Chapter 3 Madhyamaka Methods of Argument¶

The preceding chapters explained what Madhyamaka seeks to do—refute intrinsic nature while establishing no thesis—and traced its early transmission. This chapter examines how it does so. It lays out consequence arguments, the tetralemma, and several recurring patterns of reasoning in terms accessible to modern readers. In modern language, the fundamental aim of the Mūlamadhyamakakārikā is to refute every philosophical attempt to establish an "independent, self-sufficient, permanent ground of existence" behind phenomena. Whenever someone posits a "truly real X," whether primordial matter, atoms, puruṣa, or a dharma-nature, the text asks: on what basis can X be independently established? This is the underlying logic of "refuting without establishing" and the common foundation of every method in this chapter. The methods themselves form the focus of the next chapter's disagreement between Svātantrika and Prāsaṅgika.

1. General Method: Consequence and Tetralemmatic Negation¶

Madhyamaka's techniques ultimately reduce to two.

The first is consequence (prasaṅga). Rather than directly establishing a contrary thesis, Madhyamaka accepts an opponent's premise—that something has intrinsic nature—follows it through, and derives a contradiction or absurdity, allowing the premise to collapse by itself. Because it refutes without establishing, Madhyamaka can claim to have no thesis (chapters 1 and 2).

The second is tetralemmatic negation (catuṣkoṭi). It lays out four possibilities: is, is not, both is and is not, and neither is nor is not; then it denies all four. What exactly is denied must be clear. Madhyamaka denies that any alternative is established with intrinsic nature; it does not deny the conventional existence of phenomena. This connects the tetralemma with the two truths, as section 5 will explain. Why four alternatives rather than a binary? Why leave all four behind rather than merely reject two extremes? Section 5 addresses these questions.

Before considering specific arguments, a technical distinction must be established; without it, the later analysis repeatedly misses its target. Madhyamaka negation is a non-implicative negation (prasajya-pratiṣedha), not an implicative negation (paryudāsa-pratiṣedha).

An implicative negation denies P while implying or affirming non-P. In ordinary speech, "this is not white" implies that it is another color: denying one property places the object within the opposite class. A non-implicative negation denies only P and affirms nothing else. "There is no king here" says only that a king is absent; it does not imply that something else is present.

Madhyamaka negation is non-implicative. Denying that "X possesses intrinsic nature" does not imply that "X is nothing" or that "emptiness truly exists." The distinction avoids two traps. If the negation were implicative, denying intrinsic nature would establish that "nothing exists" and fall into annihilationism. If the argument instead established that "emptiness truly exists," it would rebuild ontology at the other extreme. Nāgārjuna's warning that those who take emptiness as a view are incurable blocks precisely these paths. With this distinction in place, the refutation of all four alternatives in section 5 becomes easier to follow. When alternative ② is rejected, Madhyamaka non-implicatively denies that "X possesses intrinsic nature" without asserting that "X is nonexistent" or anything else.

2. Several Recurring Arguments¶

Madhyamaka repeatedly employs fixed patterns to refute intrinsic nature. Four of the most common are:

The best known is fourfold non-arising. The Mūlamadhyamakakārikā begins: "Dharmas do not arise from themselves, from another, from both, or without cause; therefore they are known not to arise."² If a thing possessing intrinsic nature "arises," it must arise in one of four ways, yet none is coherent:

The flowchart provides an intuitive summary of fourfold non-arising and follows the route common in traditional commentaries such as those of Piṅgala and Candrakīrti. Some scholars criticize the precise arguments found in these commentaries. Criticizing a commentary's reasoning, however, is not the same as refuting the root verse; the two must be distinguished. If the root claim contains a genuine philosophical problem, its source does not lie here. The alternatives of "arising from another" and "arising without cause" can be stated more tightly, deriving contradiction solely from the presuppositions rather than empirical observation.

Arising from another: suppose A produces B and B possesses intrinsic nature. Would B still arise without A? Either answer is troublesome. If B still arises, it does not depend on A and the causal claim "A produces B" fails. If B does not arise, its existence depends on A and it lacks an independent intrinsic nature. The premise that B possesses intrinsic nature is refuted. "B has intrinsic nature" and "A produces B" cannot both be true.

