Some Logical Issues in Madhyamaka Thought

“Some Logical Issues in Madhyamaka Thought” — Galloway, Brian. Journal of Indian Philosophy 17:1 (March 1989), pp. 1–35. Kluwer Academic Publishers.

added because gokhale-ways-of-argumentation-2008 leans on it at two points: the common-presupposition defence of the catuṣkoṭi, which Gokhale accepts locally and rejects globally, and the answer to Robinson’s fallacy charge, which Gokhale endorses without addition.

Thesis / main argument

Three claims, pursued with the apparatus of elementary set theory and the predicate calculus. First, the prasajya negation of Madhyamaka is not the prasajya negation of the other schools. In the non-Madhyamaka grammatical usage, prasajya-pratiṣedha negates the predicate and paryudāsa-pratiṣedha complements the term, and both yield a statement with content. For the Mādhyamika, any negation that carries an implication is a paryudāsa, whatever its syntax, and the properly Madhyamaka negation yields what Galloway calls a zero statement — a statement with no information content at all, written 0 by analogy with the empty set. Term and predicate are both negated prasajyavat. Second, set theory clarifies the laws of the excluded middle and of non-contradiction, and shows that the catuṣkoṭi is a four-part division of a special type in which the parts may overlap, so that Aristotle’s four quantified forms are not its analogue. Third, and this is the part that matters for this wiki, Nāgārjuna violates neither the excluded middle nor contraposition, and the two standing charges that he does can be answered without positing a deviant logic.

The pivot of the whole essay is the claim that when a catuṣkoṭi is negated in all four corners, what fails is not the logic but the subject. Galloway is explicit that a fourfold negation is impossible for a really existing x under an applicable predicate: one of the four must be true. Nāgārjuna’s response is not to reject the law but to reject the bhāva. The negation of each corner leads to the zero statement, their conjunction therefore leads to the zero statement, and no contradiction follows.

