Chapter 1　The proposition¶

This chapter lays out all the foundations the essay needs: three definitions, one proposition at three strengths, and three supplementary clauses governing scope, the limits of definition, and weakening. It states these without proving them. The main proof comes in Chapter 4, the documentary warrant for the definitions in Chapter 2, and the logical tools in Chapter 3. Only five symbols need to be learned here: ∃ (the existential quantifier), ∧ (conjunction), ¬ (negation), → (implication), and ⊥ (contradiction). Every numbered definition and proposition has a fully symbolic counterpart in Appendix A.

A word on procedure. None of the following definitions is this book's invention. The criteria for real existence come from the Sarvāstivāda and Saṃghabhadra, and the three conditions for intrinsic nature come from the "Examination of Existence and Nonexistence" in the Mūlamadhyamakakārikā. Chapter 2 supplies the original wording. A proof can have force only if its target is something the opponent has established.

D1 (three senses of existence). This essay distinguishes three senses of the word "existence," designated E1, E2, and E3.

E1, quantificational existence. To say that x exists is simply to say that the domain under discussion contains an x satisfying a given description. "There is a tree on the hill" and "The equation has two real roots" are E1 assertions.

E2, designated existence. Names and conventions individuate x; a network of designation supplies its identity conditions. Wednesday, a national border, and an army are standard examples of E2.

E3, real existence. The existence of x does not depend on names or on the course taken by analysis. We use the opponents' own two criteria. The Sarvāstivāda test asks whether something falls apart under decomposition and analysis. What does is nominally existent; what does not is really existent, as established in Essay 15, Chapter 1. Saṃghabhadra's test takes what can give rise to cognition as its object to be really existent.¹ These criteria serve different purposes. The first provides a testing procedure; the second, an identifying mark. They need not coincide. The proof in this essay requires only one thing: that the opponent acknowledge some x as really existent by a criterion that the opponent accepts.

D2 (an ontological entity). x is an ontological entity if and only if x has intrinsic nature. Following the "Examination of Existence and Nonexistence," we specify three conditions for intrinsic nature.² First, it is not constituted in dependence on other dharmas. For x to be x, it depends on nothing different from x. Second, it does not change with conditions. As conditions shift, x does not alter with them. Third, it is not produced by conditions. Causes and conditions do not bring x into being. These are not three parallel requirements. The first is the root; the other two are its manifestations in the directions of change and origin. This connection will be used in the derivation in Chapter 4. For the correspondence between these three conditions and modern accounts of intrinsic nature, see Westerhoff's dedicated discussion.³ The formal comparison comes in Chapter 2. Below, D2(x) means that x satisfies this definition.

D3 (scope of application). The metaphysical propositions addressed in this essay are all assertions of the form ∃x[E3(x) ∧ D2(x)]. They assert that at least one thing both really exists by the opponent's own criterion and has intrinsic nature satisfying all three conditions. Three scope clauses apply. Existence assertions in ordinary and scientific discourse that belong to E1 or E2 are entirely outside the scope. Mathematical objects are also outside it unless given an E3 reading. The essay never targets existence assertions as such. Its target is solely the combination of real existence and intrinsic nature.

The limits of definition. Thus far, the definitions have used such terms as identity, difference, dependence, and change without defining them. This is no oversight. Definition must stop somewhere, or the regress never ends. This essay makes its stopping points explicit in three classes. First, logical constants. Identity and difference receive rules, not definitions. Chapter 3 states Leibniz's law and the limits of its use. Any definition of identity and difference would have to use them covertly in the defining formula. Second, reducible terms. Change is not introduced as another primitive. For x to change is for x to differ across conditions or times. Change reduces to difference across indices; this is the reading used in the second condition of D2. Third, terms for which the opponent takes responsibility. Dependence, constitution, and production are terms the opponent uses to state a position, and this essay uses them as the opponent does. That is precisely what licenses a reductio: use your terms, in your way, to derive your contradiction. If the opponent claims that these terms can be given no use, the first thesis to lose its content is the opponent's own.

