This Is Not A Term Paper.

by existential calvinist on 2006年12月14日 11:21 PM

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Mâdhyamika Ontology and the Problem of Ultimate Analysis

Prelude

This is not a term paper. The ink on this paper is not a term paper, because a term paper is an extended series of arguments for some premises, but if ink on paper were a series of arguments, anyone in sensory contact with the ink could know the arguments being made, not merely the literate. What you can read as a literate person is not a term paper, because a term paper is a single coherent document, but this is one sheet of paper in front of one’s face with only part of it in visible focus. The visible portion does not form a term paper, because it is only a few words and thus too short to be a term paper. These many pages together cannot form a term paper, because they cannot be seen at the time without becoming illegible, but a term paper must exist all at once. The many words read all together cannot form a term paper, because they are processed sequentially, but a term paper exists at once. Otherwise, a student would be permitted to say her term paper is complete so soon as she gained the ability to promise more will be available to be read later!

[Qualm]: What if I memorize these many words? Surely then I would remember a term paper.

[Mâdhyamika]: Even still, this is not a term paper, because a term paper is a detailed argument existing at once, but though you can bring any words from the argument or any particular argument from it into recollection, still you cannot recollect the whole at once, and a term paper is not merely recollecting a part, or else a student would be able to recollect a single argument and receive credit for course!

Ink on paper is not a term paper; what is seen is not a term paper; many words are not a term paper; remembering many arguments is not a term paper; being able to recollect any single argument in a series is not a term paper. We have searched for the term paper and have not found it. Therefore, the term paper is an illusion, and this is merely the-experience-of-reading-a-term-paper.

1. Introduction

The preceding argument is a reconstruction of the classic argument known as the Diamond Splinters argument often used in Mâdhyamika philosophy. The form of this argument is familiar to any scholar or religious inquirer acquainted with Mâdhyamika thought, but what it actually means is less than clear. Can arguments of this sort be applied indefinitely? Even to themselves? Does this imply that nothing exists at all? Or is it just a kind of verbal trick the Mâdhyamika perform to help cultivate detachment? Could it be that these arguments only work on one level of reality but not another? And why do these arguments always seem to rely on reductio ad absurdum? Is that a necessary property of the argument? Why? The version of the argument presented here also contains an additional assertion usually absent from the argument (that this is the-experience-of-reading-a-term-paper) whose consequences I shall return to later.

In this experience-of-reading-a-term-paper, I will explore different interpretations of Mâdhyamika in the context of exploring just what sorts of problems any ultimate analysis will encounter. For this exploration, I will first borrow a framework of terminology from Rescher concerning principles that any ultimate theory will need to deal with then explicate the logical possibilities they present. With these possibilities in mind, I will briefly explain Kant’s ontology and method in order to show how they relate to Murti’s analogy of Mâdhyamika philosophy to a Kantian system. Against this, I will present Priest’s investigations of the limits of inquiry and objections concerning the difficulties of dualistic systems, as well as his interpretation of Nâgârjuna, before offering a unified interpretation of the Mâdhyamika argument and its consequences, especially with regard to the nature of illusion.

2. Fundamental principles and possibilities

2.1 Principles

In a chapter entitled “The Price of an Ultimate Theory” in his Nature and Understanding, Nicholas Rescher lists four principles, admittedly not originals, which are commonly implicit in the scientific pursuit of “a Theory of Everything” or TOE. The first principle, which has been formalized since at least Leibniz, is the Principle of Sufficient Reason:

(∀t) (ﾖt′) (t′∑t)

Put into plain English, “for any theory or fact, there exists a higher theory or fact whose explanatory power subsumes the original.” We can explain the fact that apples can be seen falling toward the earth at various times by means of a naive theory of geocentric gravity. With a more sophisticated theory of gravity, we can additionally describe the motions of the sun and the moon as a consequence of the same imputed fact. It is the hope of theoretical physicists today that a further theory will also be able describe gravitational, electrical, and nuclear forces as aspects of the same force. The alternative to the Principle of Sufficient Reason is the possibility that there may be events that are not only without apparent cause but without a hidden cause as well. Naturally, our intuition is distrustful of such a possibility. Some (including Priest) might object that some interpretations of quantum theory violate the Principle of Sufficient Reason. However, even in quantum theory, things happen for a reason, it is just that the reason affects things probabilistically rather than deterministically when extrapolating forward from presently know conditions. In any event, Bell’s theorem only precludes local hidden variables not non-local ones, so determinism can still be potentially be saved by abandoning locality. Of course, the exact parameters of this debate are outside the scope addressed here, so we will leave the issue at that.

