Chapter 3. Madhyamaka's methods of argument¶

The preceding chapters explained Madhyamaka's purpose, refuting intrinsic nature without establishing a position, and its early transmission. This chapter examines how it proceeds, presenting reductio, the four alternatives, and several recurring arguments in terms accessible to modern readers. In modern language, the Mūlamadhyamakakārikā fundamentally seeks to refute every philosophical claim that establishes an independent, self-sufficient, permanent ground of existence behind phenomena. Whenever someone posits a truly real X, whether primordial matter, atoms, a spiritual self, or the substance of phenomena, its arguments ask what allows X to be established independently. This is the underlying logic of refutation without a position and the common basis of every method in this chapter. The methods themselves become the focus of the Svātantrika–Prāsaṅgika disagreement in the next chapter.

1. Reductio and the negation of the four alternatives¶

Madhyamaka's methods come down to two.

The first is reductio (prasaṅga). It advances no contrary thesis. It takes the opponent's presupposition that something has intrinsic nature and derives a contradiction or absurd conclusion from it. The presupposition thus fails on its own terms. Precisely because it refutes without establishing a position, Madhyamaka can claim to have no thesis, as Chapters 1 and 2 explained.

The second is refutation of all four alternatives (catuṣkoṭi). It sets out four possibilities: is, is not, both is and is not, and neither is nor is not, then rejects all four. Section 5 distinguishes rejection from negation. Its target must be clear. It denies establishment through intrinsic nature, while leaving the conventional existence of things intact. This connects with the two truths and will be distinguished further in Section 5, which also explains why there are four alternatives rather than a dichotomy and why Madhyamaka must leave all four rather than merely deny two extremes.

Before examining particular arguments, a technical distinction must be established or the later analysis will repeatedly miss its target. Madhyamaka uses pure negation (prasajya), not implicative negation (paryudāsa). These labels follow Part II, Essay 18, Chapter 3. The older Chinese labels "无遮" (wuzhe) and "有遮" (youzhe) refer to the same two kinds.

Implicative negation denies P while implying or incidentally affirming not-P. In ordinary speech, "this is not white" implies that it is another color. Denying one property places it in the opposite class. Pure negation only denies P without affirming anything else. "There is no king here" says only that the king is absent, without suggesting that something else is present.

The distinction is not imposed from Western logic. The opposing camp established it too. In the Nyāyānusāra, the Sarvāstivāda thinker Saṃghabhadra divides negative expressions into two kinds: "All expressions of negation either signify something or signify nothing. Those that signify something include expressions such as 'not a Brahmin' and 'impermanent.' Those that signify nothing include 'nonexistent' and 'nothing.'" "Not a Brahmin" applies to Kṣatriyas and others. Excluding Brahmins places the person in another of the four castes, so the expression signifies something. "Nonexistent" and "nothing" signify nothing. Madhyamaka uses the latter kind of negation. A realist wrote this classification himself; the two sides do not dispute the distinction.¹

Madhyamaka's negation is pure. Denying that X has intrinsic nature does not also affirm that X is nothing or that emptiness is substantially real. This avoids two traps. If the negation were implicative, denying intrinsic nature would also affirm that nothing exists and fall into annihilationism. If emptiness were then established as real, ontology would be rebuilt at the opposite extreme. This is what Nāgārjuna's warning that those who take emptiness as a view cannot be cured by the buddhas seeks to prevent. With the distinction understood, Section 5's analysis of the four alternatives is easier to follow. Rejecting alternative ① is pure negation and does not assert ② or anything else.