One final distinction must be explicit. Identity and difference as used here at the meta level are comparisons within a framework for some domain. There is no logical problem with them. The identity and difference the ontologist requires are comparisons independent of any framework. The latter are not among this essay's undefined terms. They are precisely what Chapter 4 will prove unavailable. A related question needs an immediate answer. If the essay allows identity and difference as primitives, why not allow an individual's numerical identity as a primitive? The answer concerns levels, not preferences. Our identity and difference are tools for work at the meta level. Clause (b) in Chapter 5 puts them, together with logic, on the inventory of resources, expressly stating that they are not posited as E3 items. They are used, not posited. The opponent wants an object-level posit and expressly asserts its real existence. Further, this essay has no dispute whatever with primitive individual identity within a framework. That belongs to E1 and E2 and is outside the scope. Only identity independent of any framework is at issue. It is the same thing as identity and difference independent of any framework, and Chapter 4 handles them together. This boundary is explicit from the outset, not drawn ad hoc to ward off a particular opponent.

T (the central proposition at three strengths). T-strong, the semantic version. Any D3-type proposition, together with the definitions and a relational premise P, entails ⊥. The content and status of P are the subject of Chapter 4. Here we merely register it: the identity conditions of any existent necessarily involve difference and relations. T-middle, the assertion version. Any act of asserting or arguing for a D3-type proposition must use the relational resources of causation, cognition, and reference, while the proposition's content declares precisely these resources inapplicable to the x asserted. The contradiction is between the act of assertion and the proposition's content, not inside the proposition. T-weak, the exhaustive version. Each kind of really existing ontological entity actually proposed is subjected, one by one, to reductio. T-weak is not a universal proposition. It is a programme together with a body of existing results, whose original record is the twenty-seven chapters of the Mūlamadhyamakakārikā. Each version has a different quantifier. T-strong governs all possible D3 propositions; T-middle, all asserted D3 propositions; T-weak, all D3 propositions already proposed. Their strength declines in that order, as do their required premises.

Two readings of self-contradiction. Calling a proposition self-contradictory can mean two different things. On the semantic reading, its content, together with the relevant definitions and analytically true premises, entails ⊥. T-strong uses this reading, so its standing depends on whether P is analytically true. On the assertion reading, the proposition's content need not itself generate a contradiction, but the act of asserting it presupposes what it denies. Someone loudly declaring "I am not speaking at this moment" exemplifies this structure. T-middle uses this reading. Keeping the two readings separate is a basic measure in Chapter 7's tests of failure modes.

The weakening clause. The aim is to carry T-strong as far as it can defensibly go. If P cannot retain the status of an analytic truth, T-strong falls back to T-middle. If universality at the level of assertion cannot be maintained either, we retreat to T-weak. Let the clause stand formally here. There are three exits, and reaching any one yields a positive result for the essay. Weakening is not failure. The proof that a weaker version is required identifies the exact level at which this kind of metaphysical assertion breaks down.

What this chapter leaves undone. It gives no proof, which is Chapter 4's task; supplies no documentary warrant, which is Chapter 2's; prepares no tools, which is Chapter 3's; and does not discuss what remains of the world once the theorem holds, which is the task of Chapters 6 and 9. Starting with the next chapter, the chain tightens link by link.

What follows restates this chapter. Only the language changes; no content is added. Wherever it diverges from the upper half, the upper half governs.

Start with three kinds of existence. The first is the most ordinary. Saying there is a tree on the hill or that this equation has two solutions is taking an inventory. What can be counted in counts as existing. Call this E1. The second is established by convention. Wednesday, a national border, an army: their existence rests on a network of names and rules. How the network is woven determines what counts as one of these things. Call this E2. The third is something only philosophers have a use for. It depends neither on the framework of an inventory nor on a network of conventions; it is solidly there in its own right. What qualifies for this third kind? The book invents no standard but uses the opponent's. The Sarvāstivāda test is decomposition. Take the candidate apart layer by layer. What cannot be broken up at the end counts as really existent; what falls apart counts as nominally existent. Saṃghabhadra's mark is its capacity to give rise to cognition by serving independently as an object. Call this E3.

