Logic and Inference in Indian Philosophy

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By the fifth century BCE great social change was taking place in India and a period of intense intellectual activity came into being. Rational inquiry into a wide range of topics was under way, including agriculture, architecture, astronomy, grammar, law, logic, mathematics, medicine, phonology, and statecraft. Aside from the world's earliest extant grammar, Pāini's (c. 400 BCE) Aādhyāyī, however, no works devoted to these topics actually date from this period. Nonetheless, scholars agree that incipient versions of first extant texts on these topics were being formulated.

One text dating from this period and important to tracing the development of logic in classical India is a Buddhist work, Moggaliputta Tissa's Kathā-vatthu (Points of controversy; third century BCE), which exhibits awareness of the fact that the form of argument is crucial to its being good. The text gives the refutation of some 200 propositions over which the Sthavīravāda, one of the Buddhist schools, disagreed with various Buddhist schools. The treatment of each point comprises a debate between a proponent and opponent. Throughout book 1, chapter 1, one finds refutations of precisely the following form:

Proponent:Is A B?
Proponent:Is C D?
Proponent:Acknowledge defeat, since if A is B, then C is D.

The author clearly presumes it to be self-evident, first, that it is wrong to hold inconsistent propositions and, second, that the propositions assented tocorresponding to the propositional schemata of α, ¬Β, α Β are indeed inconsistent.

The first 500 years of the Common Era saw the redaction of treatises devoted to the systematic exposition of the technical subjects mentioned earlier, as well as of philosophical treatises in which proponents of diverse religious traditions put forth systematic versions of their worldview. These latter works bear witness, in a number of different ways, to the intense interest of the period in argumentation. To begin with, the authors of many of these texts submit arguments and, in doing so, explicitly appeal to such well-known logical principles as those of noncontradiction, of excluded middle and of double negation, though they adduce them, not as principles of logic, but as self-evident ontic facts. Thus, the Buddhist philosopher Nāgārjuna (c. 150250) often invokes an ontic principle of noncontradiction, saying such things as "when something is a single thing, it cannot be both existent and non-existent" (Mūlamadhyamakakārikā chapter 7, verse 30), which is clearly reminiscent of Aristotle's own ontic formulation of the principle of noncontradiction, namely, "that a thing cannot at the same time be and not be" (Metaphysics book 3, chapter 2996b2930).

Next, many of the arguments formulated correspond to such well-recognized rules of inference as modus ponens (i.e., from α and α Β, one infers Β ), modus tollens (i.e., from ¬Β and α Β, one infers ¬α ), disjunctive syllogism (i.e., from ¬α and α Β, one infers Β ), constructive dilemma (i.e., from α Β, α γ and Β γ, one infers γ ), categorical syllogism (i.e., from α Β and Β γ, one infers α γ ), and reductio ad absurdum (i.e., if something false follows from an assumption, then the assumption is false). This last form of argument, termed prasaga in Sanskrit, is extremely common. Indeed, so common are such arguments in Nāgārjuna's works that his follower, Buddhapālita (470540), took all of Nāgārjuna's arguments to be prasaga arguments. As a result, Buddhapālita and his followers were and are referred to as prāsagikas (absurdists).

Finally, many of the texts are either devoted to, or have passages devoted to, the enumeration, definition, and classification of public discussion, or debate (vāda ). The same texts or passages also identify the parts of argument, the flaws found in poor arguments, including such fallacies as circularity (anyonya-āśraya, reciprocal dependence) and infinite regress (an-avasthā, ungroundedness), as well as quibbles (chala ) and sophistical refutations (jāti ) (see Solomon 1976, vol. 1, chapter 5). They also set down ways in which a discussant's behavior warrant his or her being judged the loser of the debate (nigraha-sthāna ) (see Solomon 1976, vol. 1, chapter 6).

