Dignāga 陳那 (ca. 5th century) revolutionized the Indian theories on how to properly construct an argument. The set of statements with which a 'proof' (sādhana) is constructed is sometimes called the 'Indian syllogism' in the secondary literature, due to some affinities with Western syllogisms, though the differences between the structure of Indian arguments and Western syllogisms are sufficiently significant to have led some scholars to deny that 'syllogism' is an appropriate label. While the structure of Buddhist arguments continued to develop after Dignāga (notably with Dharmakīrti 法稱 and his followers, and later in Tibet), and non-Buddhist Indian schools dramatically revised their own pramāṇa theories in reaction to Dignāgaʼs innovations, only Dignāgaʼs system was introduced to East Asia (in the translations of Xuanzang 玄奘 and Yijing 義淨), so those later developments remained unknown in East Asia until the modern era.

For Sāṃkhyans 數論, a proper argument required ten members (or statements); for Nyāya, five members. Dignāga proposed that only three members (三分, 三支; three avayava) were necessary.

A standard Nyāya five-part argument (parārthânumāna, inference for the sake of [convincing] others) consisted of the following five members.

One looks at a mountain and sees smoke there. Fire is not observable, but one can infer its presence in the following manner:

1. pratijñā 立宗 (thesis; hypothesis): 'This mountain is fire-possessing.'
2. hetu 因 (reason): 'Because it is smoke-possessing.'
3. udāharaṇa 譬喩, 喩 (principle and examples): 'Whatever is smoke-possessing is fire-possessing, like kitchen stove, unlike lake.'
4. upanaya 合 (application): 'This mountain, since it possesses smoke, possesses fire.'
5. nigamana 結 (conclusion): 'This mountain is fire-possessing.'

Analysis: The first statement consists of two items. The thing or substrate in which the property to be proved resides is called the pakṣa 宗. The pakṣa is also called the 'subject' of the inference. In the above argument, the pakṣa is 'this mountain' since that is the thing in which the property-to-be-proven, i.e., fire, would reside. The property-to-be-proven is called the sādhya 所成立; in the above argument that would be 'fire-possessing.' The sādhya is what is to be inferred since, unlike the mountain and the smoke which are being perceived, the fire is not seen; therefore one has to infer its existence. Arguments, in other words, are inferences (anumāna, 比量) for 'proving' something that is not presently being perceived or is at present unknown (or uncertain).

The second statement gives the reason (hetu), a property that is accepted as residing in the pakṣa. For the inference to be valid, this property must reside in the pakṣa and also be invariably connected with the sādhya. In the above example, the reason for why fire is inferred is that smoke is seen on the mountain and where there is smoke, there is fire.

The third statement makes the basis of the invariant connection between smoke and fire explicit ( 'whatever is smoke-possessing is fire-possessing…' ) and then offers two examples. The first is a positive example (sapakṣa 同品), which illustrates the concomitance between the inferred property ( 'fire-possessing' ) and the established property ( 'smoke-possessing' ); the second is a negative example (vipakṣa 異品) in which those properties are absent. 'Kitchen stove' serves as a positive example because, back in the day when everyone cooked on fuel-burning stoves, the concomitance between fire and smoke was an unimpeachable common, everyday occurrence, thus 'establishing' the concomitance. The negative example, 'unlike lake,' implies additional arguments: Obviously fires do not typically occur in lakes since lakes are composed of water; but more importantly, the negative example is designed to rule out mistaken or dubious or ambiguous cases that might undermine the concomitance. Mist and fog—which look similar to smoke—may be seen on a lake; but they are not smoke, despite the pseudo-similarity. Hence fog on a lake does not indicate the presence of fire.

Note that the 'basis' portion of the third statement still implied the locus of both properties while focusing on the properties' concomitance by phrasing the concomitance as a co-occurrence in or of some locus ( ' whatever is smoke-possessing is fire-possessing…' ). The 'whatever' indicates the mountain, the stove, etc., i.e., any locus in which both properties invariantly co-occur.

The fourth statement applies or reiterates the basic proof, putting the pakṣa together with both properties (the hetu and the sādhya) being attributed to it: the accepted property ( 'smoke-possessing' ) and the inferred property ( 'fire-possessing' ). The inference paraphrased asserts: There is smoke on the mountain; wherever there is smoke, there must be fire, since smoke only occurs in a locus containing fire, such as the mountain. Since the mountain possesses smoke, it must also possess fire.

Finally, the fifth statement brings the argument to a close, repeating the original hypothesis (pratijñā), this time as a proven inference.