Next, an ontological entity. For a thing to count as one, it must have intrinsic nature, and intrinsic nature must meet three conditions. It does not rely on anything else to constitute itself; however surrounding conditions change, it does not change with them; and it has not been produced. Of the three, the first is the root. The other two are the same thing viewed in the directions of change and origin.

Next, who comes within this essay's reach? Only one kind of statement: that the world contains at least one thing which both solidly exists in the E3 sense and meets all three conditions for intrinsic nature. Tables and chairs are outside its remit, as are electrons, quarks, and numbers. Ordinary and scientific discourse carry on. Only that double combination falls within its reach: solidly existing and constituting itself.

We still need to say where definitions stop. Definitions need an endpoint, or we would go on defining forever. Here they stop in three places. First come basic logical terms such as identity and difference. They receive rules rather than definitions, just as in chess we give the moves for each piece without defining what a piece is. To define identity and difference, we would have to smuggle them into the definitions. Second come words we can do without. Change is not a new term. Compare again under another condition or at another time; finding a difference is what we call change. So "not changing with conditions," one of the three conditions for intrinsic nature, still uses the word "difference." Third come the opponent's own words. Dependence, constitution, and production are words the opponent uses in arguing a case. We take them up in that use. This is what licenses reductio as a form of proof: using your words as you use them to derive your contradiction. If you say those words cannot be made clear, the first thing left unclear is your own position.

One more point matters. We always compare identity and difference within some framework, which poses no problem. The ontologist wants a comparison that relies on no framework at all. What this lacks is not a definition. Chapter 4 will show that it is simply unavailable. Someone is bound to ask why we may treat identity and difference as undefined basic terms while denying the opponent that option for a thing's numerical identity. The answer is a matter of levels. Our identity and difference are working tools. Chapter 5 will put them on the inventory of resources alongside logic, explicitly saying that we use these tools without crediting them with solid existence in their own right. What the opponent wants is something set in the world, explicitly asserted to exist solidly there. Besides, we never dispute whether identity within a framework is primitive. That belongs to the first two kinds of existence and has always been outside this essay's remit. Only the kind independent of any framework is at issue. It is the same matter as identity and difference independent of a framework, and Chapter 4 deals with both. This line is visible from the outset, not hastily drawn to fend someone off.

Now for the central proposition's three strengths. The strongest says that this kind of double claim simply cannot be coherently written, like a square circle. Set out the meanings of the words and one premise about identity, and the contradiction appears by itself. This version stands or falls with that premise's truth purely by virtue of meaning, which Chapter 4 addresses directly. The middle version steps back half a pace. Perhaps the statement itself has no fault, but anyone who asserts it or argues for it must take the relational routes of causation, cognition, and reference. The statement's content declares all those routes inapplicable to the very thing it speaks of. Speaking clashes with what is said, like someone shouting "I am not speaking at this moment." The weakest version offers no guarantee. Refute each candidate as it arrives, and stop when it has been refuted. This is the work done in the twenty-seven chapters of the Mūlamadhyamakakārikā. The three versions cover successively smaller domains: everything that could possibly be said, everything actually asserted, and everything already proposed.

Finally, the weakening clause, which is also the essay's honesty clause. Aim for the strongest version. If the premise cannot retain its truth purely by virtue of meaning, fall back to the middle version. If the middle version's universality cannot hold either, fall back to reductio case by case. Whichever version we reach counts as a result. Finding the exact level at which these claims fail is itself a gain. Chapter 7 lays out every anticipated gap for self-examination. Chapter 8 takes the tools outside Buddhism for a trial application. Chapter 9 gives the verdict.

The next chapter first checks one thing. Are these definitions the opponents' own?

References¶