One of the earliest examples of an argument in a form that clearly adumbrates the canonical form the classical Indian inference eventually takes is found in a passage in the Caraka-sahitā (CS book 2, chapter 8, section 31), a medical text, which defines an argument to have five parts: the proposition (pratijñā ), the ground or reason (hetu ), the corroboration (dānta ), the application (upanaya ), and the conclusion (nigamana ). The following is an example:

Proposition:The soul is noneternal
Ground:because it is detectable by the senses.
Corroboration:It is like a pot.
Application:As a pot is detectable by the senses, and is noneternal, so is the soul detectable by the senses.
Conclusion:Therefore, the soul is noneternal.

This form of the argument clearly reflects the debate situation. First, one propounds a proposition, that is, one sets forth a proposition to be proved. One then states the ground, or reason, for the proposition one is propounding. Next, one corroborates with an example the connection implicit between the property mentioned in the proposition and the property adduced as its ground. The immediately ensuing step, the application, spells out the analogy between the example and the subject of the proposition. Notice that this part of the argument retains the vestiges of the analogical reasoning that is no doubt its predecessor. Finally, one asserts the proposition.

As was obvious to the thinkers of this period, not all arguments of this form are good arguments. However, no clear criteria are set forth whereby good arguments or inferences can be distinguished from bad ones. At best, some authors simply list good arguments, as does the Buddhist idealist Asanga (flourish fourthfifth century CE) in a section at the end of a chapter of his Yogācārabhūmi-śāstra (Treatise on the stages of yogic practice). Other works provide lists of both good and bad arguments, the latter often referred to as nongrounds (a-hetu ) or pseudogrounds (hetu-ābhāsa ) (see Solomon 1976, vol. 1, chapter 7). It is difficult to be sure what the basis for the classification is in these early texts. In the Nyāya-sūtra (Aphorisms on logic), a work attributed to Gautama Akapāda (flourished second century CE), the author gives neither a definition nor an example. Even in cases where definitions and examples are given, as in the Caraka-sahitā mentioned earlier, the modern reader is rarely sure of what is intended.

Other passages from these earliest texts treat inference. In these passages inference is taken to be knowledge of one fact arising from knowledge of another. Often, as in the passages of the Caraka-sahitā (CS book 1, chapter 11, sections 2122) and the Nyāya-sūtra (NS book 1, chapter 1, aphorism 5), no mention is made of any knowledge of what links the two facts. Moreover, the classification of inference in these two texts seems to be based on characteristics completely extrinsic to the logical features of the inferences adduced, for example, according to whether the property permitting the inference precedes, is simultaneous with, or succeeds the property to be inferred.

In contrast, passages from other texts of this period provide definitions of inference that require, besides knowledge of the two states of affairs, knowledge of the relation linking the two. However, instead of providing a formal relation, they provide a miscellany of material relations. The ai-tantra (Sixty doctrines), which is attributed by some to Pañcaśikha (flourished second century BCE) and by others to Varaya (fl. after the second century CE), enumerates seven such relations, while the Vaiśeika-sūtra (Aphorisms pertaining to individuation; VS book 9, aphora 20), a text attributed to Kaāda (flourished first century CE), enumerates five: the relation of cause to effect, of effect to cause, of contact, of exclusion, and of inherence. In each of these texts the miscellany of material relations serves to classify inferences. Thus, although in these two works the parts of an inference have been made explicit, the formal connection among these parts remained implicit.

The works of the Buddhist philosopher Vasubandhu (flourished fourth century CE) seem to be the earliest extant works that provide a formal characterization of the inference. He holds that inference has only three parts: a subject (paka ) and two properties, the property to be established (sādhya ) in the subject and another that is the ground (hetu ). Exploiting an idea ascribed by his coreligionist Asanga in his Shùn Zhèng Lùn to an unknown school (thought by at least one scholar to be the Sākhya school), Vasubandhu maintained that a ground in an inference is a proper one if, and only if, it satisfies three conditionsthe so-called tri-rūpa-hetu (the grounding property hetu in its three forms). The first form is that the grounding property (hetu ; H) should occur in the subject of an inference (paka ; p). The second is that the grounding property (H) should occur in those things similar to the subject insofar as they have the property to be established (sādhya ; S). And third, the grounding property (H) should not occur in any of those things dissimilar from the subject insofar as they lack the property to be established (S). These conditions can be viewed as a partial specification of the validity of inferences of this form:

Thesis:p has S.
Ground:p has H.
Indispensability:Whatever has H has S.

