Chapter 7: Does It Go Through¶

The self-audit. The rule of procedure comes first, and it is the demanding one the author has set for the whole part: push the strong version as far as it can be defended, and mark honestly the step at which it stops; if a hole is genuinely found, that too counts as a gain, and if none is found, then that is rather fine. This chapter proceeds accordingly. Each failure mode that can be anticipated is brought on in its strongest form; if it breaks through, a demotion is recorded, and if it does not, what the exchange has newly brought into view is recorded instead. When the four modes have been gone through, the dialetheist reading is met face to face, and at the end a draft verdict is prepared for each of the three exits.

Failure mode one: the worry that the two cannot be kept apart. The strongest form of the charge is not a rehearsal of the distinction between epistemic and ontic dependence, which was dealt with in Chapter 4; it is the retreat to the last line: determinacy owes nothing to statement. A thing may simply be this one, and its being this one may be constituted by no statable condition at all — medieval scholasticism coined a term of its own for it, thisness (haecceitas). If that route goes through, P loses its standing as an analytic truth and the strong version demotes. The first step of the reply stands as before: the word thisness cannot itself bear the claim made with it, since this one is a contrastive term by birth, and to point at all is already to take one out of many; a this one that could have no that one over against it has singled nothing out. The concept of thisness is introduced by means of the very contrast it denies.

A shortcut that has to be refused. At the second step there is a way that looks like a saving of labour, and it has to be refused on the spot: when the opponent retreats once more and says that the introduction of the concept is contrastive while the property the concept names is itself primitive, to answer that this step has taken him out of statement altogether and so beyond the reach of D3. Primitive does not entail unstatable. To take identity as a primitive is a position with content, and it has consequences, the most conspicuous being that the identity of indiscernibles fails; the modern literature has built a model for it, two spheres alike in every property and two in number. It has a literature defending it and a literature refuting it.¹ To enter it as a mute realism is to enter an opponent who speaks as one who does not, and the shortcut therefore fails. The first step of the reply reaches only as far as the procedure by which the word is introduced, a layer the opponent may legitimately set aside; the second step must begin afresh and answer the position head-on.

Two retreats to be kept apart. The retreat to the primitive and the retreat to the unstatable are two different retreats, and Chapter 4, in the passage on one turn further, has already set them out as four routes. He who retreats to the unstatable loses the determination of his D3 claim, passes to T-middle and the thesis-domain clause, and is taken over by the middle version; that route needs no further discussion. He who retreats to the primitive while continuing to state it is the real opponent of this mode, and the answer comes in three parts.

First: how the primitive itself gets individuated. The question of Chapter 4 comes down to earth here: the thisness of A and the thisness of B, in virtue of what do they differ? In virtue of their bearers, and the account is circular, thisness having been posited to account for A and B differing in the first place; primitively, and difference now stands at the ground floor alongside sameness, while one and different, by the grading of Chapter 4, stand squarely within the family of mutually dependent terms that both parties acknowledge. Either way this primitive is set back into relativity, and relativity is exactly the level the first condition of D2 refuses. The difference between this answer and the first step matters: the first step speaks of a word, this answer speaks of what makes the posited item this one.

Second: thisness has a party to this very dispute. The fifth of the six Vaiśeṣika categories, difference (viśeṣa), is primitive thisness itself. It resides in the eternal substances — the atoms of earth, water, fire and air, together with ether, time, space, self and mind, one to each — and it has one office, to tell apart atoms that are partless and alike in every property, without which the atomism does not stand. Xuanzang's rendering gives it a definition of one sentence: it is permanent, it operates in substances, it resides in a single substance, and it is the cause of the cognition that excludes that one and the cause of the cognition that presents this one.² The first three items register its standing; the whole of the substance lies in the last, and the last is a pair of acts, excluding that and presenting this. The word that matters is that. Piṅgala, expounding not dependent on what is other for its establishment, offers as his own foil precisely long and short, that and this, which have no fixed nature and are had only in dependence on another; and the chapter on time enters one and different in the family of mutually dependent terms. In defining the most fundamental primitive he has, the opponent used a word out of that same family, and gave no alternative account free of that. The Sanskrit side runs the same way: it differentiates of itself (svato-vyāvartaka), differentiating what it resides in and differentiating itself, differentiation terminating there without further regress. This is not a proof; it is a record. The one school that made thisness a category of its own, having every opportunity to give it a non-contrastive specification, gave a contrastive one, and gave only that. The list of the six categories and its symmetry with the Sarvāstivāda catalogue are already on record in Part I, Chapter 3, section 6; the case has been in this book all along.