Dignāgaʼs Innovation: Dignāga considered the fourth and fifth parts of the Nyāya argument structure unnecessary and redundant, and, in addition, he tightened the stipulations of the first three statements as to how they should be properly formed so that the inter-relation of the various parts of the argument would validly support the inference. An example of the three-membered inference is:

1. pakṣa 立宗 (thesis): Sound is impermanent (śabdaḥ anityaṃ; 聲無常者)
2. hetu 因 (reason) [or liṅga 相, mark]: because produced. (kṛtakatvāt; 所作性故)
3. dṛṣṭânta 喩 (example):

   [a] Whatever is produced, that is known to be impermanent, like a pot, etc. (yat kṛtakaṃ tad anityaṃ dṛṣṭaṃ yathā ghaṭādir; 若所作見彼無常。譬如瓶等;

   [b] Whatever is permanent, that is known to be unproduced, like ākāśa, etc. (yan nityaṃ tad akṛtakaṃ dṛṣṭaṃ yathākāśam; 若是常見。非所作如虛空等)

Analysis: Dignāgaʼs nomenclature for the components of the argument is similar to those used by Nyāya, with some differences. The entire thesis is called the pakṣa rather than pratijñā (though the latter term does appear in Nyāyapraveśa). The sādhya 所立, i.e., the property-to-be-proven, is 'impermanent.' Sometimes sādhya can imply the entire thesis statement (since it is the sādhya of that specific pakṣa). As in the Nyāya argument, the hetu (or liṅga) must be a property of the pakṣa ( 'sound' ) and concomitant with the sādhya ( 'impermanent' ). Since whatever is produced is impermanent, and sound is produced, sound must be impermanent. That is, while the sādhya is an alleged property of the pakṣa still awaiting proof, the hetu is an accepted property of the pakṣa ( 'sound' ).

The pakṣa can also be differentiated into the 'qualifier' (viśeṣaṇa 能別) and a 'qualified' (viśeṣya 所別). In the pakṣa 'sound is impermanent,' the qualifier is 'impermanent' which qualifies, or indicates the highlighted quality of 'sound,' which is thus the qualified.

The dṛṣṭânta (example) consists of a positive example (sapakṣa 同品) and a negative example (vipakṣa 異品). 'Positive' here means similar to, of the same class or type, or shares the same property (sadharma, 同法), and 'negative' means dissimilar to, of an opposed class or type, or containing dissimilar properties (vaidharma, 異法). More importantly, the property (dharma 法) that one is trying to prove concerning the pakṣa must reside in the positive example, and must be absent in the negative example.

A property-of-the-pakṣa is called a pakṣadharma 宗法. In this example, the pakṣadharma is 'impermanence,' the property being attributed to the pakṣa 'sound.' A property (dharma 法) resides in a dharmin (有法, lit. 'property possessor' ), which is its substrate, or better, its locus. For a sādhana 能立 (a well formed argument) to be valid, the property indicated by the hetu ( 'is produced' ) (1) must be concomitant with the pakṣa; (2) it must be present in the sapakṣa 同品 (similar example, 'like pot, etc.' ); and (3) it must be absent from the vipakasa 異品 (negative example, 'unlike ākāśa, etc.' ). The hetu, then, is the logical linchpin between the pakṣa, sapakṣa, and vipakṣa, which validates the sādhya as a legitimate pakṣadharma.

Notice that in the 'full' form of the argument the examples include 'principial' statements: 'Whatever is produced, that is known to be impermanent, like a pot, etc.' (sapakṣa), and 'Whatever is permanent, that is known to be unproduced, like ākāśa, etc.' (vipakṣa), as did the Nyāya version. Since these principial statements are already implicit in the syntax of the argumentʼs structure, they may be omitted in practice (though recitable, should that be necessary). In streamlined form, a three-part Dignāga argument would be:

1. pakṣa: Sound is impermanent
2. hetu: because produced.
3. dṛṣṭânta: like a pot; unlike ākāśa.

Dignāga also provides detailed rules and tests for detecting fallacies in the various statements and the relations between them. A fallacious pakṣa or pseudo-pakṣa (pakṣâbhāsa 似立宗) is one that is contradicted (viruddha, 相違) by some established form of knowledge or that contains an axiom that either of the disputants considers unacceptable (aprasiddha, 不極成). Prasiddha 極成 means something that is considered to be established, common knowledge, a nonproblematic premise, and aprasiddha is its opposite. Dignāga placed great stress on the two disputants finding axioms that both considered prasiddha in order to allow cross-sectarian debate to be open and fruitful.