2. Some recurring forms of argument¶

Madhyamaka repeatedly uses several fixed forms to refute intrinsic nature. Four of the most common are outlined here:

The full argument of causation in three times occurs in the Twelve Gates Treatise's eleventh gate: "Cause and what has a cause cannot be found to arise before, after, or at the same time." It successively refutes cause before effect, effect before cause, and their simultaneity, concluding that "therefore cause and effect cannot be found in any of the three times." Each case receives an example. A potter making a pot, a teacher being a teacher because of disciples, and lamp and light illustrate the three cases respectively. All three examples are rejected. The Vigrahavyāvartanī contains another dispute about three times, but it concerns the order of negation and what is negated. Its examples of prior, subsequent, and simultaneous causes are spoken by the opponent to refute Nāgārjuna, not offered as Nāgārjuna's own refutation of causation.²

The best known is nonarising through four alternatives. The Mūlamadhyamakakārikā opens: "Phenomena do not arise from themselves, nor from others, nor from both, nor without cause; hence they are known not to arise."³ A thing with intrinsic nature could arise in only four ways, and none works:

The diagram gives an intuitive outline of the four alternatives and the route usually taken in commentaries such as Qingmu's and Candrakīrti's. Some scholars have criticized arguments of this kind in the commentaries. Refuting a commentary's particular reasoning does not, however, falsify the root verses' claims. The two must be distinguished. If the root verses do have a real philosophical problem, it does not lie in the commentaries' reasoning. Production from other and production without cause allow tighter arguments that derive contradictions from within their presuppositions, without depending on observation.

Production from other, where A produces B and B has intrinsic nature. If both are true, would B still arise without A? Both possibilities cause trouble. If B still arises, it does not depend on A, so the causal relation "A produces B" fails. If B does not arise, its existence depends on A, and it lacks an independent intrinsic nature that depends on nothing else. This overturns the presupposition that B has intrinsic nature. Both routes fail. B's having intrinsic nature and A's producing B cannot both hold.

Production without cause, where A arises without a cause. If A's arising depends on no conditions, none constrains it. Wherever there is time and space, A should therefore arise at all times and in all places. This means that A exists permanently and is never absent. But if it has never been absent, there has never been a moment at which it arises, whereas production without cause presupposes an event of arising. This is a contradiction.

These are the clearest examples of reductio. Take the presupposition that B has intrinsic nature or that A arises without cause, follow it to a contradiction, and let it collapse.

Refutation through mutual dependence targets paired concepts such as doer and deed, fire and fuel, and long and short. Each acquires meaning through its counterpart. Without short there is no long; without a deed, no doer can be spoken of. Because each depends on the other, neither can exist independently. Intrinsic nature is defined precisely as independent existence. Whatever is established through mutual dependence therefore lacks intrinsic nature.

Going and coming in three times, in the Mūlamadhyamakakārikā's chapter of that name, ranks alongside the four alternatives of nonarising among its best-known arguments and deserves equal treatment. Its central question is how motion, or going, can be established within a framework of intrinsic nature.

The argument has three steps. First, what has been traversed (gata), completed motion, contains no motion now occurring because it has ended. Motion is not in what has been traversed. Second, what has not been traversed (agata), motion not yet begun, likewise contains no current motion because it has not started. Third, what is being traversed (gamyamāna), present going, is where motion occurs. Yet for present going to mean anything, it must already have begun and not yet have ended. It is partly traversed and partly untraversed. It therefore depends on what has and has not been traversed to be identified as current going. If the traversed and untraversed each have independent intrinsic nature while present going depends on them, present going has none. If present going has independent intrinsic nature, it should be independent of the traversed and untraversed. Then what distinguishes it from what has not been traversed? Why does one count as going now and the other not?