Third: the Sarvāstivādin is no haecceitist, and cannot become one. The Sarvāstivādin individuates a dharma by its own mark: obstruction is the definition of form, feeling is the definition of sensation, and the skandha-by-skandha catechism of the Vibhāṣā is on record in Part II, Chapter 15, section 3. If numerical identity were primitive and non-qualitative, the own mark would descend from being the identity condition of the dharma-substance to being one attendant property among others, and the whole catalogue of seventy-five dharmas in five classes would lose its ground of individuation. What the Sarvāstivādin needs is that form is form in virtue of obstruction. The posit brought in to save the first condition of D2 cancels the very work that own-being was set up to do.

Audit product one, re-derived from E3. A bare thisness with no own mark cannot pass E3: Saṅghabhadra's criterion is that a cognition arises upon it without dependence on anything else, his positive cases being form and feeling and his negative cases the pot and the army, and the whole criterion rests upon the own mark; the criterion of analytical dissection has no mark to work upon and comes up empty. So bare thisness falls outside the range of the theorem for a reason internal to D1: by the opponent's own criteria it does not count as really existent. The conclusion is unchanged, the range of the quantifier in T-strong still being settled as all D3-type claims; the road to it has been replaced, and the new road owes nothing to the step refused above.

Finding and remainder. What the strong version collects is the haecceitist who gives thisness an office: once his primitive takes up the work of telling A from B, it falls back into relativity. Should anyone hold that identity facts come first and difference facts supervene upon them, and say no more than that, then he is taken over by the route through E3 and the route through T-middle, and not by the semantic collision of T-strong; that entry stays with the middle version. Mode one causes no demotion, but it forces a correction in the bookkeeping: from here on the gains of the strong and the middle versions are entered separately, the credit of the strong version being confined to the axis of dependence and the domain of conditions, with the remainder assigned to the middle version, and no single gain wagered on two accounts at once.

Failure mode two: the suspicion of a realism about relations. The charge: P is full of difference and relation, and you have merely handed the throne of substance over to relations; if relations are really existent, it is the same medicine in a new broth, and if relations too are empty, does not P destroy itself? Reply. First, P is a claim about determination: a statement of identity conditions must necessarily draw on relational vocabulary. It does not claim that relations are E3 items. Second, that relations too are empty is no patch of convenience but the natural extension of the same lever: a relation standing on its own without depending on its two terms could reach neither of them, as the difference horn of Chapter 3 proved; a relation possessed of intrinsic nature is no relation at all. So relations fall entirely at the E2 level, and relations at the E2 level are precisely all that P requires: determination, framework, vocabulary. Third, the deeper misgiving, which must be reckoned up: if individuation depends throughout on frameworks, has idealism been smuggled across? Answer: that individuation is framework-relative does not amount to things depending on mind; a framework is a public practice, not a private consciousness. As for the question of what, after all, stands behind the framework, it asks after an E3 item; the question itself falls within the scope and is rejected under the rule. Fourth, the charge pressed to its tightest notch: P says that identity conditions must involve relations, and the reply just given assigns relations wholly to the E2 level; put the two together, and does it not follow that anything's being what it is passes through the network of names and conventions, so that E3 is sealed off in advance against every candidate, and the promise of the range clause (that this part never attacks assertions of existence as such) falls to the ground? A boundary marker is driven in here: this part sets up no transfer from the level of conditions to the level of existence. That identity conditions involve relations at the level of names and conventions is a fact about determination; whether some thing is established in dependence on names and conventions is a matter for the E3 test, decided by the two criteria of surviving analysis and of generating a cognition by being an object, and not decided by the vocabulary its determination happens to employ. There is no bridge between the two levels, and this part has not once crossed one: the conclusion of the theorem is everywhere that a conjunctive claim destroys itself, and nowhere that some thing does not exist. The symmetrical question that follows is the crux: since we deny that transfer, why may the opponent not use the same denial to fend off the core derivation? The answer lies in the structure: the core derivation contains no step of transfer to be denied. The first condition of D2 itself stands at the level of conditions (not established in dependence on anything other than itself says that its being what it is depends on nothing else), and what P says is a must-depend at that very same level. The oath and the conceptual grammar collide at one and the same level, and the contradiction requires no carriage across levels. Should the opponent rewrite the oath onto the level of existence to avoid the collision, the first condition is thereby abandoned and what he posits is no longer intrinsic nature in the sense of D2, so that by the range clause this part has no quarrel with him; and as for a candidate who declares that in its own case the two levels were one level all along, the simplicity clause is waiting at route one of Chapter 8. Finding: mode two causes no demotion, and it yields a proof in return — that relations too are empty is compelled by the lever itself, and was not devised in order to rescue P.

