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Syllogism from Western and Indian perspective
-Dr Vinay P Assistant Professor
Department of Vedanta,
Karnataka Samskrita University
Abstract
Western logic and Indian logic are two different approaches to reasoning and argumentation. Western logic, also known as formal logic or Aristotelian logic, is based on the principles of deduction and inference. It uses a set of formal rules to evaluate the validity of an argument and relies heavily on symbolic notation and mathematical language. Western logic also emphasizes the concept of binary truth, which means that a statement is either true or false.
On the other hand, Indian logic, also known as Nyaya, is based on the principles of inference and analogy. It focuses on the analysis of language and emphasizes the importance of context and meaning. Indian logic also recognizes a range of degrees of truth, rather than binary truth, and acknowledges the possibility of contradictory statements being simultaneously true.
Both Western logic and Indian logic have contributed to the development of philosophy, science, and mathematics. While they differ in their approaches and methodologies, they both seek to provide a systematic and rigorous means of evaluating arguments and arriving at conclusions. The present paper aims to make a survey of the western and Indian traditions’ perspective of formalizing a structure of an argument in the form of a syllogism. The divergences in face of format, language and conceptual utilities between the two are noted.
Keywords: Western Logic, Indian Logic, Aristotle, Gotama, Syllogism
The manner and method of argument had always been on the spotlight of appraisal and formatting by thinkers of idiosyncratic traditions, western and oriental alike. A definite format of representing any argument, nay in its simplest and first-order form has given rise to syllogistic representations of arguments in the logical systems of Ancient Greece and India. The greek tradition beginning predominantly with Aristotle and the Indian tradition with Akshapāda Gautama[1] of Nyaya systemized the format of syllogism, particularly categorical, rather independent of each other. As it is true in all cases of natural laws, the idea and the most effective way of representing an elementary argument gave rise to distinct traditions with glaring similarities of formal structure and the norms guiding it.
The psychological implications inherent in formatting the structure of the syllogism in both the traditions are examined in the present paper. The linguistic and syntactical influence, though very significant particularly in the sanskritized version of the Indian tradition, is briefed in the paper, as a more elaborate treatment is a matter of an independent study.
The western tradition views the syllogism as a means of formal inference leading to a reliable conclusion if adhering to the norms governing its validity. The term syllogism is derived from the Greek συλλογισμός – syllogismos – “conclusion,” “inference” referring to the inference drawn from the entailing laws of the argument. The Indian tradition terms inference in general as anumāna pramāņa[2] referring to its role as a valid means of knowledge, being supplementary to pratyaksha or direct sensual knowledge. Though the term refers in common to introspective reasoning (svartha anumāna) and inference for others (parārtha anumāna), it is the latter which gained the much needed importance in all the standard works of logic, being at the spotlight of rigorous formalization of an argument’s presentation.
Another notable feature of a syllogism in both the traditions is its singular stature as a deductive argument in formal structure. Given the premise to be true, the conclusion should necessarily follow from the steps in the deductive syllogism. Induction, a method of conclusion by repeated observation is not entertained within the scope of a syllogism in the strict sense, as the former can only be at best a matter of undenied probability.[3] The Indian tradition too clearly segregates the induction as not useful in most rigorous arguments.[4]It should not, however, be mistaken that the induction is brushed aside in the Indian tradition. The role of sambhavana or induction is appreciated in daily experience, though not on par with the anumāna.[5]
The very basic element in the structure of a categorical Aristotelean syllogism is the simple proposition. The major premise, minor premise and the conclusion are propositions in a syllogism connected to each other in terms of a common term, either minor, major or middle. This structuring, warranted the absence of fallacies, is bound to award the intent of the conclusion. It may be observed in the oft-quoted example of an Aristotle categorical syllogism:
Model of Western Syllogism
| All men are mortal | Major Premise |
| Socrates is a man | Minor Premise |
| Socrates is mortal | Conclusion |
The constituent elements in the respective propositions are:
Constituents of Western Syllogism[6]
| Middle term vis Major term | Major Premise |
| Minor term vis Middle term | Minor Premise |
| Minor term vis Major term | Conclusion |
This may be compared with the structure of parārthaanumāna of the Indian tradition:
Model of Indian Syllogism[7]
| The mountain is fiery | Pratignā[8] | Conclusion |
| As it (mountain) has the smoke | Hetu[9] | Minor Premise |
| All that is smoky is fiery | Udāharaņa[10] | Major Premise |
It may be noted that the order of the Major Premise, Minor Premise and the Conclusion are inverted in the ParārthaAnumāna of the Indian tradition. The order is governed by the law of ākānkśa or verbal expectancy[11]. When it is declared imperatively as “the mountain is fiery”, it invokes a semantic expectancy as “how can the mountain be proved as fiery?”. This naturally leads to the Minor Premise or Hetu Vakya as “Because the mountain is smoky”. This in turn leads to an another semantic expectant as: “why should the mountain be fiery as it is smoky?”. This is answered by the Major Premise or the Udaharana Vakya as: “All that is smoky is fiery”. This satisfactorily ends the chain of semantic expectancy. Hence, the Indian tradition inverts the order and prefers a more orderly ground of leading to the series of syllogistic elements. This may not be seen in the order of the propositions in the Aristotlean categorical syllogism. The Aristotlean categorical syllogism begins with the Major Premise as “All men are mortal”. This does not invoke a semantic expectancy. Hence, moving on to the Minor Premise as “Socrates is a man” is only a matter of deliberate effort on the part of the one proposing the syllogism and is not warranted intrinsically. As the drop-down method of deriving an argument is adopted in the ParārthaAnumāna of the Indian tradition, the formal derivative pattern of premises to conclusion too is not violated[12].