Arising without cause: suppose A arises without any cause. Its arising then depends on no condition. If unconstrained by conditions, A should arise at every time and place. But that would mean that A is permanently present and never absent. If it is never absent, no moment exists when A "arises"; yet arising is the premise of causeless arising. Contradiction.

These are especially clear examples of consequence. Accept the premise that "B possesses intrinsic nature" or "A arises without cause," follow it through, and arrive at contradiction, allowing the premise to fall.

The refutation through mutual dependence examines paired concepts: agent and action, fire and fuel, long and short. Their meanings emerge through mutual contrast. Without "short" there is no "long"; without something done, there is no agent. Because each depends on the other, neither can independently subsist, while intrinsic nature is defined precisely as independent subsistence. Whatever is established mutually therefore lacks intrinsic nature.

The three times of motion, in the Mūlamadhyamakakārikā's "Examination of Motion," is as famous as fourfold non-arising and deserves equal development. The question is how motion—"going"—can be established under assumptions of intrinsic nature.

The argument has three steps. First, what has gone (gata) is completed motion and contains no motion occurring now, since it has ended; motion is not in "what has gone." Second, what has not gone (agata) is motion not yet begun and likewise contains no present motion; motion is not in "what has not gone." Third comes "the going" (gamyamāna), what is currently moving, which appears to be where motion occurs. But for "the going" to be meaningful, it must already have begun—part is "gone"—and not yet have ended—part remains "not gone." It therefore depends on what has gone and what has not gone in order to be identified as "currently going." If those two possess independent intrinsic natures while the going depends on them, the going lacks independent intrinsic nature. If the going possesses intrinsic nature, it should be independent of what has and has not gone; but then nothing explains what it possesses beyond the not-gone state, or why one is "currently going" while the other is not.

Conclusion: under assumptions of intrinsic nature, motion can be placed in no temporal position. This does not deny conventional motion, which plainly occurs. It says that a "motion with fixed intrinsic nature" has nowhere to stand logically. The argument concretely illustrates section 3's incompatibility of intrinsic nature and change. Motion requires crossing temporal positions; crossing temporal positions depends on temporal relations; temporal relations preclude independent intrinsic nature. The consequence is complete.

All the arguments share a structure: first assume that the object possesses intrinsic nature—independent, unchanging, and self-sufficient—then show that it cannot be established in arising, motion, relation, time, or anywhere else, thereby deriving that lack of intrinsic nature is emptiness.

3. The Incompatibility of Relation, Change, and Intrinsic Nature¶

The previous section introduced the refutation through mutual dependence: whatever depends on another lacks intrinsic nature. This section presses deeper and asks why intrinsic nature is fundamentally incompatible with both relation and change. Here we move beyond a single argument to the deepest logical basis of Madhyamaka's critique.

Intrinsic nature excludes relation. By definition, intrinsic nature subsists independently, depends on nothing else, and remains what it is. Relation means that some aspect of a thing is determined by its connection with another: without short there is no long; fire ceases without fuel; a cause has no "causal efficacy" apart from an effect. The conflict is direct. Something possessing intrinsic nature cannot enter a genuine relation, because relation makes some part of it determined by another and contradicts independent subsistence. Anything capable of genuine relation therefore lacks independent intrinsic nature.

The "Examination of Fire and Fuel" takes the argument further. Suppose fire possesses intrinsic nature. It should burn independently of fuel, but in experience fire ceases without fuel. Suppose fuel possesses intrinsic nature. It should always be "combustible," yet without ignition it does not burn. If "burning" is a third thing added to fire and fuel, what supports this third thing? If it too must connect with fire and fuel, a fourth thing is required to carry that connection, producing infinite regress; the relation never becomes grounded.

A comparison of doctrines, without implying historical influence, can be made with F. H. Bradley (1846–1924), who encountered the same fissure within Western metaphysics. If relation R is an entity independent of relata A and B, a new relation R₁ is needed to connect R and A; R₂ is then needed to connect R₁ with R and A, and so on without end. Relation is never grounded. Bradley's solution moved toward absolute idealism; Nāgārjuna's was emptiness. But both perceived the same break: independent substances and external relations cannot be coherently joined.