Applying the Principle of Sufficient Reason, we naturally suppose there must that by following the chain of reasoning from a fact or theory t to an explaining fact or theory t′ then to an explanation of the explanation t″ and on to the limit of the series, we will at last encounter some ultimate theory or fact, T∗, which explains all prior theories and facts. This intuition is formalized as the Comprehensiveness of T∗:

(∀t) (T∗∑t)

“For all theories or facts, T∗ explains it.” So far so good, but it should be apparent to the reader that a conflict is in the offing. If according to the Principle of Sufficient Reason all theories can be explained, what explains T∗? To be consistent, we must either say that T∗ is only an implicit limit and not actual since the regress is infinite, or T∗ is actual, and T∗ explains itself. We hereby introduce the principle of Finality:

~(ﾖt) ((t∑T∗) & (t ≠ T∗)) or equivalently,
(∀t) ((t∑T∗) → (t = T∗))

“Nothing else can explain T∗. If a fact or theory can explain T∗, then that it is T∗ itself.” Opposing this is the principle of Non-circularity:

~(ﾖt) (t∑t)

“No fact or theory can explain itself.”

2.2 Possibilities

At this point, our intuitions about the possibility of an ultimate theory have reached an impasse. On the one hand, the Principle of Sufficient Reason seems to imply an additional principle of Non-circularity, so that no theory is allowed to justify itself, and thus bring the search for more powerful explanations to a halt prematurely. On the other hand, it seems impossible that there are no bedrock necessary facts which ground all other facts. Thus, the logical possibilities can be categorized like so:

1. There exists a finite number of justifications which satisfy Finality.
- 1a. The ultimate justifications are self-justifying at the cost of circularity.
- 1b. The ultimate justifications have no further justification and violate of the Principle of Sufficient Reason.
2. There is an infinite regress of justification which satisfies Finality.
- 2a. The infinite regress is self-justifying at the cost of circularity.
- 2b. The infinite regress has no further justification and violates of the Principle of Sufficient Reason.
3. There are no ultimate justifications.
4. Things are contradictory.

Worth noting here is that so far, we have allowed epistemology and ontology to be considered interchangeable. It is possible that epistemology conforms to one possibility and ontology another. For example, it might be the case that our empirical explanatory process can continue indefinitely, but there are only a small number of bare facts which secretly undergird reality itself. Or perhaps, what we can know is limited and must halt upon reaching certain theories, but those theories are secretly supported by an infinite regress of further facts that are beyond our ability to know.

Historically, many philosophers have been vague about which of these possibilities they suspect to be the case. Theists generally consider God to be the ultimate reason for everything (or at least, God plus free will), but they have been less clear about whether God constitutes the reason for Himself, or whether God is without further justification (possibility 1a or 1b). Recently, some string theorists and other scientists seem to think a perfected explanation of the Big Bang itself may constitute a brute fact with no possible further explanations, but others propose a “bubble multiverse” in which our universe is the product of an infinite line of prior universes that split off from one another in Big Bang-like events. The determination of which of these possibilities Mâdhyamika analysis entails is the concern of the remainder of this experience-of-reading-a-term-paper, but first a short digression into Kant’s exploration of these possibilties is necessary.

3. Kant

The investigation into the limits of rationality by Immanuel Kant in The Critique of Pure Reason is relevant to the explanation of Mâdhyamika philosophy for two reasons. First, Kant’s dualistic system of phenomenal reality and noumenal reality bears a striking resemblance to the Mâdhyamika system of conventional truth and ultimate truth. Second, the contradictions by reductio ad absurdum that Kant gives in the Antinomies section of the Critique bear a resemblance to the prasaṅgika method of reductio ad absurdum employed by some Mâdhyamika. To begin, we will give an explanation of Kant’s ontological system.

3.1 Ontology

Kant calls his view of fundamental ontology “transcendental idealism” and contrasts it with all preceding views, which he calls “transcendental realism.” Explaining the difference on A369–70 he writes,

By transcendental idealism of all appearances I mean the doctrinal system whereby we regard [appearances], one and all, as mere presentations and not as things in themselves… the transcendental realist conceives outer appearance (if their actuality is granted) as things in themselves that exist independently of us and of our sensibility, and that would therefore be outside us even according to pure concepts of understanding. It is, in fact, this transcendental realist who afterwards plays the empirical idealist. Having wrongly presupposed that if objects of the senses are to be external then they must have their existence in themselves, ie. even apart from the senses, he then finds from this point of view all of our presentations of the senses are insufficient to make the actuality of these objects certain.

The transcendental idealist, on the other hand, can be an empirical realist or, as he is called, a dualist… Hence matter is for him only a kind of presentations (intuition), called external; they are called external not as referring to objects in themselves external, but because they refer perceptions to the space… although the space itself is in us.