Failure mode three: the doubt about the inductive leap. The charge: the twenty-seven chapters are a finite sample, and the jump from twenty-seven reductios to all D3-type claims is induction, not proof. Reply: the doubt mistakes the architecture of this part. The strong version rests not on an enumeration of cases but on the analytic argument of Chapter 4; the conflict between P and the first condition of D2 is derived from the concepts, and its universal force comes from conceptual grammar and not from the number of samples. The standing of the chapters is that of demonstration and re-check: the lever runs in place at each historical site, which is corroboration and not premise. The text's own universal sentence — there has never been a single dharma that does not arise from causes and conditions (cited in Chapter 6) — is likewise used here only as a record of textual intent, and not as a premise of the argument. There is only one place where a gap might really open: some candidate claiming the full strength of D2 and yet escaping the derivation. But the derivation used only the first condition of D2 and P, and both are universal conceptual truths; the only road of escape left is to deny that one is bound by identity conditions at all, which falls back into the remainder of mode one and has been dealt with already. Finding: mode three dissolves; between the weak version and the strong there is no induction, but only analysis together with its historical corroboration.

Failure mode four: the status of the truth predicate. The charge: if everything is conventional designation, then true is a conventional designation too; is your theorem true or is it not? This is the deepest of the four. The reply goes by layers. Truth at the everyday level is settled within a framework (to speak by conventional reasoning of there being a pot and the like is real and not false), and both parties grant it, so that no defence is called for. The truth of the theorem is an analytic truth, and its framework is conceptual grammar and logic themselves. This framework has one property that no other framework has: it admits of no replacement. Any framework that can individuate, can assert, and can reason is already using same and different, and within it the lever is in force. So the truth of the theorem is not a truth looked down upon from nowhere, but a truth there is no escaping inside each and every framework; and with this the final formalization of ultimate truth is obtained — not a higher domain of objects, but the invariant of all frameworks. Chapter 6 said that what the two truths divide is levels of assertion; this chapter supplies the other half of the sentence: conventional truth is truth within a framework, ultimate truth is the invariant truth across all frameworks. One reflexive difficulty must be settled here along with the rest: if the theorem is true in every framework, does it not exclude nothing, and therefore, by this part's own principle that content is exclusion, say nothing at all? To resolve it, three dimensions and two kinds of saying nothing must be distinguished. Exclusion has three objects: situations, frameworks, claims. In the dimension of frameworks the theorem does indeed eliminate nothing, and that is what being an invariant means; but the law of non-contradiction eliminates no workable framework either, and no one says on that account that the law of non-contradiction says nothing, because the normative work is done in the dimension of claims. Within every framework the theorem forbids a family of assertions that were actually put forward, and closes off a stretch of country that stood genuinely open in epistemic terms; two hundred fascicles of the history of debate are the surviving evidence that the country once stood open. As for the silence in the dimension of situations, two kinds of saying nothing must be told apart. The theorem's saying nothing is the duty of its office: a meta-constraint is employed to issue rules and is not employed to describe situations, just as the law of non-contradiction has nothing to say about situations. The saying nothing of the intrinsic-nature theorist's sentence x is x is dereliction of office: an identity condition is employed to separate x from what is not x, and this one separates nothing whatever. The criterion in one sentence: what says nothing and cannot be discarded is a rule; what says nothing and can be discarded is idle talk. Cannot be discarded means that to discard it is to lose the framework, and what cannot be discarded is, strictly, the working parts the theorem names (same and different, individuation, the law of non-contradiction) on which the opponent's own framework has always run, which is exactly the charge the assertoric version brought in its day. Can be discarded means that the framework runs on once it is gone, and the essence clause is precisely such a discardable part, as direction (a) of the Preservation Theorem demonstrated on the spot. The two silences are separated by two offices and two examination papers, and the opponent has no way to borrow the silence proper to the level of rules to stand in for his own idling. As for anyone who would enshrine truth as an E3 item (truth in itself, correspondence with the real, and the like), clause (c) of Chapter 5 is waiting: a reified truth falls within the scope and is handled under the rule. Finding: mode four causes no demotion, and the second audit product is the statement of the invariant just given.