The chapter has another aspect beyond those three steps. The goer and going individuate each other. This connects directly with the book's central proposition. Qingmu identifies it as "first establishing the goer through going, and second establishing going through the goer." If the goer already contains going by intrinsic nature, saying that the goer goes counts going twice. The root verse says, "If the goer has going, there are two goings: one is the goer's going, the other the going of going." Conversely, remove going from the goer and what remains no longer deserves the name goer. The root verse says, "Apart from the goer, going cannot be found." The enumeration ends: "The goer does not go; the non-goer does not go; apart from the goer and non-goer, there is no third goer." No place remains for a goer. Taken together, the goer's identity conditions include going, and going's identity conditions include the goer. Yet intrinsic nature's first requirement is independence from anything different, so a goer with intrinsic nature cannot include anything different within its identity conditions. One side requires inclusion; the other forbids it. That is the contradiction. Part II, Essay 18, Chapter 4 treats this as the core derivation in its original setting and notes that conventional walking is untouched. Its individuation is supplied by a network of relations.⁴

The conclusion is that motion fits into none of the three times within a framework of intrinsic nature. Conventional motion plainly remains; its existence is not denied. Rather, motion with fixed intrinsic nature has no logical place from beginning to end. This is a concrete argument for Section 3's incompatibility of intrinsic nature and change. Motion requires passage across times, which depends on temporal relations; temporal relations exclude independent intrinsic nature. The reductio is complete.

These arguments share a structure. First assume that an object has intrinsic nature, meaning that it is independent, immutable, and self-sufficient. Then show that it cannot be established in arising, motion, relations, or time. From this follows absence of intrinsic nature, or emptiness.

3. Relations and change are incompatible with intrinsic nature¶

The preceding section introduced refutation through mutual dependence and the absence of intrinsic nature in mutually dependent things. This section takes the point deeper, asking why intrinsic nature is fundamentally incompatible with both relations and change. The issue exceeds a single argument and reaches the deepest logical basis of Madhyamaka's criticism.

Intrinsic nature excludes relations. Intrinsic nature means independent, self-subsisting existence, eternally the same. A relation means that some aspects of a thing are determined by its connection to other things. Without short there is no long, fire dies without fuel, and a cause has no causal efficacy apart from its effect. The conflict is direct. A thing with intrinsic nature cannot actually enter a relation. Doing so means that something about a thing is determined by another, contrary to independent self-existence. Anything that can actually enter relations therefore has no independent intrinsic nature.

The chapter on fire and fuel pushes this logic further. If fire has intrinsic nature, it should burn without fuel, yet experience shows that without fuel it goes out. If fuel has intrinsic nature, it should always be in its combustible state, yet experience shows it does not burn without ignition. If burning is a third thing added to fire and fuel, what establishes it? If it too must be connected to fire and fuel, a fourth thing must bear that connection, producing infinite regress. The relation never acquires a basis.

A philosophical comparison, without historical influence, is F. H. Bradley (1846–1924), who identified the same problem within Western metaphysics. If relation R is an entity independent of its terms A and B, a new relation R₁ must connect R and A, and another R₂ must connect R₁ with R and A, indefinitely. The relation is never grounded. Bradley's answer led to absolute idealism; Nāgārjuna's led to emptiness. Both saw the same problem. Independent entities and external relations cannot be combined.

Change presents a deeper problem. If X has fixed intrinsic nature, its nature at t₁ should be the same as at t₂, because eternal immutability is part of the definition. Change means that X differs in some respect between t₁ and t₂. Together, these imply that X with intrinsic nature cannot really change over time, yet experience shows everything changing.

Sāṃkhya is the clearest example of this contradiction, which Āryadeva presses in the Catuḥśataka, as listed among the opponents in 5.2. The spiritual self (puruṣa) is pure, eternally unchanging consciousness, witnessing primordial matter (prakṛti) evolve before it. The problem is that witnessing suffering now and pleasure later places it in different relations to the contents witnessed. If the difference belongs to the self, the self has changed and is not permanent. If it does not belong to the self at all, and the self remains the same in relation to suffering and pleasure, who distinguishes them? Without the distinction, liberation from suffering cannot be discussed. Sāṃkhya's theory of liberation thus loses its foundation. Madhyamaka offers no replacement explanation; it identifies the source of the contradiction. Once the spiritual self receives fixed intrinsic nature, it can neither actually enter relations nor change as relations change, yet it is required to do both. Intrinsic nature, relations, and change cannot all belong to it without one failing.