In other words, for Kant the tragedy of all prior philosophy had been that philosophers supposed that if there were objectively real things, such things would have to exist independently of the mind, however since by definition the mind cannot know anything that is independent from the mind, it cannot know these real objects. Kant reverses this pattern of thinking. For Kant, to be an objectively real thing is to depend on the mind and its a priori categories. As such, through the application of universal reason, we can give an objectively valid description of the unity which reason is compelled to impute in appearances. Unfortunately, even an objectively real synthesis of appearances cannot be the object in itself, which he also called a noumenon. The synthesis is only an appearance or phenomenon, though no less objective for it. Kant is insistent that we can only “think” the noumena which give rise to phenomena, never cognize or know them. (This, as we shall see, presents problems for Kant later.)

3.2 Method

Kant’s argument for his bifurcated system comes in two main parts: the Transcendental Aesthetic and the Transcendental Logic. In the Transcendental Aesthetic, he argues (somewhat unconvincingly, at least in the view of this author) that the possibility of our experience requires an a priori intuition (in Kant’s sense of intuition as a kind of non-conceptual sense data) of space and time. The Transcendental Logic breaks down into two further systems, the Transcendental Analytic and the Transcendental Dialectic. The Transcendental Analytic continues the exploration of the a priori concepts behind the a priori intuitions of the first section. The Transcendental Dialectic is more interesting. In it, he explores problems inherent with supposing that one can have a coherent system that does not rely on a phenomena/noumena distinction. In particular, in the Antinomies, he gives reductio arguments both for and against the infinity of space, the beginning of time, the infinite divisibility of substance, causation through freedom, and a necessary being. To resolve these contradicting arguments, Kant proposes that the objects under consideration can only be considered to exist as noumena, and hence outside of the a priori categories of our judgments.

In terms of the possibilities listed in the previous section, Kant differentiates between what he calls “mathematical series” and “dynamical series.” (The difference need not concern us here. The distinction mostly seems to exist to serve Kant’s preexisting religious commitments.) We must consider time infinitely long, space infinitely large, and substance infinitely divisible, because they are mathematical series, but we should consider causality through freedom and a necessary being to exist as unified absolutes rather than series, since they are dynamical. In all cases, however, if we try to move beyond the possibility 1 or 2 to determine whether the respective a or b subdivision of the possibility applies (that is, whether the absolute or series is self-justifying or without justification) then we move well beyond phenomenal experience and into the realm of the noumenal, in which such answers are not to be found. And this motion into noumenal is what allows the construction of the paradoxical assertions of the Antinomies. The respective absolutes and infinities of each series are mere epistemic imputation based on the a priori requirements of reason but are nevertheless objectively real, since all reasoning individuals will reach the same result through investigation. Going beyond them, since the noumena are not available as objects of inquiry, we cannot say whether the possibility justifies itself or is without justification. In any event, since the answer is beyond all possibility of experience, for Kant the question is unanswerable by our speculative reason.

So we see that Kant hopes to rescue the final basis for being from contradiction by placing it outside the realm of judgment in a noumenal realm to which the categories of judgement do not apply. Whether this attempt is either successful or relevant to an explanation of Mâdhyamika will next be elucidated further.

4. Murti

In 1955, T. R. V. Murti helped bring Mâdhyamika to the attention of Western philosophy with his seminal The Central Philosophy of Buddhism. Unfortunately, as detailed as this work is, it suffers from the author’s misinterpretation of some subtle points of Mâdhyamika ontology. Murti states on pages 332–333:

His [the Mâdhyamika] position is akin to that of Kant. … The difference between the two… is that Kant seeks to realize these noumenal realities in a non-intellectual mode — Faith and practical Reason; the Mâdhyamika does it in Intellectual Intuition — Prajñâpâramitâ. The Mâdhyamika is spiritual to the core. His absolute is not void, but devoid of finitude and imperfection. It is nothing but Spirit.

In a footnote on 333, he quotes Professor Radhakrishnan approvingly on the topic of shûnyatâ, “To call it being is wrong, only concrete things are. To call it non-being is equally wrong. It is best to avoid all descriptions of it.”

4.1 Mâdhyamika ontology compared with Kant

A Kantian interpretation of the argument in the prelude might be that we do not find the paper in experience, because we are searching for the paper as a thing in itself (noumenon). Our experience of a phenomenal object cannot possess the requisite totality of properties that one would expect of a true thing in itself. Instead, what we do find in experience is the imputation of an objective totality of a term paper that arises from the partial experiences of it. For Kant, this phenomenal imputation is not a subjective illusion, for all beings possessing reason would create the same imputed object (presentation) given the sense data (what Kant calls intuition). Furthermore, it is impossible to suppose that we could be given the totality of experience regarding a phenomenal object, because our experiences are necessarily rooted in space and time, whereas for things in themselves, space and time are merely ideal.

