Chapter 1: The Proposition¶

This chapter lays the foundation of the whole part at one go: three definitions, one proposition in three strengths, and three further clauses covering the range, the boundary of the definitions, and demotion. The chapter states and does not prove. The body of the proof stands in Chapter 4, the provenance of the definitions is redeemed in Chapter 2, and the logical tools used along the way are forged in Chapter 3. The reader has only five symbols to take on here: ∃ (the existential quantifier), ∧ (conjunction), ¬ (negation), → (the conditional), and ⊥ (contradiction); for every numbered definition and proposition a fully symbolic form is given as well, in Appendix A.

One word on procedure. Not one of the definitions below is of this book's own devising. The criterion of real existence is taken from the Sarvāstivāda and from Saṅghabhadra; the three conditions of intrinsic nature are taken from MMK 15; and the word-for-word redemption of each against its original is the work of Chapter 2. Only where the target has been set up by the opponents themselves can a proof have any force at all.

D1 (the three senses of existence). This part divides the word existence into three senses, written E1, E2 and E3.

E1, quantificational existence: to say that x exists is to say no more than that in the domain of objects under discussion there is an x answering to such-and-such a description. There is a tree on the hill; the equation has two real roots. Both are E1 assertions.

E2, conventional existence: x is individuated by name and convention, and its identity conditions are given by a network of names and conventions. Wednesday, a national border, an army are the standard samples of E2.

E3, real existence: the existence of x hangs neither on names nor on the route that analysis happens to take. The criterion is taken in the two forms the opponents use themselves. The Sarvāstivāda test: whether a thing breaks up under analysis — what breaks up under analysis is nominally existent, what does not is really existent (established in Part 15, Chapter 1). Saṅghabhadra's mark: whatever is capable of generating a cognition by being an object is really existent.¹ The two criteria divide the labour differently. The first supplies a procedure of testing, the second a mark of adjudication, and the two need not coincide. What the proof of this part requires is one thing only: that the opponent, by the criterion he himself acknowledges, grants some x to be really existent.

D2 (entity). x is an entity if and only if x has intrinsic nature. Intrinsic nature (svabhāva) is fixed by the three conditions of MMK 15.² First, not established in dependence on anything other than itself: what makes x the thing x is does not depend upon anything other than x. Second, not altered as conditions change: conditions come and go, and x does not alter with them. Third, not produced: x is not brought into being by causes and conditions. The three conditions are not three requirements standing side by side. The first is the root, and the other two are what it looks like in the two directions of change and of origin; this relation among them will be used in the derivation of Chapter 4. On the correspondence between the delimitation of the concept of intrinsic nature in modern scholarship and these three conditions, see Westerhoff's chapter on the subject;³ the formal control is drawn up in Chapter 2. In what follows, D2(x) records that x satisfies this definition.

D3 (scope). The metaphysical claims treated in this part are all assertions of the following form: ∃x[E3(x) ∧ D2(x)] — the assertion that there is at least one thing which is both really existent by the opponent's own criterion and possessed of intrinsic nature in the three conditions. Three clauses fix the range. Assertions of existence in ordinary and in scientific discourse, being E1 or E2, are outside the scope without exception. Mathematical objects, unless they are read as E3, are outside the scope likewise. And this part never attacks assertions of existence as such; what it attacks is only the combination of real existence with intrinsic nature.