Śaṃkarasvāminʼs 商羯羅主 Nyāyapraveśa 因明入正理論 lists nine types of pseudo-pakṣas:

A pseudo-pakṣa is a pakṣa (1) contradicted by perception (pratyakṣa-viruddhaḥ, 現量相違), (2) contradicted by inference (anumāna-viruddhaḥ, 比量相違), (3) contradicted by the teachings of oneʼs own tradition [which would make one inconsistent] (āgama-viruddhaḥ 自教相違),(4) contradicted by worldly consensus (loka-viruddhaḥ 世間相違), (5) contradicted by oneʼs own [prior] statements [i.e., self-contradiction] (sva-vacana-viruddhaḥ, 自語相違), (6) when the qualifier is not accepted by one of the disputants (aprasiddha-viśeṣaṇaḥ 能別不極成), (7) when the qualified is not accepted by one of the opponents (aprasiddha-viśeṣyaḥ, 所別不極成), (8) when both the qualifier and qualified are not accepted (aprasiddhobhayaḥ, 倶不極成), and (9) when the relation between the qualifier and qualified is too well known to require additional proof (prasiddha-saṃbandhaś ceti 相符極成).

The first five should be apparent, but the remaining four might require additional comment. The example given in Nyāyapraveśa 因明入正理論 of a pakṣa that is fallacious because 'the qualifier is not accepted by one of the disputants' is when a Buddhist tries to propose to a Sāṃkhyan that 'sound is destructible.' This is unacceptable to the Sāṃkhyan because he holds that sound is eternal and indestructible. This would be a case of the disputants not sharing the same premise, which renders the pakṣa unusable even though the Buddhist would certainly hold that particular claim to be true. It would appear that the pakṣa 'sound is impermanent' would nonetheless be an acceptable pakṣa for a Buddhist debating a Sāṃkhyan, even though the Sāṃkhyan holds that sound is permanent, since that is a more basic tenet that can be questioned. To characterize sound as destructible, on the other hand, already presupposes that sound cannot be permanent, and thus biases any subsequent discussion. Similarly, the example given for 'the qualified is not accepted by one of the opponents' is a Sāṃkhyan proposing to a Buddhist that 'the self (ātman) is conscious,' since the 'qualified' in that statement, i.e., the ātman, is not accepted as a legitimate locus for properties by Buddhists.

'Both the qualifier and qualified are not accepted' is illustrated by the example of a Vaiśeṣika proposing to a Buddhist that the self is the inherent cause (samavāyi-kāraṇaṃ 和合因緣) of happiness, etc. (vaiśeṣikasya bauddhaṃ prati sukhādi-samavāyi-kāraṇaṃ ātmeti; 如勝論師對佛弟子立我以為和合因緣). As above, the Buddhist does not accept the self as a legitimate locus, much less an actual cause of anything. In addition, however, Buddhists also reject the Vaiśeṣika theory of 'inherence.' Vaiśeṣika proposes a number of ultimately real metaphysical categories which they call padârthas 句義. Inherence (samavāyi, 和合) is the sixth padârtha. It refers to an eternal relation (nitya-saṃbandha) of perpetual co-inherence, inner or intimate relation, constant and intimate union, inseparable concomitance, such as the relation they posit to exist between a substance and its qualities, between a whole and its parts [e.g. between a cloth and the yarn composing it], between a genus and its individuals, and so. Such relations, for Buddhists, are conceptual (kalpanā, 分別), not metaphysical, and certainly not eternal. Hence discussing a Vaiśeṣika postulate that the self exhibits inherence would make no more sense to a Buddhist than discussing what color hair the son of a barren woman possesses.

The example given for a 'relation between the qualifier and qualified too well known to require additional proof' is 'sound is audible.' This would be a pseudo-pakṣa for a couple of reasons: first, sound, by definition, is what is audible, so this is tautological and in need of no additional 'proof' ; second, audibility is not a matter that inference can resolve, but something affirmed or denied by perception.

Similarly detailed lists of types of fallacies concerning the hetu (hetvābhāsa 似因) and dṛṣṭânta (dṛṣṭāntābhāsa 似喩) are given in Nyāyamukha (因明正理門論, T 1628 or 明正理門論 T 1629), Pramāṇasamuccaya, and Nyāyapraveśa. Dignāga may have written an entire work devoted to identifying such fallacies but it has not survived. His extant works, fortunately, retain the details. Śaṃkarasvāmin added a number of fallacies to Dignāgaʼs list, and Kuiji 窺基 in his commentary on the Nyāyapraveśa (因明入正理論疏, T 1840) collated and expanded the fallacy lists. Subsequent East Asian works on Buddhist logic have drawn from and embellished Kuijiʼs exposition.