Change lies deeper still. If X has fixed intrinsic nature, X's intrinsic nature at t₁ should be the same at t₂, because permanence and immutability are part of the concept. But "change" means that X differs in some respect between t₁ and t₂. Placed together, an X with intrinsic nature cannot genuinely change through time, although experience shows every phenomenon changing.

Sāṃkhya provides the clearest example. Āryadeva subjected it to sustained pressure in the Catuḥśataka, as the opponent table in 5.2 noted. Puruṣa is permanent, unchanging pure consciousness; primordial nature evolves before it while it "witnesses." But puruṣa witnesses suffering now and pleasure later, and its relation to the witnessed contents differs across the two moments. If the difference belongs to puruṣa, then puruṣa changes and is not permanent. If it does not belong to puruṣa at all, and puruṣa is entirely indifferent to suffering and pleasure, what distinguishes them? Without a distinction, liberation—release from suffering—cannot be discussed. Sāṃkhya's liberation theory loses its foundation. Madhyamaka does not supply an alternative explanation. It identifies the source of the contradiction: once puruṣa receives fixed intrinsic nature, it cannot truly enter relations or change with them, though the theory requires both. Intrinsic nature, relation, and change cannot all belong to puruṣa.

A modernized argument: agent, action, and intrinsic nature. The following reconstructs the logic behind the "Examination of Action and Agent" using more precise causal language. Introduce the following roles: the agent, which produces an influence; the action (karman), here specifically the agent's potential influence on a patient rather than the final realized effect; the patient, which receives the influence; the environment, all other relevant conditions; and the final effect, the actual result jointly imposed on the patient by action and environment. Distinguishing potential influence from final effect matters because the latter varies with conditions, while the former should belong to the agent. If the agent possesses intrinsic nature, its potential influence ought to be fixed.

Now suppose that the agent possesses intrinsic nature. The relationship between agent and action must be either identity or difference.

If agent and action are identical, they are one intrinsically existent thing. "Action" merely redescribes the agent and is not an independently existing intermediate step. But what we seek is a causal link between agent and patient. An identical substance cannot serve as a link, because a link requires two endpoints. The intermediate element required by "the agent affects the patient" disappears, and "action" is no longer the relation we sought.

If agent and action are different, ask whether action itself possesses intrinsic nature. If it does, the fourfold non-arising argument above shows that something with intrinsic nature cannot be produced. But action means precisely the potential influence produced by the agent; if it cannot be produced, it is not action in the relevant sense. Contradiction. If action lacks intrinsic nature, it changes according to conditions. The same agent then produces different potential influences under different conditions; what the agent can do to the patient depends on conditions rather than inhering in the agent. Since the agent's causal properties vary with conditions, it lacks a fixed, unchanging nature, contradicting the premise that the agent possesses intrinsic nature.

Neither alternative succeeds; therefore the agent cannot possess intrinsic nature. Structurally, the argument embodies the spirit of mutual dependence: an agent's identity depends on action, the content of action depends on agent and conditions, and neither has an independently self-subsisting fixed nature. □

The outline of Madhyamaka that emerges is negative. Everything that participates in relation or change lacks fixed intrinsic nature. All dharmas participate in relation and change; therefore all are empty. This does not mean that "only relations exist." If relation itself possessed intrinsic nature as a reality independent of its relata, the same consequence argument would apply: can a "relation" existing independently of its relata still be a relation? Madhyamaka rejects it too. Nor does it claim that "change is an illusion"; that route belongs to Vedānta or Sāṃkhya, not Madhyamaka.

Another modern doctrinal comparison may help, without implying influence. In quantum field theory, elementary particles do not appear as independent entities but as excitations of fields. Fields themselves can be described only through interactions with other fields, leaving no "thing" independent of relation. Ontic structural realism goes further and holds that relations are more fundamental than relata, with "particles" merely nodes in relational networks. Both approaches move in a direction resembling Madhyamaka's implicit outline. The difference is that Madhyamaka would reject the claim that "relations themselves possess intrinsic nature and form a more fundamental reality." That would be intrinsic-nature theory at the level of relation and could be reduced to absurdity in the same way. Madhyamaka is closer to saying that any fixed bearer one attempts to secure beneath relation or change is empty—and the proposition "only relations, without relata" is empty as well.