A modern argument: the doer, action, and intrinsic nature. The following reconstructs the logic of the chapter on action and the doer with more precise causal language. The argument distinguishes several roles. The doer, or agent, is the subject producing an influence. Action (karman) here means specifically the potential influence the doer can exert on a patient, rather than a realized final effect. The patient receives the influence. The environment comprises the other relevant conditions. The final effect is the actual result of action and environment jointly acting on the patient. The distinction between potential influence and final effect matters because the latter varies with conditions, while the former should belong to the doer itself. If the doer has intrinsic nature, that potential influence should be fixed.

Now suppose that the doer has intrinsic nature. Its relation to action can only be identity or difference.

If doer and action are identical, they are the same entity with intrinsic nature. Action merely restates the doer itself and is no independently existing intermediate link. What we seek is a causal connection between agent and patient. A single identical entity cannot provide that link, because a link requires two ends. The intermediate connection needed for the doer to influence the patient disappears; action is no longer the relation we sought.

If doer and action are different, we must ask whether action itself has intrinsic nature. If it does, the earlier argument of nonarising through four alternatives shows that it cannot be produced. Yet action means the potential influence produced by the doer. If it cannot be produced, it is not action in our sense, a direct contradiction. If action lacks intrinsic nature, it varies with conditions. The same doer then produces potential influences of different content under different conditions. What influence it can exert on the patient depends on conditions and is not inherent in the doer. Its causal properties vary with conditions and therefore have no fixed, unchanging nature, contradicting the premise that the doer has intrinsic nature.

Both routes fail, so the doer cannot have intrinsic nature. The argument structurally follows refutation through mutual dependence. The doer's identity depends on action; action's content depends on the doer and conditions. Each defines the other, and neither has an independently existing, fixed nature. □

The action is a potential influence; its final effect depends on the recipient of the action and the surrounding conditions.

The resulting outline of Madhyamaka is negative. Whatever enters relations or undergoes change lacks fixed intrinsic nature. All phenomena enter relations and change, so all are empty. This does not mean that only relations exist. If a relation itself had intrinsic nature, really existing independently of its terms, the same reductio could ask whether a relation existing without its terms is still a relation. Madhyamaka would refute it too. Nor does it say that change is an illusion; that is the path of Vedānta or Sāṃkhya, not Madhyamaka.

The book offers another philosophical comparison, without implying historical influence. In quantum field theory, elementary particles appear as excitations of fields rather than independent entities. Fields themselves can be described only through interactions with other fields, leaving no things independent of relations. Ontic structural realism goes further, holding relations to be more fundamental than their terms, with particles merely nodes in a relational network. These contemporary positions move toward Madhyamaka's implicit outline. The boundary is that Madhyamaka would not accept relations themselves as a more fundamental reality with intrinsic nature. That would be a theory of intrinsic nature at the relational level, equally open to reductio. Madhyamaka is closer to saying that any fixed bearer one tries to establish beneath relations or change is empty. The proposition that only relations exist, without relata, is empty too.

Part II returns to this passage. Essay 18, Chapter 7 takes it as the answer to the second mode of failure. Anyone trying to rescue the relationality premise by treating relations as a more fundamental reality still falls under the central proposition's argument. Asking what lies behind the framework remains within its scope. Chapter 4 of the same essay records this section's emptiness of relations and comparison with Bradley as a preliminary version of that answer. Part II formulates the theorem anticipated in Part I, completing the connection between the two parts.⁵

4. Answering objections: can empty words refute an opponent?¶

The opponent immediately counters. If everything is empty, are the words you use against me not empty too? Empty words have no weight, so how can they overturn my position? This is the challenge addressed by the Vigrahavyāvartanī.