The interlocutor: dialetheism. Priest and Garfield, and the line that reads the Mūlamadhyamakakārikā with them, hold that there are true contradictions at the limits of thought: to say what cannot be said is a case in point, and Nāgārjuna was a forerunner of that discovery.³ This part honours the reading as an opponent who argues, and the pressure it has seen is real: a statement about a limit seems obliged to cross the limit. The disagreement is over the solution. They solve it with true contradictions, at the cost of taming explosion and redefining negation, which is a major overhaul of the logical machinery; this part solves it by levels, with the hierarchy clause plus typed rejection, and the machinery is left untouched. Two reasons support the conservative case. Cost: with the presupposition-cancellation reading in hand, not one verse compels us to accept a true contradiction, and the third limb of the tetralemma is throughout an object of rejection and never an asserted truth. Text: the sorting by closing formula (Chapter 3) shows that the refutative family of tetralemmas closes with a rejection and the pedagogical family closes by fitting the teaching to the hearer, and that neither family closes by holding a contradiction true. Hence the position of this book: the conservative case is established as the correct reading, and the dialetheist reading is entered as a complete alternative scheme held in reserve — should the method of levels give way at some point, the line of retreat is ready-made; no such point has been seen to this day. A line must also be drawn clearly: dialetheism is a logical proposal bound by norms, and has nothing to do with the door of Chapter 2 by which logic is rejected outright. It belongs among those who argue: an opponent, not a deserter.⁴

The three exits, and the draft verdicts. Exit one, established as analytic: the four modes have been tested through and not one of them has forced a demotion; the strong version stands at the strength of an analytic truth, its field of engagement being the axis of dependence acknowledged by both parties and the domain of conditions, with the remainder cases entered separately under the middle version (mode one), and three audit products appended: the settling of the domain of theses, the statement of the invariant, and the result gathered in Chapter 4 that independence is itself a relative property. Exit two, demotion to a priori truth: the trigger would be someone's exhibiting a non-contrastive individuation, and this chapter has been unable to construct such an exhibit, since the very description of one is obliged to use contrast; for the present this exit has no entrance. Exit three, demotion to an empirical generalization: it requires that both of the first two fail, and it lies further off still. This book holds that the verdict falls at exit one; the formal announcement, together with the premise audit table, belongs to Chapter 9. The author's keynote is settled here as follows: holes were looked for in earnest and one was found and closed on the spot (failure mode one), the repair being harder than the reply it replaced; and besides that, three things clearer than had been expected.

What this chapter hands in. The findings on the four failure modes; one self-audit correction; three audit products; the record of the exchange with dialetheism and its standing as a reserve; the draft verdicts for the three exits. Chapter 8 takes the theorem out of doors and tries its edge beyond the field; Chapter 9 convenes the court and pronounces.

[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.]

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