Key claims

• The zero statement (pp. 6–9). Applied to a statement A(x), the Madhyamaka prasajya “allows us to conclude neither A(x) nor ¬A(x), because it allows us to conclude nothing whatever.” Galloway glosses it as “the negation of the statement leads nowhere; we deny the validity of the statement but accept no implication of any other statement” (p. 7). He grounds the reading in Bhāviveka’s Prajñāpradīpa discussion of the possible negations of “things arise from themselves”: Bhāviveka rejects “things do not arise” as annihilationist and “things arise, just not from themselves” as eternalist, and accepts only “things do not (arise from themselves)”, from which he draws no implication. The Tibetan renderings corroborate the reading, since med par dgag pa and ma yin par dgag pa were coined on two verbs of being with a distinction of implication that neither Sanskrit nor English marks.
• The zero statement is the absence of pratijñā (n. 5, pp. 26–27). Using Ruegg’s 1983 distinction between two senses of pratijñā, Galloway reads VV 29’s nāsti ca mama pratijñā as “I make only zero statements”: in sense 1 a pratijñā is a statement with content, which Nāgārjuna makes none of; in sense 2 it is any verbal formulation at all, which he makes constantly, but only procedurally, to refute others. So the No-thesis doctrine is the output of the negation-theory rather than an independent doctrine.
• Against the Tsongkhapa–Lopez gloss of VV 29 (n. 5, p. 27). Galloway quotes Lopez 1987 p. 51 — Nāgārjuna “has no inherently existent position” — and rejects it: on that reading “one could hold any position at all”, asserting even that things arise from what is other than themselves, provided one added the qualifier. He also refuses Lopez’s inference from having no position to nihilism, on the ground that having no philosophical view paramārthavat is not nihilism, and that the Candrakīrti passage adduced concerns asvabhāvatā rather than apratijñātva.
• The negative catuṣkoṭi is possible because the subject is denied (pp. 18–19). For a limited universe there is no problem, since the subject may lie outside it (his baboon example). For an unlimited one there is, and Galloway’s answer is that the commentators take each corner separately, obtain the zero statement at each, and conjoin them; the fourfold negation goes through “because for him there is no real x or bhāva that could arise” (p. 18). He notes that Buddhapālita disposes of the third and fourth corners summarily once the first two fall, and that the Akutobhayā treats arising from no cause as absurd on its face.
• MMK 15.4 preserves the excluded middle and throws out the bhāva (pp. 19–20). A bhāva must lie in the set of svabhāva or the set of parabhāva; 15.1–2 empties the first and 15.3 the second; so x lies in neither, and it is x that must go. “Those who believe that Nāgārjuna rejects the law should show us where he so states.” Buddhapālita and Candrakīrti are quoted in support, and Galloway reads Candrakīrti’s svabhāvo vā bhavet, parabhāvo vā as an explicit affirmation of the law.
• Murti’s two counter-examples fail (pp. 20–22). Murti 1955 p. 147 offers “an integer between 3 and 4 is prime” and the rope-snake as cases where the excluded middle lapses. Galloway answers that the first is meaningless because its bhāva does not exist, and meaninglessness is not a third truth-value; and that the rope-snake dissolves once the conflated predicate or the conflated subject is separated (“the rope-snake exists as rope” is true, “as snake” false). No third existential status is needed: tertium non datur.
• The contraposition charge answered by reading yadi as “only if” (pp. 22–24). Robinson’s charge of denying the antecedent, restated as a violation of contraposition, is pressed at MMK 13.7 (“if there were anything non-empty there would be something empty; but there is nothing non-empty, so whence will the empty be?”). Galloway’s reply is that the relation is symmetrical, because empty and non-empty are pratidvandvins — correlative opposites, each meaningful only if the other is (Ruegg 1977, p. 56) — so the inference runs by contraposition and modus ponens rather than by denying the antecedent. He defends the re-reading by appeal to metre, to approximative language, and, explicitly, to the nītārtha / neyārtha distinction: some passages are to be taken literally and others led out.
• The Two Truths may descend from nītārtha / neyārtha (n. 8, p. 28). In a footnote: a conventional truth is true within its own limited sphere, and the Buddhist insistence on two truths is “a distinction that may derive from the old nītārtha/neyārtha dichotomy in textual analysis.” He adds that “on the paramārtha level the conventional truth is not negated; it remains true but becomes irrelevant”, and sets the unification of the two truths aside as an ontological and soteriological question rather than a logical one.
• Emptiness is not a dharma among dharmas (n. 7, pp. 27–28). Against the suggestion that śūnyatā was borrowed from the mathematicians’ śūnya, Galloway draws the disanalogy: the achievement of the Indian mathematicians was to treat zero as a number like other numbers, whereas the Prajñāpāramitā and the Kāśyapaparivarta “spend more time warning against misapprehension of śūnyatā as an entity than they do uncritically advocating it.” The zero statement can be a step towards śūnyatā as upāya but not ontologically. He also collects the Pāli antecedents of suññatā — the Cūḷa- and Mahā-suññata-suttas, the three gates of liberation, and a Cullavagga passage identifying the suññatā-vihāra with the mahāpurisa-vihāra.
• The medical function of the concepts (p. 24). “Empty” and “non-empty” are ultimately just concepts whose function is medical: as in Indian medical theory a medicine leaves the body once it has done its work, so śūnyatā is meant to leave the mind once it has removed false conceptions.
• The middle is not a third position (n. 18, p. 31). Ontologically the middle way “is merely the absence of error on one side together with its absence on the other; a twofold absence of deviation is not a third deviation.” Supported with Śāntideva (via Ruegg 1977 p. 49), Samādhirāja 9.27 (“therefore avoiding both extremes, the wise takes up no middle position”), and the Kaccāyana material Nāgārjuna cites at MMK 15:7 and returns to at 15:10.
• The catuṣkoṭi has no Aristotelian analogue (n. 21, p. 33). Aristotle’s four quantified forms are not four mutually exclusive possibilities — the third and fourth turn out identical once compatibility is ruled out — and nothing in his system corresponds to the fourth corner.