The opponent here is one Madhyamaka itself constructs. Nāgārjuna places the challenge in an imagined opponent's mouth and then answers it. This is also the kind of challenge Madhyamaka most wants to meet. The question is conveniently formulated so that emptiness itself supplies an answer. Empty words can still function through dependent origination. Within this framework, the response is straightforward. Whether an actual opponent would stop at the same point or accept the same formulation is uncertain. Madhyamaka has chosen the ground best suited to its own argument, and some reservation is warranted.

Nāgārjuna replies that his words are indeed empty and lack intrinsic nature. Precisely because they are empty, dependently arisen, and capable of acting, they can refute the opponent's equally empty position. He uses the comparison of one magically conjured person restraining another. Emptiness does not mean powerlessness. Absence of intrinsic nature and dependence on conditions make action possible, as in 5.1's two truths and the claim that all phenomena can be established because of emptiness. He also asks how the valid means of cognition (pramāṇa) demanded to establish his thesis are themselves established. If by others, infinite regress follows. If by themselves, comparisons such as a lamp illuminating itself also fail. The requirement for self-evident means of cognition cannot sustain itself.⁶

This treatment of means of cognition already touched a deeper disagreement in Nāgārjuna's time and directly anticipates the next chapter's dispute. He returns the epistemological demand to the opponent. He has no thesis needing establishment, and the demand makes sense only where there is a thesis. It misses someone who has none. Further, if the opponent insists that means of cognition must first be established, what means establishes them? There are only three routes: another means, producing infinite regress; the same means establishing itself, producing circular reasoning; or assuming its validity without proof, leaving it unsupported. All three are problematic, and the opponent's own epistemological foundation cannot stand.

The reply leaves a gap. Madhyamaka's negative arguments, its reductios, are valid logical deductions, which require recognizing the validity of some rules of inference. Must Madhyamaka account for their epistemological basis? Svātantrika answers yes. Bhāvaviveka holds that its arguments need independent logical support or the opponent need not accept them. Prāsaṅgika answers no. Following Nāgārjuna's absence of a thesis, Candrakīrti refuses to establish a separate epistemology for Madhyamaka's negations. This is the subject of 5.4.

5. Does rejecting all four alternatives violate logic?¶

The reading must be settled first, or every later step will go astray. Throughout, the four cells are objects of rejection, not propositions being asserted. Rejecting a sentence and asserting its opposite are different acts. Presupposition failure offers the clearest example. "The present king of France is bald" is unacceptable. Its negation also takes the king's existence for granted and cannot be asserted either. The only correct act here is to reject the whole sentence. Part II, Essay 18, Chapter 3 establishes this as a lemma: rejecting A does not entail asserting not-A, where the negation in question inherits the subject's presupposition.⁷

Once this reading is fixed, simplification in classical logic has no application. One route writes ③ as P ∧ ¬P and ④ as ¬P ∧ ¬¬P, then simplifies ④ by double negation to ¬P ∧ P, judging both contradictory. That approach presupposed four propositions being asserted. Since the alternatives are objects of rejection, there is no conjunction to simplify. The entire step is inapplicable. This section follows Part II's principal reading.

An example unrelated to intrinsic nature can build the intuition. Buddhist texts contain questions the Buddha leaves unanswered (avyākata), including whether the Tathāgata after death exists, does not exist, both exists and does not exist, or neither exists nor does not exist. A dichotomy provides only two options. The four alternatives set out four ways of repairing the question to keep it alive:

All four must be rejected because they exhaust these four repairs. Only then can the failure be located in the presupposition that there is a fixed subject whose state after death can be questioned. The failure lies in no particular predicate.⁷

The Buddha's refusal therefore conceals no correct answer among the four options awaiting decipherment. It exposes the failure of the question's entire form, which treats the Tathāgata as a substantial object whose ultimate state can be determined in this way. Leaving the four alternatives means that the question's form fails, rather than that a fifth answer is found.

