Chapter 4　The main argument¶

The tools are ready. This chapter begins the proof in the following order. First it establishes the relational premise P, arguing positively for the analytic-truth option among its three possible foundations. It then puts the opponent's strongest opening on the table, the distinction between epistemic and existential dependence, and closes it while honestly accounting for the cost. Next the core derivation unfolds in numbered steps. The strong version rests on P; what remains unclosed is taken over by the middle version. Two worked examples at the end, from the "Examination of Going and Coming" and the "Examination of Conditions," show how this derivation operates word by word in the original text.

P and its three possible foundations. P: the identity conditions of any existent necessarily involve difference and relations. "Existent" is taken broadly here, to mean anything that can be individuated as the subject of an assertion. There are three possible foundations. Analytic truth: P is guaranteed by the grammar of the concept of identity conditions; denying it means losing that concept. Transcendental truth: P is a condition of the possibility of identification and reference, arising from our conceptual framework. The opponent can then retreat to an unthinkable thing in itself, leaving the theorem to close off only the thinkable world. Empirical generalisation: everything examined so far has been this way, which warrants only reductio case by case. These decline in strength in that order. The chosen target is analytic truth, for which this chapter argues positively. If it cannot be defended, Chapter 1 has already specified the path of weakening.

The positive case for analytic truth. Three steps. First, content is exclusion. An identity condition is a determination with content; it says what x is. A statement that excludes nothing says nothing. Exclusion here is assessed at an epistemic level of granularity. To say something is to close options still open as far as we know. The options closed by mathematical theorems have always been of this kind, not possible worlds. A determination is a determination because it draws a boundary, and drawing a boundary brings in what is excluded. Spinoza's old maxim says that determination is negation.¹ Second, identity and difference come as a pair. Chapter 1's boundary clause established them as a pair of logical constants. To have one is to have the other; a concept of identity containing identity alone, without difference, is no concept at all. Individuation is contrast: x is individuated if and only if there is a criterion separating x from non-x. Third, the classical witness. Qingmu's commentary says it all in one sentence: "Since self is absent, other is absent too; there is other because there is self."² Self and other are established in dependence on one another. This is a grammatical statement about the pair of terms, not an empirical discovery about the world. The three steps together yield this result. Any identity condition with content must involve difference, and involving difference means involving a relation, at least a relation of difference from what is excluded. P is analytically true.

One further test. Imagine a singleton domain, a world containing x and nothing else. P still holds there. Saying what x is still draws a boundary against the kinds of thing that x is not. Difference can be a difference of types, not necessarily of things. Besides, none of this essay's opponents argues within a singleton domain. The first of the four Chinese characters 各住自性, "each abides in its own intrinsic nature," already presupposes plurality. Each dharma possesses its own intrinsic nature precisely in contrast with the other dharmas that possess theirs. Chapter 2 has already supplied the source.

The opening: epistemic and existential dependence. The opponent's strongest reply must be presented in its strongest form. It says that P confuses two things. Our recognition of x requires contrast, which is an epistemic matter. Whether x's being x depends on contrast is an existential matter. Dependence on relations for recognition does not amount to dependence on relations for existence. At most, you have proved that nothing can be recognised without contrast, not that nothing can exist without it. Saṃghabhadra stands precisely in this opening. His test for real existence is giving rise to cognition as its object. The recognition side plainly relies on relations, while he still insists that a dharma's entity abides in itself and depends on no other, as discussed in Chapter 2 and Essay 17, Chapter 7. The coexistence of ontological and cognitive dimensions in modern interpretative history reflects this same opening.³

Closing the opening. The argument that closes it proceeds by content, not by cognition. No step here may be left vague. Identity conditions are constitutive determinations, not procedures for recognition. They say what x's being x depends on. Now ask what content a constitutive determination involving no difference at all could have. It cannot say that x is such-and-such, because such-and-such classifies, and classification contrasts. All it has left is "x is x." But "x is x" holds of anything. It does not separate x from non-x and cannot serve as x's identity condition. Saying nothing here is a failure of duty, not the fulfilment of one. An identity condition's job is to separate x from non-x; a statement that holds of everything idles at that task. There is another kind of saying nothing which does fulfil its duty, the silence of rules, distinguished in Chapter 7. The two horns now close. Either the constitutive determination has content, in which case it involves difference and violates D2's first condition, or it has no content, in which case the bearer of intrinsic nature in the D3 assertion has received no determination at all. The speaker merely points at it and says that it is itself. This does not constitute a thesis. The first horn supplies T-strong's contradiction. The second falls under T-middle: the claim that there is a constitutive but inexpressible essence is itself still a statement. A signpost can be placed here for a return in Chapter 8. When a self-existent being must state what it is, grammar leaves it only the form "x is x." The two horns have exhausted the reasons why.