The first condition corresponds to the premise labeled ground in the schema above, while the second two correspond to the premise labeled indispensability. In his Vāda-vidhi (Rules of debate) Vasubandhu makes clear that the relation, knowledge of which is necessary for inference, is not just any in a miscellany of material relations, but a formal relation, which he designates, in some places, as a-vinā-bhāva literally, not being without (compare to the Latin expression sine qua non)and in others, as nāntarīyakatva literally, being unmediated.

The following are two examples of inferences satisfying the previous schema:

Thesis:p has fire.
Ground:p has smoke.
Pervasion:Whatever has smoke has fire.
Thesis:p is a tree (i.e., has tree-ness).
Ground:p is an oak (i.e., has oak-ness).
Pervasion:Whatever is an oak (i.e., has oak-ness) is a tree (i.e., has tree-ness).

The previous schema is the one that Buddhist thinkers insisted on for all sound inference or argument. Brahmanical thinkers came to insist on a the form found in the Caraka-sahitā, but with the form of the application modified to express a universal claim, thereby giving it the same logical core as the form accepted by the Buddhists.

It is important to note that, no matter how different the metaphysical assumptions of the various philosophical schools, they all used a naive realist's ontology to specify the states of affairs used to study inference. According to this view, the world consists of individual substances or things (dravya ), universals (sāmānya ), and relations between them. The fundamental relation is the one of occurrence (vtti ). The relata of this relation are known as substratum (dharmin ) and superstratum (dharma ), respectively. The relation has two forms: contact (sayoga ) and inherence (samavāya ). So, for example, one individual substance, a pot, may occur on another, say the ground, by the relation of contact. In this case the pot is the superstratum and the ground is the substratum. Or, a universal, say brownness, may occur in an individual substance, say a pot, by the relation of inherence. Here, brownness, the superstratum, inheres in the pot, the substratum. The converse of the relation of occurrence is the relation of possession.

Another important relation is the relation that one superstratum bears to another. This relation, known as pervasion (vyāpti ), can be defined in terms of the occurrence relation. One superstratum pervades another just in case where ever the second occurs the first occurs. The converse of the pervasion relation is the concomitance relation.

As a result of these relations, the world embodies a structure: If one superstratum, designated as H, is concomitant with another superstratum, designated as S, and if a particular substratum, say p, possesses the former superstratum, then it possesses the second. This structure is captured by both the inferential schema for Buddhist thinkers and the inferential schema for Brahmanical thinkers.

Dignāga (flourished fifth century CE), another Buddhist philosopher, consolidated and systematized the insights into the formal basis of inference found in Vasubandhu's works. First, distinguishing between inference for oneself and inference for another, he made explicit what had previously been only implicit, namely, that inference, the cognitive process whereby one increases one's knowledge, and argument, the device of persuasion, are but two sides of a single coin. Second, he undertook to make the three forms of the grounding property (tri-rūpa-hetu ) more precise, pressing into service the Sanskrit particle eva (only). And third, and perhaps most strikingly, he created the hetu-cakra (wheel of reasons), a three-by-three matrix, set up to classify pseudogrounds in light of the last two forms of the three forms of a proper ground. On the one hand, there are the three cases of the grounding property (H) occurring in some, none, or all of substrata where the property to be established (S) occurs. On the other hand, there are the three cases of the grounding property (H) occurring in some, none, or all of substrata where the property to be established (S) does not occur. Letting S be the substrata in which S occurs and S ̅ be the substrata in which S does not occur, one arrives at the following table:

H occurs in:all Sall Sall S
all S ̅no S ̅some S ̅
H occurs in:no Sno Sno S
all S ̅no S ̅some S ̅
H occurs in:some Ssome Ssome S
all S ̅no S ̅some S ̅

Dignāga's works set the framework within which subsequent Buddhist thinkers addressed philosophical issues pertaining to inference and debate. Thus, Śankarasvāmin (flourished sixth century CE) wrote a brief manual of inference for Buddhists, called the Nyāya-praveśa (Beginning logic), based directly on Dignāga's work. Not long thereafter, Dharmakirti (flourished seventh century CE), the great Buddhist metaphysician, also elaborated his views on inference and debate within the framework found in Dignāga.

Dharmakirti made at least two contributions to the treatment of inference. Recall that one of the developments found in Vasubandhu's work was the identification of the formal contribution of what corresponds with the premise labeled indispensability in the inferential schema above making explicit that the corresponding relation is a formal one. One of Vasubandhu's terms for it, namely, a-vinābhāva (not being without), made it clear that inference involves some form of necessity. The question raised by Dharmakirti is: What is the basis for the necessity? Recognizing that the necessity does not arise from a simple enumeration of cases, Dharmakirti postulated two relations to vouchsafe the necessity of inference: causation (tadutpatti ) and identity (tādātmya ). A second contribution was his attempt to bring knowledge of absences, or roughly negative facts, within the purview of inference.

Another important Buddhist thinker who treated inference was Dharmottara (flourished eighth century CE), who wrote a useful commentary on Dharmakirti's widely read Nyāya-bindu.

Dignāga not only had a profound influence on his Buddhist followers but he also influenced his non-Buddhist contemporaries and their followers. It would be wrong, however, to conclude that every adoption of ideas similar to those used by Dignāga in his works should be attributed to him. After all, one cannot be certain that Dignāga's contemporaries did not arrive at similar ideas independently or that they might not have got their ideas from sources common to them and Dignāga. In any event, Praśastapāda (flourished sixth century CE), an adherent of the Vaiśeika school and a near contemporary of Dignāga, also defined inference in a way that not only made clear its formal nature but also used the quantificational adjective sarva (all) to make the formal connection precise.

At the same time, some authors of this period seem to have retained a view of inference akin to the one found in the ai-tantra and the Vaiśeika-sūtra, in which the formal role of what corresponds with the inferential schema's pervasion (vyāpti ) had yet to have been identified. This is true both of Vātsyāyana (flourished fifth century CE), the author of the earliest extant commentary on the Nyāya-sūtra and of Śabara (flourished sixth century CE), the author of the earliest extant commentary on Jaimini's Mīmāsā-sūtra. However, it was not long before the advocates of both Nyāya and Mīmāsā adapted to the formal view of inference. On the one hand, one finds that the Mīmāsā thinker Kumārila Bhaa (flourished 730 CE), adopted, without special comment, the formal perspective. On the other hand, one also finds that, though the Nyāya thinker Uddyotakara (flourished late sixth century CE) argued vigorously against many of Dignāga's views, he nonetheless advocated a view that presupposed the formalization found in Dignāga's works. Thus, Uddyotakara classified grounds (hetu ) as: concomitant (anvaya ), where nothing distinct from particular substratum p (in the inferential schema) fails to have the property S; exclusive (vyatireka ), where nothing distinct from p (in the inferential schema) has the property S; and both concomitant and exclusive, where some things distinct from p have the property S and some fail to have the property S. This classification becomes the standard classification for the adherents of Nyāya during the scholastic period.

See also Knowledge in Indian Philosophy; Mind and Mental States in Buddhist Philosophy; Negation in Indian Philosophy; Truth and Falsity in Indian Philosophy; Universal Properties in Indian Philosophical Traditions.


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Brendan S. Gillon (2005)