4. The Rejoinder: Can Empty Speech Refute Anyone?¶

The opponent immediately turns the argument back. You say that everything is empty. Are your own words of refutation not empty too? Empty speech carries no weight, so how can it overturn my position? The Vigrahavyāvartanī addresses this objection.

The "opponent" should first be identified as an imagined interlocutor constructed within the work. Nāgārjuna places the challenge in a fictional opponent's mouth and answers it himself. It is precisely the form of challenge Madhyamaka most wants to meet: the problem is constructed in a shape that emptiness itself can answer. Nāgārjuna's loop—"empty speech also functions through dependent arising"—works conveniently within that frame. Whether an actual opponent would stop at the same point or accept the same formulation of the problem is uncertain. Madhyamaka chooses terrain particularly suited to its method, which warrants some reservation.

Nāgārjuna responds that his words are indeed empty and possess no intrinsic nature. Precisely because they are empty, dependently arisen, and able to function, they can refute an equally empty opposing position. An illusory person can still stop another illusory person. Emptiness does not mean impotence; exactly because something is empty—lacking intrinsic nature and dependent on conditions—it can act. This is the same point as the two truths in 5.1 and "because emptiness is possible, all dharmas are possible." Nāgārjuna also asks in return: you demand that I establish my claim using "valid instruments of knowledge" (pramāṇa), but through what are those instruments themselves established? If another instrument establishes them, infinite regress follows; if they establish themselves, analogies such as a lamp illuminating itself fail. The demand that "self-evident instruments of knowledge must come first" therefore lacks a foundation.¹

This treatment of pramāṇa already touches a deep division in Nāgārjuna's period and directly anticipates the next chapter. He pushes epistemological demands back on the opponent: I have no thesis requiring proof; such demands are meaningful only where a thesis is asserted and therefore fail against someone with no thesis. If the opponent insists that an instrument of knowledge must itself be established, three possibilities remain. Another instrument establishes it, producing infinite regress; it establishes itself, producing circularity; or it is simply postulated as valid without proof, producing an unsupported assumption. Every path is defective, and the opponent's own epistemological foundation is unstable.

The response leaves a fissure. Madhyamaka's negative arguments—its consequences—are valid logical inferences, and valid inference requires acknowledging some valid rules. Must Madhyamaka explain an epistemological foundation for them? Svātantrika answers yes. Bhāviveka holds that Madhyamaka must supply independent logical support for its arguments, or opponents need not accept them. Prāsaṅgika answers no. Candrakīrti follows Nāgārjuna's no-thesis route and refuses to establish a separate epistemology for Madhyamaka negation. This is the subject of 5.4.

5. Does Refuting All Four Alternatives Violate Logic?¶

We begin with formal logic: why does the tetralemma contain four possibilities rather than a binary pair?

An example unrelated to intrinsic nature can establish the intuition. Among the questions the Buddha refused to answer—the undeclared questions (avyākata)—is whether the Tathāgata after death exists, does not exist, both exists and does not exist, or neither exists nor does not exist. Binary logic offers only two alternatives: the Tathāgata exists after death or does not. The tetralemma lays out every mode of assertion:

If the four alternatives are forcibly translated into classical propositional logic while P remains the same proposition at the same level and in the same sense, ③ is the contradiction P ∧ ¬P. Alternative ④, represented as ¬P ∧ ¬¬P, simplifies under double negation to ¬P ∧ P and is likewise contradictory.

Alternative ③ requires qualification. In Buddhist contexts it does not always mean the bare "P and not-P." More often it can mean existent from one standpoint and nonexistent from another. Asked whether a chariot exists, for example, ③ might mean that the chariot exists as a convention dependently established through assembled parts but does not exist as an intrinsically real entity. The predicates belong to different levels and do not collide; the form is closer to P(conventional) ∧ ¬P(ultimate). The problem is sharper in the example of the Tathāgata after death. If P is fixed in one sense—"the Tathāgata exists after death"—③ truly becomes a bare P ∧ ¬P with no compatible interpretation.