The cost must be accounted for. Does this closure smuggle in verificationism? No. Content as exclusion means semantic exclusion: a sentence must exclude some possible circumstances to say anything. It does not require those excluded circumstances to be testable. A proposition can exclude circumstances we could never test and still have content. The closure needs only one thing, that D3 be a thesis with content. The opponent's own practice supplies it. Opponents classify, state theses, refute others, and pronounce "The evaluation states." Two hundred fascicles of debate are evidence that D3 has content. If the opponent now retreats to contentless mystery, what is left behind is the class of theses. The record at the end of Chapter 2 then applies.

Grading the collision: the senses of dependence. Steps 3 and 4 of the core derivation collide. To determine the level of that collision, we must first grade the word "dependence." This is the passage whose structure most needs to be explicit in the whole essay; no step can be left vague. Three conceivable readings form a scale. The narrowest is causal: dependence means arising in dependence on conditions. The broadest is the level of statement: every determination uses contrast. Between them lies contrastive dependence: for a property to be the property it is, it depends on what stands opposite it, as long does on short, this on that, and identity on difference. Which level does D2's first condition exclude? The warranting texts and the opponent's usage supply the evidence in court. At the very passage "not constituted in dependence on other dharmas," Qingmu provides his own control group: "unlike long and short, this and that, which have no determinate nature and therefore exist in dependence on another." The same commentary rejects other-nature with "constituted through dependence" and "mutually dependent." The "Examination of Time" works throughout with mutual dependence, taking "each constituted separately in itself" as its opposite pole, and expressly includes identity and difference among things that depend on one another: "Because there is identity, there is difference; because there is difference, there is identity." On the opponent's side, the Mahāvibhāṣā defines dependent origination as "arising in dependence on conditions," and the Abhidharmakośabhāṣya states "impermanent because dependent on conditions." But the Mahāvibhāṣā's five kinds of existence list relative existence separately and classify it as nominal existence. Whatever exists through contrastive dependence is thereby excluded from real existence. This is the opponent's own taxonomy, cited in Chapter 2. The Sanskrit text is clearer still. Being unmade and being independent are two separate requirements. Dependence does not mean being produced by conditions; apekṣā is precisely the word for mutual or contrastive dependence. Later commentarial traditions distinguish three kinds of dependence: on causes, on parts, and on contrastive designation. Modern research likewise draws a line between existential and contrastive dependence, taking the independence of intrinsic nature to require freedom from both.⁴ The ruling is that the dependence excluded by D2's first condition includes at least the contrastive level. This is common ground between the two sides' texts and the commentarial tradition, not an addition by this essay. P therefore need not establish existential dependence. It need only establish that any determinate nature depends contrastively, at least at the level of types, on what it excludes. That is exactly the level supplied by the three steps for analytic truth. The collision occurs on the axis of dependence acknowledged by both sides. No further common premise is needed.

Closing in one step further: independence is itself a contrastively dependent property. Ask one more question. What sort of property is independence itself? "Constituted without depending on any other dharma" is a determination whose content comprehensively negates all other dharmas and all relations of dependence. It stands in dependence on what it negates and is the most thoroughgoing contrastively dependent property. "There is other because there is self" now displays its full force. What takes independence as its nature thereby has a nature that contrastively depends on other dharmas. The content of D2's first condition carries the very contrast it seeks to abolish. The opponent now has only four exits, each assigned to its proper version. First, take independence itself as one's nature. That nature is contrastively dependent and cancels itself; the strong version takes the case. Second, offer some other determinate F as one's nature. The determinacy of F is contrastive dependence at the level of types; it enters the collision directly, and the strong version takes it. Third, retreat to primitive identity while continuing to make statements. Primitive does not mean inexpressible. This is a position with content and requires a direct answer, given in the next paragraph. Fourth, retreat to an inexpressible nature. The D3 assertion loses its determination and passes to T-middle and the thesis-domain clause. This case is credited to the middle version, not claimed as an achievement of the strong one. The four paths are each recorded under their own names and listed separately in the audit table. The third and fourth were originally combined, treating an opponent who speaks as one who does not. The correction and its reasons appear under failure mode 1 in Chapter 7.

