<ref name=Ganeri/>

In this terminology, it can be seen that the seven predicates get translated to the following seven possibilities. Each proposition ''p'' has the following seven states:<ref name=Ganeri/>

# ''p'' is a member of every standpoint in ''S''.
# Not-''p'' is a member of every standpoint in ''S''.
# ''p'' is a member of some standpoints, and Not-''p'' is a member of the rest.
# ''p'' is a member of some standpoints, the rest being neutral.
# Not-''p'' is a member of some standpoints, the rest being neutral.
# ''p'' is neutral with respect to every standpoint.
# ''p'' is a member of some standpoints and Not-''p'' is a member of some other standpoints, and the rest are neutral.

== Comparison with Catuskoti and Aristotelian Logic ==
In common propositional logic, a contradiction <math>P\land \neg P</math> and the rejection of the Excluded Middle statement <math>\neg(P\lor \neg P)</math> can both be rejected, i.e. proven ''False'', and they are there thus formally equivalent. Indeed, this already holds in [[minimal logic]], for example.
The situation is more refined in the other logics discussed:
{| class="wikitable"
|+
![[Saptabhangi]] Logic
![[Catuṣkoṭi]] Logic
![[Aristotelian logic|Aristotelian]] logic
|-
|It is
:<math>P</math>
|It is
|It is
|-
|It is not
:<math>\neg P</math>
|It is not
|It is not
|-
|It is and it is not
:<math>P\land \neg P</math>
|It is and it is not
| rowspan="5" |
|-
|It is unassertible
:<math>U(P)</math>
| rowspan="4" |It is neither
:<math>\neg(P\lor \neg P)</math>
|-
|It is and it is unassertible
:<math>P\land U(P)</math>
|-
|It is not and it is unassertible
:<math>\neg P\land U(P)</math>
|-
|It is and it is not and it is unassertible
:<math>P\land \neg P\land U(P)</math>
|}

{| class="wikitable"
|+Truth table for the negation
!<math>P</math>
!<math>\neg P</math> 
|-
|''True''
|''False''
|-
|''Unassertible''
|''Unassertible''
|-
|''False''
|''True''
|}

==Further reading==
*For the implementation of a generic computational argumentation system to Jaina seven-valued logic, see {{cite journal|author1=Ohta, Shogo |author2=Hagiwara, Takeshi |author3=Sawamura, Hajime |author4=Riche, Jacques |title=Specializing the Logic of Multiple-Valued Argumentation to the Jaina Seven-Valued Logic|journal=Proceedings on the International Conference on Artificial Intelligence|date=2013|pages=1–7|url=https://worldcomp-proceedings.com/proc/p2013/ICA7331.pdf|accessdate=5 June 2022}}
*For an exposition of the Jaina concept of logic, see {{cite journal|last1=V. K. Bharadwaja|title=The Jaina Concept of Logic|journal=Indian Philosophical Quarterly|date=July 1982|volume=IX|issue=4|pages=362–376|url=http://www.unipune.ac.in/snc/cssh/ipq/english/IPQ/6-10%20volumes/09%2004/PDF/9-4-3.pdf|accessdate=27 November 2016}}
*For an exposition stating that ''Saptabhangi'' cannot be considered as logic in the modern sense of the word, see {{cite journal|last1=Fabien Schang|title=A One-Valued Logic for Non-One-Sidedness|journal=International Journal of Jaina Studies |date=December 2013|volume=9|issue=4|pages=1–25|url=http://www.herenow4u.net/index.php?id=103720|accessdate=28 November 2016}}
*For an exposition of ''Saptabhangi'', see {{cite journal|last1=Pragati Jain|title=Saptabhaṅgī: The Jaina Theory of Sevenfold Predication: A Logical Analysis|journal=Philosophy East and West|date=July 2000|volume=50|issue=3|pages=385–399|url=http://www.sjsu.edu/people/anand.vaidya/courses/comparativephilosophy/s1/The-Jain-Theory-of-Sevenfold-Predication-by-P.-Jain.pdf|accessdate=28 November 2016}}
*For a discussion on ''Syadvada'', see {{cite web|last1=J. B. S. Haldane|title=The Syadvada System of Predication|url=http://www.jainworld.com/jainbooks/firstep-2/sspredication.htm|website=Jain World|accessdate=28 November 2016|archive-url=https://web.archive.org/web/20080616063433/http://www.jainworld.com/jainbooks/firstep-2/sspredication.htm|archive-date=16 June 2008|url-status=dead}} (Sankhya 18, 195–200, 1957)
*Marie-Hélène Gorisse, Nicolas Clerbout and {{ill|Shahid Rahman|fr}} developed a dialogical approach to the theory of standpoints.<ref>“Context Sensitivity in Jain Philosophy. A Dialogical Study of Siddharsigani’s Commentary on the Handbook of Logic”. S. Rahman/ N. Clerbout/ M. H. Gorisse. ''Journal of Philosophical Logic'', volume 40, number 5 (2011), pp. 633-662</ref>

==References==
{{reflist}}

{{Jainism topics}}
{{Indian Philosophy}}
{{Non-classical logic}}
{{Authority control}}

[[Category:Many-valued logic]]
[[Category:History of logic]]
[[Category:Jain philosophical concepts]]