Alternative ④, "neither existent nor nonexistent," likewise requires care. Represented as ¬P ∧ ¬¬P, it does reduce to ¬P ∧ P under classical double negation and is contradictory. But its tetralemmatic intention is not to propose a compound statement within classical logic. It rejects the applicability of the predicates "existent" and "nonexistent" themselves. It rejects the entire mode of assertion rather than selecting another combination of existence and nonexistence. Classical simplification obscures this metalevel intention.

The real point of rejecting all four does not depend on whether ③ and ④ are formal contradictions. At a deeper level, rejecting ① commonly leads people to assume that ② follows automatically: "the Tathāgata does not exist after death." Yet nonexistence is equally an assertion and presupposes a fixed subject whose postmortem status can be investigated—an entity continuing along a timeline and capable of being judged existent or nonexistent. Once not-self is accepted, the presupposition collapses. The Buddha did not hide a correct answer among the four alternatives. He identified the question's entire framework as misplaced. It treats "the Tathāgata" as a substantial object whose ultimate status can be determined in these terms. The tetralemma exhausts every mode of assertion to reveal that "exists, does not exist, both, neither" all share the same reifying premise.

Leaving the four alternatives means not discovering a fifth answer but recognizing that the form of the question has failed. The object it presupposes cannot be established.

Apply the same logic to intrinsic nature, with H = "X possesses intrinsic nature":

Alternative ② is crucial. Reducing ① to absurdity does not make ② automatically true. Madhyamaka negation is non-implicative: it denies only "being this way through intrinsic nature" and does not affirm a contrary entity. Awareness that "X lacks intrinsic nature" is unproblematic when used to remove attachment. Freezing it into an ultimate declarative proposition rebuilds ontology in the opposite direction. This is precisely the point of the warning in 5.1 that those who take emptiness as a view are incurable.

Alternative ④ works similarly. Formally it simplifies to contradiction, but its intention is a metalevel refusal. The mode of asserting that "X possesses or lacks intrinsic nature" does not apply. Because this refusal can itself be interrogated, it too falls within the scope of negation.

One difficulty remains. If is, is not, both, and neither are all denied, does this not violate excluded middle or even contradict itself?

Several responses can be listed. First, non-implicative negation, as explained above, denies only "being so through intrinsic nature" without affirming the opposite; rejecting all four does not therefore mean affirming and denying the same thing. Second, the two truths distinguish levels. Ultimately none of the four is established; conventionally phenomena continue to function. Statements at two levels do not directly conflict. Third is a more radical modern reading. Graham Priest and Jay Garfield argue that Madhyamaka encounters genuine contradictions at the limits of thought and accepts them—the position called dialetheism.³ This book's view is that on a conventional reading of Nāgārjuna, "non-implicative negation + the two truths" adequately explains why the tetralemma does not violate logic. Dialetheism is provocative and illuminating but more radical; it is presented without being adopted.

6. The Method of Refuting without Establishing—and Its Concern¶

The method is extraordinarily precise. Centered on consequence, it repeatedly applies the tetralemma, mutual dependence, and temporal arguments to the presupposition of intrinsic nature while declaring that it establishes nothing of its own. Emptiness itself is empty. The argument is only a raft for crossing or a ladder to discard after climbing (5.1).

The concern left in 5.2 must nevertheless be repeated. A method that calls itself "refuting without establishing" became a demanding art of controversy. By the end, "refutation" itself could be grasped as a new scholastic method. This book stated its position in Part III and at the close of the preceding chapter: the method was a product of historical conditions, especially the competitive arena of debate described in 3.6. It is brilliant, but not necessarily the ideal course for the path of not-self. In any case, once the method took shape, the next problem was unavoidable. When Madhyamaka refutes opponents, should it use consequence alone and establish nothing, or may it also offer independent arguments? The disagreement produced Svātantrika and Prāsaṅgika. The next chapter turns to it.

References¶