Answering the third path: how is the primitive itself individuated? Whatever someone who takes identity as primitive posits must distinguish a from b. If it cannot, positing it is useless. So ask: what makes a's thisness different from b's thisness? Only two answers are available. Appeal to their respective bearers, a and b, and the account is circular, since thisness was posited to explain the difference between a and b. Say instead that the two are primitively different, and difference already stands at the base alongside identity. But identity and difference, under the grading just established, belong to the class of mutual dependence acknowledged by both sides. The "Examination of Time" explicitly says, "Because there is identity, there is difference; because there is difference, there is identity."⁴ Both answers return the primitive to contrastive dependence, precisely the level D2's first condition excludes. Notice where the pressure lies. It is not on how the word "thisness" is introduced; the procedure for introducing a word is a level the opponent may legitimately set aside. It is on what makes the posit itself this one rather than that one. This question has the same form as the previous paragraph's. That paragraph asked what independence as a property depends on; this one asks what a primitive's being this particular primitive depends on.

The core derivation. The numbered steps follow; the fully symbolic form belongs to Appendix A. First, suppose there is an x such that E3(x) and D2(x). This is the content of a D3-type assertion. Second, as the subject of an assertion, x has already been individuated. Third, by P, x's identity conditions involve difference and relations. Fourth, by D2's first condition, "not constituted in dependence on other dharmas," x's being x does not depend on anything different from x. Its identity conditions may not involve difference. Fifth, the third and fourth steps concern the same object in the same respect. One requires involvement, the other forbids it. They yield a contradiction. Therefore any D3-type proposition, together with the definitions and P, entails a contradiction. T-strong is now established. Its standing depends on P's status as an analytic truth, for which the argument has been given above.

How the middle version takes over. If the opponent withdraws before step 3, declaring x's constitutive determination inexpressible, the derivation changes course. It attacks the act of assertion rather than the proposition's content. To assert how x is, a speaker must first individuate x. Individuation requires contrast. The act of assertion therefore presupposes contrastive identity conditions for x, while its content denies precisely those conditions. The contradiction moves from inside the proposition to the space between speaking and what is said. This is T-middle, the level of the Vigrahavyāvartanī. Someone may ask why contrastive conditions are needed if reference can be fixed by a causal chain. The answer is that causal chains fix the names of ordinary things. No one has causal acquaintance with the special subject posited by a D3-type assertion. Its reference is fixed solely by a schema, every sentence of which is a contrastive determination: really existent, not dependent on other dharmas, not changing with conditions, not produced by conditions. The speaker has no other route into the subject.

The weak version's place. The twenty-seven chapters apply this inference individually to every bearer of intrinsic nature actually proposed. The conflict between not depending and necessarily depending on other dharmas recurs. T-strong extracts a general rule from these cases. Whether that extraction reaches universality, the concern over an inductive leap, receives its own treatment under failure mode 3 in Chapter 7.

The three versions can now be brought together in the shortest statement. The theorem sentence: Definition requires identity and difference; intrinsic nature cancels identity and difference; hence contradiction. Its twin at the level of assertion says that assertion requires identity and difference, intrinsic nature cancels identity and difference, and hence the assertion defeats itself. Every reductio in the chapters is an instance of this inference. One further point must be recorded. Cancel difference and identity idles too; identity and difference are tools that work as a pair. All a bearer of intrinsic nature can then say about itself is "x is x." This is the root of the signpost to Chapter 8.

Here Rel(x) means that x's identity conditions involve difference and relations; “no difference” in Step 4 means that these conditions may not involve difference.

The third box in the bottom row, “primitive but stated,” is a compressed label. Chapter 7 limits this branch of the strong version to a primitive item assigned the task of distinguishing A from B. The remaining case—identity facts taken as prior to facts of difference, with no further account—is handled by E3 and the middle version, not counted as a semantic collision established by the strong version.

