Nāgārjuna's reconciliation of the Buddhist empty-existence conflict by means of catuṣkoṭi and prasajya-pratiṣeda
Nāgārjuna (150 – 250 C.E.) is believed to originate from South India. At his time, Buddhism in India faces a big split between the school of emptiness in the south (Mahāsaṃghika 大眾部, a branch which is believed by modern scholars to be the initial development of Mahāyāna Buddhism, Williams, 2004: 181-2) and the school of existence in the north (Sarvāstivāda 說一切有部, in which the founder of Yogācāra, Vasubandhu, is said to begin his monk career). Nāgārjuna learns Buddhism in the south first and then moves his base to the north as a Sarvāstivādin monk, critically absorbing and appreciating the ideas of the north school, especially the conditional existence of phenomenon. Then Nāgārjuna returns to South India and dedicates himself to the promotion of the liberal idea of Mahāsaṃghika (Yinshun, 1952/2012: 1-2). The Sarvāstivādin influences on Nāgārjuna's workings is shown in his sophisticated analyses and arguments for the idea of emptiness, which is lack in the previous Mahāsaṃghika thinkers, obviously since Mahāsaṃghika splits from Sarvāstivāda exactly because they reject the value and canonicity of these Sarvāstivādins' scholastic, scientific and philosophical reworkings of Buddha's teachings. Also, Nāgārjuna shows his surpassing philosophical talent in his consistent and systematical considerations that we can smell from each of his set of arguments and his comprehensive and coherent series of treatments of the scattered issues in the abhidharmas. Because he reconciles the two core ideas, existence and emptiness, by introducing “the middle way” (madhyamā-pratipad中道) and refining “two truth theory” in the tradition, cleverly overcoming the philosophical difficulties on both sides (removing Sarvāstivādins' problematic fundamental thesis – the ultimate existence of atoms – and supporting the goal of Mahāsaṃghika with systematic philosophy) with one single reminder: “if you make sense of emptiness, everything makes sense,” he is agreed by later Mahāyāna Buddhists to be a successful intervener and the common founder of all schools of Mahāyāna Buddhism (ibid.).
The middle way, as Nāgārjuna himself characterizes in MMK 15.7, is to leave the side of existence (bhāvānta) and the side of non-existence (abhāvānta) not for the middle position between the two ends but for another different dimension. Let's see the passage in Saṃyuktāgama (《雜阿含經》) Nāgārjuna refers to first:
Buddha told Kātyāyana: “There is a duality (dvayaṃ) that the world relies on (依), namely, existence (atthitañ/astitā) and non-existence (natthitañ/nastitā), which are to be taken (取) via the touch [of cognitive faculty, object and consciousness] (觸). What is taken via the touch is [the world that relies on] either existence or non-existence. Without taking, the dependent relation between mind and object ceases itself to take [any object], to dwell [in any object] or to believe in [the reality of it-]self. [Without taking,] let it suffer when suffering comes; let it cease [to suffer] when suffering goes, and to this one holds no doubt because this is known not via the other. This is the right view (sammādiṭṭhi/samyagdṛṣṭi), and this is called the right view that is established by Buddha. Why is that? Arising (集) of the world as how it is correctly seen and understood shows the non-existence of the non-existing side of the world, while cessation (滅) of the world as how it is correctly seen and understood shows the non-existence of the existing side of the world. That is called the middle way which avoids the two sides....”
On the one hand, via the touch (觸), namely, via the realization of cognition, the world arises and ceases; on the other hand, without the touch, taking is impossible and hence not only taking ceases but also existence and non-existence cease. When the arising and cessation is impossible, i.e., when the world that arises and ceases is viewed correctly (that the world arises or ceases just in our taking the touch), then “the non-existence of the world by itself (the impossibility of the world by itself without our taking the touch)” and “the existence and non-existence of the world that are taken via the touch” entail each other. The middle way is thus understood as a view to strictly confine the changes (arising and cessation) within the realm of phenomenon, where everything is only possible after the touch is taken, i.e., everything is only possible as the object of realized cognition; at meanwhile, the very same view also bears with an awareness that without taking the touch, i.e., without the realization of cognition, arising and cessation is not possible. In another words, the right view of the middle way demands an introduction of epistemological consideration (with or without taking the cognitive touch) into the simple phenomenal duality, which reveals the lack of the non-phenomenal support for the phenomenal dualism. However, although this passage obviously introduces the other perspective of epistemology, Nāgārjuna's elaboration of this introduced view nonetheless struggles with the phenomenal world mainly.