The constituent elements of the Indian tradition are classified as follows:
Contrast of syllogistic elements
| Minor Term (Mountain/Socrates) | Pakśa (āsraya[13]) |
| Major Term (Fire/Mortality) | Sādhya (vyāpaka[14]) |
| Middle Term (Smoke/Humanity) | Hetu (vyāpya[15]) |
The common elements between the premises and their interlinks may be contrasted as follows:
Western Tradition
| Middle term vis Major term | Major Premise |
| Minor term vis Middle term | Minor Premise |
| Minor term vis Major term | Conclusion |
Indian Tradition
| Pakśa vis sādhya | Pratigņa |
| (Pakśa) vis hetu | Hetu[16] |
| Hetu vis sādhya | Udāharaņa[17] |
The law of entailment between the Middle Term (Hetu) and the Major Term (Sādhya) has been naturally the central element of governing the validity of the syllogism. The Indian tradition terms it as Vyāpti, often translated as invariable concomitance.[18]
It may be noted that the simple Aristotelean categorical syllogism differs right at the outset with the Parārtha Anumāna of Indian tradition in its further representations as well. There shall be no logical connectives or operators between the premises. The Indian tradition, however, connects the Pratigņa and hetu vākyam with the entailing connector[19], as this is very much necessary for the proof of the syllogism’s validity. It is already been shown that it has the further advantage of satisfying the needed factor of premise-series with semantic expectancy.
Another glaring contrast of the western tradition’s syllogism with further usage is the representation by diagrammatic presentations such as venn diagrams and the square of opposition. Even the Indian tradition did thought about the same in examples like hetu-cakra of diņņaga[20], not much attention was paid to such efforts, particularly in the nyāya tradition of compound structures of precision.
It may be concluded that the intellectual traditions of the west and the east thought much about the same things of logic and syllogisms, though differing in many ways of its representations. It is indeed recognized as a formal tool on par with that of the mathematical precision, the influence of which is evident in symbolic logic, proof theory and mathematical deductions on the side of western tradition and on philosophy, linguistics, hermeneutics, natural sciences, medicine and even on aesthetics on the face of the Indian tradition.
Bibliography
- Nyaya Sutras with the Commentary of Vatsyayana, translated by Ganganatha Jha – Published by Motilal Banarsidass Publishers
- Tattva-Cintamani of Gangesa Upadhyaya, translated by J.F. Staal – Published by Motilal Banarsidass Publishers
- The Navya-Nyaya Doctrine of Negation: The Semantics and Ontology of Negative Statements in Navya-Nyaya Philosophy, by Sthaneshwar Timalsina – Published by Springer
- The Art of Reasoning: An Introduction to Logic and Critical Thinking, by David Kelley – Published by W.W. Norton & Company
- Indian Logic: A Reader, edited by Jonardon Ganeri – Published by Routledge.
- The Organon: The Works of Aristotle on Logic, translated by W.D. Ross – Published by Oxford University Press
- Tractatus Logico-Philosophicus, by Ludwig Wittgenstein – Published by Routledge
- A Treatise of Human Nature: Being an Attempt to Introduce the Experimental Method of Reasoning into Moral Subjects, by David Hume – Published by Oxford University Press
- An Introduction to Formal Logic, by Peter Smith – Published by Cambridge University Press
- Being and Time, by Martin Heidegger – Published by Harper & Row Publishers
***
[1] Traditionally recognized as the author of Nyāya sūtras. It may be noted that the fusion of twin systems as nyāya-vaiśeśika is a latter arrangement in incorporate logic and natural science.
[2] The term māna refers to valid means of knowledge in general. The inference being auxiliary and based on direct sensual experience is terned anu-mana.
[3] Vide bhūyo darśana in maņi of gangeśa
[4] Gangesa notes that even the law of entailment is bound by invariable concomitance and not warranted by induction which may raise serious questioning.
[5] Utkateka prakaraka jnana…
[6] The italics and underlined are the common terms. Same in all the followings.
[7] The most widely accepted view of tri-structure has been dealt. The Upanaya and Nigamana are cases for independent study
[8] Pakśa vacanam pratigņa
[9] Vyāpya ghataka pakśa dharmata bodhaka vākyam
[10] Vyāpti nischyaka vākyam
[11] Not to be confused with the same term of one of the factors leading to verbal cognition according to the Indian semantic tradition
[12] The purist neo-logic tradition hangs upon subsumptive correlation and conclusion for the syllogism. Vide Avayava and gadādhara and others on it.
[13] As in “āśrayāsiddhi”
[14] Adhika deśa vritti. Vide close connotation in western tradition as “Major”
[15] Nyūna deśa vritti. Vide close connotation in western tradition as “Minor”
[16] Not to be confused with the middle term, as it here denotes the Minor Premise.
[17] Not to be confused with Illustration, as it here denotes the Major Premise.
[18] Vide sādhyabhavavadavrittitvam and others in Maņi.
[19] Used with the Ablative case affix or Pancamī vibhakti
[20] The orthodox systems hardly recognized the same.
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