Example 1: the "Examination of Going and Coming." The opponent opens by positing action in three times: the already traversed, the not yet traversed, and the time of going. Since action is visibly present, there must be a dharma. Nāgārjuna replies: "There is no going in what is already traversed, nor in what is not yet traversed. Apart from the already and the not yet traversed, there is no going in the time of going."⁵ This verse is often read as denying motion, which is a misreading. Read going as a predication over a relational domain and its work becomes clear. Going involves a goer, a destination, and a time. On the temporal axis, action has already ceased in the already traversed and has not yet occurred in the not yet traversed. The time of going is half traversed and half not yet traversed, inseparable from the first two. On the side of mutual individuation, Qingmu's commentary makes the point in one sentence: "First, the activity of going constitutes the goer; second, the goer constitutes the activity of going. To constitute the goer and then have it use the activity of going cannot be so."⁶ "If the goer has going, there are two kinds of going: one the going of the goer, the other the going of going." If going is the goer's intrinsic nature, "the goer goes" counts going twice. "Apart from the goer, no activity of going can be obtained. Without the activity of going, how could there be a goer?" If the goer stands apart from going, removing going leaves nothing that could count as a goer. "The goer does not go; the non-goer does not go. Apart from goer and non-goer, there is no third goer." All boxes have been swept, and the base is cancelled. The conclusion of the whole chapter is not that nobody walks. It is that an E3 reading of walking cannot stand. Walking at E2 is individuated by a network of relations and loses not a single step. This is the original textual version of steps 3 and 4 of the core derivation. The goer's identity conditions must involve the activity of going; the identity conditions of a goer endowed with intrinsic nature may not involve it.

Example 2: the four conditions in the "Examination of Conditions." Here we receive the joint left for us at the end of Essay 16. The system of four conditions is the skeleton of Sarvāstivāda causation. Nāgārjuna asks only one question: "Because a dharma gives rise to an effect, that dharma is called a condition. If the effect has not yet arisen, why not call it a noncondition?"⁷ Qingmu's commentary gives the key in five Chinese characters, 缘成由于果: "A condition is constituted by its effect." Something is recognised retrospectively as a condition after its effect has arisen. Before the effect arises, water and earth are just water and earth. Retrospective recognition is individuation through the effect: the effect is written into the condition's identity conditions. A condition under the E3 reading thus defeats itself. As a bearer of intrinsic nature, it must stand independently of the effect; as a condition, its identity depends on the effect. Conditions under the E2 reading continue to work. The farmer sows and the potter mixes clay, with nothing disrupted. This closes the comparison with Essay 16. Essay 15, Chapter 5 has already followed the doctrinal difficulties of the four conditions as a relational apparatus. What is added here is their formal location. A relational apparatus cannot at the same time be a collection of bearers of intrinsic nature.

Three proofs, one comparison table. This book now contains three proofs in different forms: Qingmu's reductio of four kinds of production in the "Examination of Conditions," given as a complete example in Chapter 3; the modern reconstruction of the "Examination of Action and Agent" in Part I, Essay 5, Chapter 3, with its two-level dilemma between agent and action (if identical, the link lacks two ends; if different, ask further whether the action has intrinsic nature: with it, action cannot be produced; without it, the agent's causal properties depend on conditions and are not inherent); and this chapter's main argument. Set side by side, they reveal themselves as three stages in extracting the same inference.

Two further entries can be read from the comparison. First, dependence. At the difference horn, the reconstruction in Part I expressly cites nonarising under the four alternatives as a lemma. This chapter then establishes as conceptual grammar the inference common to the first two proofs. The three form a chain: in its original setting, partly extracted, and extracted universally. Second, anticipation. The reconstruction's step from action without intrinsic nature to the agent's causal properties depending on conditions already sketches P within the causal domain. That same chapter's passing remarks on the emptiness of relations and its comparison with Bradley anticipate the answer to failure mode 2 in Chapter 7. Part I drew the outline; this essay makes it good as a theorem. The arch closes here.