The boundary of the definitions. Up to this point the definitions have used the words same, different, depend and alter, and these have themselves gone undefined. This is not an oversight. Definition has to stop somewhere, or the retreat is without end; this part makes the stopping point a clause, in three classes. First, logical constants. Same and different are given no definition but only laws (Leibniz's law and the range of its use are settled in Chapter 3), and any definition offered for same and different would have to use same and different covertly within the defining formula. Second, reducible words. Alter is not set up as a further primitive: that x has altered is that x differs between one condition and another or between one moment and another, so that alteration reduces to difference across indices, and it is on this reading that the second condition of D2 is framed. Third, words the opponent carries. Depend, establish and produce are in service in the opponent's own theses, and this part uses them exactly as the opponent uses them; that is precisely where the credential of a reductio lies — your words, used in your way, yield your contradiction. Should the opponent declare that no use can be given for these words at all, the first thing to lose its content is his own thesis. One last distinction has to be said plainly. The same and different this part uses at the meta-level are comparisons drawn within some framework of discourse, and they are logically innocent. The same and different the ontologist needs are comparisons drawn in dependence on no framework whatever. The latter is not listed among the undefined words of this part: it is exactly what Chapter 4 sets out to prove unobtainable. A related question has to be answered on the spot: if this part admits sameness and difference as primitives, why does it refuse to admit the numerical identity of an individual as one? The answer lies in the level, not in preference. The sameness and difference of this part are working tools at the meta-level; clause (b) of Chapter 5 enters them, together with logic, in the inventory of capital and records expressly that no E3 claim is made for them: used, not posited. What the other side wants is an item at the object level, and it is expressly declared to be really existent. Further, primitive individual identity within a framework is nowhere contested here; that is E1 and E2, outside the scope by the scope clause. What is contested is only the framework-free variety, and it is the same thing as framework-free sameness and difference, dealt with together in Chapter 4. This boundary has stood in plain sight since the opening, and was not drawn to keep out any particular opponent.

T (the central proposition, in three strengths). T-strong, the semantic version: any D3-type claim, together with the definitions and one relationality premise P, jointly entail ⊥. The content and the standing of P are the main business of Chapter 4; here its existence is merely registered — whatever exists has identity conditions that necessarily involve difference and relation. T-middle, the assertoric version: any act of asserting a D3-type claim, or of arguing for one, must draw upon relational resources, causal, epistemic and referential, while the content of the claim declares precisely those resources void for the very x asserted; the contradiction lies not inside the proposition but between the act of assertion and the content asserted. T-weak, the exhaustive version: for each kind of real entity with intrinsic nature that has actually been proposed, a reductio one by one. T-weak is not a universal proposition. It is a programme together with a record of engagements, and the twenty-seven chapters of the Mūlamadhyamakakārikā are the primary archive of that record. The quantifiers of the three versions differ throughout: T-strong governs all possible D3-type claims, T-middle all asserted D3-type claims, T-weak all D3-type claims so far proposed. Strength descends along that series, and the premises required descend with it.

The two readings of self-contradictory. To call a claim self-contradictory may mean either of two different things. On the semantic reading, the content of the claim, together with the relevant definitions and premises that are analytic truths, yields ⊥; T-strong uses this reading, and the grade of T-strong therefore hangs on whether P is an analytic truth. On the assertoric reading, the content need not generate a contradiction of itself, but the act of asserting it presupposes the very thing it denies; a man announcing at the top of his voice that he is not speaking at this moment has this structure, and T-middle uses this reading. Holding the two readings apart is the basic gauge used in Chapter 7, where the failure modes are tested.

The demotion clause. The aim of this part is to carry T-strong as far as it can be defended. If P cannot hold the standing of an analytic truth, T-strong demotes to T-middle; if the universality at the level of assertion cannot be held either, the retreat is to T-weak. The clause is formally laid down here: there are three exits, and whichever of them is reached, the outcome is a positive result of this part. Demotion is not failure. The demotion proof itself marks the exact level at which metaphysical assertions of this kind cease to hold.

What this chapter does not do. It does not prove, which is the business of Chapter 4; it does not redeem provenance, which is the business of Chapter 2; it does not forge tools, which is the business of Chapter 3; and it does not discuss what is left of the world once the theorem holds, which is the business of Chapters 6 and 9. From the next chapter on, the chain tightens link by link.

[The Chinese text closes with a restatement of this chapter in plain language — the same content in a different register, the academic half governing wherever the two diverge. That restatement is not yet translated; nothing in the argument is missing from what stands above.]

References¶