Methodology

Analytic philosophy of logic applied to primary Indological materials. Galloway works from Sanskrit (Vaidya-tradition editions of the Madhyamakaśāstra, Johnston and Kunst’s Vigrahavyāvartanī) and from Tibetan (the Peking bstan ‘gyur for Buddhapālita and the Akutobhayā, Walleser’s and Kajiyama’s editions of Bhāviveka), and he quotes both. This is the notable difference from the framework-external analytic readers already in the wiki: the commentators are argued from, not merely named. Buddhapālita, Bhāviveka and Candrakīrti each supply load-bearing textual support, and the Tibetan translation practice for prasajya / paryudāsa is treated as evidence about meaning. The Sanskrit grammarians (Kajiyama’s anonymous verse, Arcaṭa) supply the account of the two pratiṣedha. The modern interlocutors are Matilal, Murti, Ruegg, Robinson, Nakamura, Schayer, Lopez, Kajiyama, and — at unusual length and unusual sharpness — Kristeva, whose semiotic formalisation of the tetralemma he corrects on several points of mathematics.

What is not here: no neyārtha / nītārtha as a working instrument (only the single appeal at p. 24 and the note at p. 28), no Three Turnings, no Tibetan commentator later than the canonical translators, and no soteriological reading of the negation beyond the medical simile.

Notable quotes

• “a twofold absence of deviation is not a third deviation.” (n. 18, p. 31)

Connections

• Gokhale / gokhale-ways-of-argumentation-2008 — the reason for the addition. Gokhale takes over Galloway’s answer to Robinson wholesale and argues that his catuṣkoṭi defence fails under iteration. See note 4 on whether the objection reaches the text.
• Wood / wood-nagarjunian-disputations-1994 — the substantive opposition, five years before Wood’s book and unaware of it. Both take the prasajya / paryudāsa distinction as the crux; Galloway makes the Madhyamaka prasajya non-implicative to the point of contentlessness, Wood makes it excluded-middle-obeying and terminal in non-existence.
• Ruegg — the essay leans on Ruegg 1977 (“The Uses of the Four Positions of the Catuṣkoṭi”, JIP 5) for the pratidvandvin point (p. 56), the semantic-well-formedness point (p. 50), and the absolute-negation reading of both syntactic types (p. 5), and on Ruegg 1983 (“On the Thesis and Assertion in the Madhyamaka”) for the two senses of pratijñā. A third Ruegg strand for the wiki, alongside the Svātantrika–Prāsaṅgika criteria and the 1986 performative-negation essay that Gokhale uses.
• Hayes / hayes-nagarjunas-appeal-1994 — the direct opposition on the central question. Galloway argues that the two standing fallacy charges fail; Hayes, five years later, cites Galloway in his tetralemma-studies footnote (n. 13) and adds a new charge, equivocation, which Galloway never considered. The two frame the logical debate Gokhale then adjudicates.
• Murti — Murti 1955 p. 147 is refuted directly on the excluded middle. Independent framework-external pressure on the absolutist reading, alongside Gokhale’s refusal of the Hegel comparison.
• Buddhapālita / coghlan-buddhapalita-2021, Bhāviveka / ames-prajnapradipa-ch2-1995, Candrakīrti / candrakirti-prasannapada-mmk1-excerpt — all three commentators are quoted as evidence, the Bhāviveka material from the Prajñāpradīpa on MMK 1.1 (Walleser’s and Kajiyama’s editions) rather than from Ames’s chapter 2.
• catushkoti-must-negate-all-four-extremes — the third route to the same block on Wood.
• No-thesis — the zero-statement reading of VV 29, and the objection to the Tsongkhapa–Lopez gloss.
• Robinson, Matilal, Nakamura, Kajiyama, Schayer, Lopez, Kristeva (no wiki pages) — the 1989 logic cohort. Robinson, “Some Logical Aspects of Nāgārjuna’s System”, PEW 6:4 (1957); Matilal, Epistemology, Logic and Grammar in Indian Philosophical Analysis (Mouton 1971); Kajiyama, “Three Kinds of Affirmation and Two Kinds of Negation in Buddhist Philosophy”, WZKS 17 (1973); Lopez, A Study of Svātantrika (Snow Lion 1987).