What this chapter delivers. The strong version: a core derivation in five steps, resting on an analytically true P, with both the argument for P and its costs on record. The middle version: its mechanism of takeover, premised on assertion requiring individuation and individuation requiring contrast, which are harder to deny than P. The weak version: the record of the chapters, with two examples demonstrating the inference at work in its original setting. It also delivers a table comparing three proofs in one chain: Qingmu in the original setting, Part I's partial extraction, and this chapter's universal extraction. This book's position is that the case for analytic truth succeeds and T-strong holds at analytic strength. Final judgment awaits Chapter 7's examination of all failure modes, and the verdict is delivered in Chapter 9. Chapter 5 first handles the blow aimed by the theorem at itself.

A plain-language restatement follows, under the same rule as before: change only the language and add no content. Where the two diverge, the upper half governs.

This chapter does just one job: prove the strongest proposition. The proof rests on one premise. To say clearly what makes a thing itself, there is no getting around other things. Called the relational premise, it is established in three steps. First, a sentence that excludes nothing says nothing. To say what x is draws a boundary, and a boundary needs an outside. Second, identity and difference are a pair. Take one without the other and you can keep neither. Recognising a thing means separating it from what is not that thing. Third, the ancients said it for us: "There is other because there is self." Self and other are a pair of terms that stand only by depending on one another. So this premise comes from conceptual grammar, not observation reports. Anyone who uses the term "identity" has already taken difference along with it. Even if only one thing remained in the world, the premise would not loosen its grip. Saying what it is still draws a line against what it is not. Besides, the opponent is not speaking in a world with only one thing. In 各住自性, "each abides in its own intrinsic nature," the very first character, 各, means "each." A collection of things, each holding its own, was always holding it in contrast with the others.

Here is the opponent's hardest move. You say that recognising things requires comparison; we say that things are there on their own. Needing relations to recognise is not the same as needing relations to be. Separating recognising from being opens an elegant gap. Saṃghabhadra guards it. To judge something really existent, he asks whether it can give rise to cognition. The recognition side is all relations. He then turns around and says that the dharma's entity abides in itself, depending on nothing else.

Close the gap by starting from saying, not recognising. Identity conditions say what a thing relies on to count as itself, not how we go about recognising it. Very well, what content could a determination have if it involved nothing else at all? It cannot say that x is such-and-such, because such-and-such sorts things into classes, and classification compares. It has only "x is x" left. But that sentence holds of anything, separates nothing, and cannot do the job of an identity condition. Only two paths remain. If the determination has content, it involves something else and collides directly with the first condition of intrinsic nature, not relying on anything else. If it has no content, then saying there is a bearer of intrinsic nature has specified nothing at all and does not count as a claim. The first path gives the strongest version the contradiction it needs. The second belongs to the middle version. Saying there is an essence that cannot be said is still a sentence spoken aloud. Plant a small flag here for Chapter 8. If someone really stands in their own right and must introduce themselves, the only thing left to say is "I am I." The two paths above have exhausted the reasons why only that sentence remains.

Someone may ask whether this is just logical positivism, saying that what cannot be verified is meaningless. It is not the same. We require only that a sentence exclude something to have content, not that the excluded circumstances be testable. Only one thing is really needed: the opponent's claim must be a statement with content. The opponent has supplied that already. They classify, state theses, refute one another, and pass judgments. Two hundred fascicles of argument are evidence that their words have content. Retreat to inexpressible mystery, and what they leave is the arena of reason. The entry at the end of Chapter 2 awaits them.

One word needs grading here: 待, "dependence." It has three levels. At the narrowest, waiting for conditions to produce something counts as dependence. At the broadest, needing contrast to speak counts too. The middle level matters most. Long depends on short, this on that. A thing counts as this sort of thing only through what stands opposite it. The old commentator's examples beside "not constituted in dependence on other dharmas" belong to this middle level, long and short, this and that. The opponent's own inventory expels this entire middle category from the ranks of solid existence. The Sanskrit verse lists being unmade and being independent as two requirements, so dependence cannot mean just being produced. The dependence refused in "not constituted in dependence on other dharmas" therefore includes at least the middle level. Both sides knew this already; it is not a premise we have added. Our premise needs only this middle level too. A determinate nature depends, at least as a type, on what it excludes in order to be determinate.