Nāgārjuna tries to show this view in various parts of MMK (representatively MMK 1 and MMK 15) by showing that the concept of phenomenal changes (arising and cessation) and the concept of non-phenomenal reality deny each other. He almost always adopts the logical apparatus of catuṣkoṭi/tetralemma, a four-cornered exhaustion of logical possibility consisting of “p, -p, both p & -p, neither p nor -p” in Indian logic, to display his argument of prasajya-pratiṣeda (proof by contradiction歸謬否定). By showing that a thesis leads to contradictions in each corner of catuṣkoṭi, the thesis is rejected. For example (MMK 1.1), given a thesis that things exist, the four corners are that they come into existence either (a) from itself, (b) from others (not from itself), (c) from both itself & others and (d) from neither itself nor others. If (a), according to Pingala's explanation, first, this contradicts the fact of dependent origination that everything must come into existence in certain conditions, and second, self-origination would invite the problem of infinite regress – infinite repeats of self's producing itself. Since (a) collapses, (b) collapses as well, because the others have to come to existence first; then it fails as we have seen in (a). (c) entails (a) and (b), so (c) cannot stand, either. It is also bizarre to say that things come into existence from nothing, because the uncaused existence would be eternal existence, which does not fit the idea of dependent origination. So (d) falls. Then, the thesis that things exist is rejected. This method is tricky, because the rejection of the thesis does not imply the establishment (or rejection) of the anti-thesis. With this method, Nāgārjuna struggles with the phenomenal predicaments and displays that every possible ontological assertion (assertions about the non-phenomenal reality) must contradict the phenomenal reality. Hence, that the concept of dependent origination and the concept of non-phenomenal reality deny each other is true.
We can understand the middle way to leave the two sides in three steps. First, existence and non-existence are both recognized and restricted to be phenomenal (dependent origination) – only as phenomenon we could know and say that something exists or not. Second, phenomenon is not recognized to have any non-phenomenal foundation; otherwise phenomenon would be unable to change (between existence and non-existence), and this is counterintuitive. Third, first and second claims one identical truth: reality is only phenomenal (“conventional” in Nāgārjuna's term), and thus phenomenon is empty (without any non-phenomenal foundation) in nature, ultimately speaking. Putting these three steps into the background of the north-south split in India, we can say that the first step is the south influence on the north thesis and remarks a new page into the Mahāyāna thesis of existence, viz., existence is only phenomenal. This signifies a clear difference between Hināyāna Sarvāstivādins which believes in atoms being the non-phenomenal substrata and the later Mahāyāna school of existence, Yogācāra, which denies the ultimate reality of atoms. The other steps are the (conventional) “construction” of the south thesis with the philosophical technology from the north. This is the conciliation of the south-north split by Nāgārjuna.
 以有空義故，一切法得成(MMK 24.14). Translation follows Luetchford (2002).
 佛能滅有無，於化迦旃延，經中之所說，離有亦離無 (MMK 15.7). Luetchford (2002): “When he taught Kātyāyana, the Buddha used the power of existence and non-existence to deny both views: that an innate essence exists and that it does not exist.” The story about Buddha's teaching Kātyāyana is found in Saṃyuktāgama《雜阿含經》vol. 12 in Taisho Tripitaka《大正藏》, T02n0099_p0085c17(00)~p0086a03(10).
 Sanskrit reconstruction refers to the citation Ye Shaoyong (2011) from Saṃyuktā-Nikāya, L. Feer, ed. 6 vols., London (PTS), (1884-1904). The translation is of the Chinese text.
 諸法不自生，亦不從他生，不共、不無因，是故知無生。Luetchford (2002): “Things do not come into existence from self or from others, nor from a combination of both. Yet things are not without cause.”
 The commentary of Pingala (青目) is now only preserved in Chinese translation byKumārajīva (鳩摩羅什, 409).
Luetchford, Michael Eido (2002). Between Heaven and Earth : a Translation of Nāgārjuna's Mūlamadhyamakakārikā, with Commentary and Grammatical Analysis. Bristol [England] : Windbell Publications.Williams, Paul (2004). The Origins and Nature of Mahāyāna Buddhism. London & New York : Routledge.
Ye, Shaoyong 葉少勇(2011). Mūlamadhyamakakārikā.《中論頌．梵藏漢合校、導讀、譯注》. Shanghai: Zhongxi Shuju中西書局。
Ven. Yinshun 印順 (1952/2012). Zhong guan lun song jiang ji. 《中觀論頌講記》. Hong Kong: Zheng-wen 正聞. Reprint in Chupei 竹北: Zheng-wen 正聞, 2012.