Apply the same reading to intrinsic nature, with H = "X has intrinsic nature":

These are not four independent negations. All four rejections are licensed by the assertion that the subject does not refer in a manner involving intrinsic nature.⁷

This common license is an instance of the Mūlamadhyamakakārikā's central proposition applied to a particular subject. Rejecting all four alternatives is its application, rather than a separate line of inference.

The table above gives the precise reason for rejecting the second corner: turning “X lacks intrinsic nature” into a categorical claim about reality rebuilds ontology at the opposite extreme.

A further distinction prevents confusion. Buddhism uses the same two-by-two grid in two ways. The Mahāvibhāṣā uses it more than three hundred times as a device of classification. It asks, for example, whether someone possesses the highest worldly dharmas without possessing the corresponding acquisition of disconnection. It answers that four alternatives should be made, then assigns a kind of person to each cell. The classification accounts for the whole domain. Nāgārjuna uses the same grid differently, rejecting all four to show that their shared basis fails. Their textual distinction lies in their closing formulas. Endings such as "是名诸佛法" ("this is called the teaching of the buddhas") and "教化" ("teaching and transforming") identify pedagogical alternatives, teachings adapted over time to their audiences. Endings such as "是故知无" ("therefore it is known not to exist") and "是事不然" ("this is not so") identify refutational alternatives, the kind discussed here.⁷ A related point of textual history is that the term catuṣkoṭi itself does not occur in the original Mūlamadhyamakakārikā, Catuḥśataka, or Prasannapadā. The label is later.

We can now return to the difficulty. Does rejecting is, is not, both, and neither violate the law of excluded middle or even contradict itself? The response has three levels of unequal weight.

The first, which bears most of the weight, is the rejection reading itself. Excluded middle governs assertions. For any proposition, either it or its negation holds. Rejection does not enter that allocation, so the four rejections do not conflict with excluded middle. The corresponding term in Buddhist logic is pure negation (prasajya-pratiṣedha), negating without establishing anything. Saying that tortoise hair does not exist establishes nothing further. The warning in 5.1 that those who take emptiness as a view cannot be cured by the buddhas guards precisely against turning this rejection back into an assertion.

The second is the distinction between the two truths. Ultimately none of the four holds; conventionally things continue to operate. It does not carry equal weight with the first response; here it serves as a supporting reading. It requires each statement to carry an implicit parameter, such as truth level, stage, or perspective, and the parameter requires independent authorization. Textual authorization is available only where the two truths are explicitly marked, whereas most of Nāgārjuna's refutations of all four do not mark them. It works where authorized and cannot be borrowed where it is not.⁷

The third is a more radical and provocative modern reading. Graham Priest and Jay Garfield argue that Madhyamaka reaches real contradictions at the limits of thought and openly accepts them, a position called dialetheism.⁸ The book holds that the rejection reading with presupposition cancellation sufficiently explains the fourfold refutation without violating logic, and does so entirely within classical logic. Dialetheism is a thought-provoking but more radical interpretation, presented here without being directly adopted.

6. Refutation without a position and its unresolved concern¶

The method is elaborate. Reductio forms its core, while the four alternatives, mutual dependence, and three-time arguments repeatedly examine the presupposition of intrinsic nature. It also declares that it establishes nothing of its own. The emptiness of emptiness rejects the reifying interpretation of the name emptiness as something with intrinsic nature, as 5.1 explains. Arguments are only rafts for crossing or ladders to be removed after climbing.

The concern left in 5.2 must nevertheless return. A method claiming to refute without establishing anything becomes a demanding art of debate. In the end, refutation itself may be grasped as a new scholastic method. Essay 3 and the end of the preceding chapter gave the book's judgment. The method is a product of historical conditions, the competitive arena of debate described in 3.6. It is impressive, but not necessarily the best way along the path of no-self. Once formed, it immediately raises a further question. Should Madhyamaka use only reductio, asserting nothing itself, or may it also offer independent arguments? Different answers produce the distinction between Svātantrika and Prāsaṅgika, to which the next chapter turns.

References¶