One more step closes things in. Independence itself is the property of relying on nothing else. Taken literally, the sentence cannot be completed without bringing in every other thing. What stands by not relying is precisely what relies most on contrast to stand. The opponent therefore has only four paths. Take independence itself as one's nature, and it cancels itself. Offer some other determinate nature, and determinacy requires contrast, producing the collision. Say the thing's identity is primitive, constituted by nothing, but continue to state this all the same. Or insist that its nature cannot be said, depriving the claim of content and passing it to the middle version; that entry belongs to the middle version and is not counted toward the strongest. The third path needs its own reply. If this primitive identity is being used to distinguish a from b, ask what makes a's primitive identity and b's primitive identity two. Appeal to a and b and we have gone in a circle, since this was supposed to explain their difference. Say that the two identities are primitively different and difference stands at the base alongside identity. Both sides already place identity and difference among things that depend on one another. Primitive does not mean unsayable. This path cannot be passed to the middle version; it needs an answer on the spot. The angle of the question matters. It goes beyond how the words "this one" came about and asks directly what makes the thing itself this one. Four paths, each recorded under its own name.

The derivation itself takes just three steps. First, suppose such a thing exists, solidly there and constituting itself. Second, to make its identity clear requires difference. That is the premise. Third, constituting itself forbids dependence on difference. That is intrinsic nature's first condition. Dependence is both required and forbidden, a direct collision. This is the strongest version. If the opponent jumps out halfway through, saying that my essence cannot be stated but nevertheless exists, the middle version takes over. To speak of it, you must first pick it out from everything else. Picking out requires comparison, while your words say it owes nothing to comparison. What you do fights with what you say. The weakest version was there all along. The chapters refute candidates one by one with the same inference. A single sentence states it: Definition requires identity and difference; intrinsic nature cancels identity and difference; hence contradiction. For someone who asserts, change one word and the same holds: assertion requires identity and difference, intrinsic nature cancels identity and difference, and hence the assertion defeats itself. This is what the whole Mūlamadhyamakakārikā is saying. Once difference is cancelled, identity idles too. All a self-existent being can say to itself is "I am I." This is the place marked earlier.

Two examples show the inference at work. First, walking. There is no present walking on a road already walked, nor on one not yet walked. The stretch now being walked is half already walked and half not yet walked, with no room for an entire present walking either. This is not saying that nobody walks. It asks where the goer who is a goer by nature can be found. Say the goer is going, and going has been counted twice. Strip going from the goer, and why should what remains still be called a goer? The goer is a goer through going; going can occur only through a goer. The two sides constitute one another. A solid goer constituting itself cannot stand, while a goer identified through relations walks perfectly well. Farmers still go to market, and postmen still deliver letters.

Take a moment to lay out the proofs we already have. There are actually three in this book. Qingmu's, refuting the four ways of being born one by one, is the inference at work in its original place. The modern reconstruction in the Madhyamaka essay in Part I, the dilemma between agent and action, extracts it halfway. When it reaches the point where the agent's causal capacity follows conditions and is not the agent's own, it has already touched the edge of our premise. This chapter's proof extracts the whole inference as conceptual grammar, covering all claims of this kind at once. These are not three separate inferences but three stages of extracting the same one, with each link citing another. The proof in Part I expressly cites Qingmu's four alternatives as a lemma. Our proof makes the shared principle of the first two a premise. Part I drew the outline then; this essay casts that outline as a theorem. The arch joining the two parts closes here.

Second, causes. What counts as a condition? Once the effect comes about, we look back and recognise something as its condition. Before that, water and earth are just water and earth. The effect gives the condition its identity. A condition that constitutes itself and owes nothing to the effect cannot be a condition. Ordinary causation loses nothing; those who sow still harvest. The joint left by Essay 16 closes here.

To finish the handover, the strongest version has been proved, resting on the premise's being a matter of conceptual grammar. The middle version stands ready. Its resources are that speaking requires picking out a subject and picking out requires comparison, which are harder to deny than the premise. The weakest version is the original work's record. This book's position is that the premise holds and the strongest version holds at analytic strength. Final judgment waits for Chapter 7 to bring every conceivable gap before the court; Chapter 9 delivers the verdict. The next chapter first wards off the returning blow. What happens when this proposition turns its blade on itself?

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