Here, we need to be careful in order to avoid an internal debate within Mâdhyamika. Depending on whom one asks, conventional truth may or may not also be empty of essence. In either event however, it is unlike that the Shantideva who wrote in Bodhicaryâvatâra 9:5, “Ordinary people see and imagine things as real and not illusory. It is in this respect that there is disagreement between the contemplatives and the ordinary people,” would accept the doctrine of empirical realism without first making a distinction about what is being accepted as empirically objective. Remember also that Kant’s method in the Transcendental Aesthetic is to ask, “What are the conditions for the very possibility of our experiencing X?” Such a question consciously presupposes that the X in question is a valid object of inquiry in some sense. The Mâdhyamika project starts with the opposite assumption. Rather than seeing how it is possible that we have come to have mostly correct views, Mâdhyamika is interested in explaining the false views that keep us bound in suffering. For Kant, universal assent to the existence of objects is a mark of their objective reality. For Mâdhyamika, it is a mark of our collective beginningless ignorance. One might argue that this a glass half-full, glass half-empty debate. Kant emphasizes how we having objective knowledge of the phenomenal, and the Mâdhyamika emphasize how we have no objective knowledge of the ultimate. This is a mischaracterization of the Mâdhyamika position. They too see the glass as half-full, but the glass is a glass of poison, not water. For Kant, our reason naturally compels us to accept various arguments, like the cosmological argument for the existence of God, which while not strictly correct, are nevertheless useful for the ordering of our lives according to practical reason. For Mâdhyamika, our reason naturally compels us to an eternity of dissatisfaction, because we mistake illusions for real things. Thus, to be an empirical realist would endanger the entire Bodhisattva path of liberation as a uniquely meaningful pursuit. As Shantideva says in verse 9:6 of the Bodhicaryâvatâra, “Even objects of direct perception, such as form and the like, are established by consensus and not by verifying cognition. That consensus is false…” Ordinary people using reason in a natural manner see objects of experience as real, external things that can be used to assuage craving and bring happiness, whereas the entire point of Buddhism is that things can never bring liberation from suffering. Thus whether objects are conventionally without essence or not, Shantideva would still be loath to admit that objectively speaking things are substantially similar the way the appear to us, since to appearance, things are craving satisfying, but this appearance is the cause of samsara. Even if one were to take Candrakîrti’s seemingly conciliatory remarks in Madhyamakavatara 6:166–7, one finds that they too reflect the same attitude as Shantideva. Candrakîrti’s remarks,

Things such as jugs, cloth, tents, armies, forests, rosaries, trees, houses, trolleys and guest-houses should be understood to exist in the way they are commonly spoken of by people because the Buddha did not argue with the world over these matters. Furthermore by applying the analysis of the cart to part-possessors and their parts, quality-possessors and their qualities, people with attachment and their desires, bases of characteristics and their characteristics and fire and the fuel it burns, one finds that they do not exist in any of the seven ways. But as long as they are not subjected to such analysis, they do exist in another way: namely in terms of their being well known to the world.

At first, it may seem that Candrakîrti is affirming the existence of conventional objects. However, when one carefully studies the sense in which conventional things exist, one sees that it is only in terms of being well known to the world. For Kant, part of what makes things phenomenally real is that they are well known to the world, but phenomenal objects are no less actual things for this, and so long as one does not look for the properties of the thing in itself, one will find the object to be quite real. For Candrakîrti things are well known to the world, but the sage must come to find that they actually possess none of the seven marks of existence, though people may generally assume that they do. Hence, a Mâdhyamika cannot be considered an empirical realist in the Kantian sense.

4.2 Mâdhyamika method compared with Kant

Murti’s real point in bringing up Kant seems to be designed more to emphasize the seeming commonality of their dialectical approach to reasoning. On page 297, he dismisses most of the Critique as uselessly in thrall to dogma:

The Transcendental illusion is the real starting point of his Critique. The consciousness of this illusion is engendered by the conflict in Reason as exemplified by totally opposed philosophies. Kant’s preoccupation with an explanation of experience serves to confound his readers and cloud the issues. And it is at variance with the anti-speculative tendency of the Critique.

For Murti, the importance of the Critique is that it is a critique at all. The earlier quote about the similarities of Kant and Mâdhyamika not withstanding, the main point that the two share is the tendency to challenge us to find the very limits of reason itself and by doing so, invite us to look beyond the phenomenal realm. Murti sees the exposure of transcendental illusion as the common feature shared by the Mâdhyamika and Kant, and thus feels justified in glossing over differences between transcendental idealism and the two truths system in order to make the commonality of method more clear. Returning to the possibilities outlined earlier, Murti would say that for Mâdhyamika, like Kant, we can expose an infinite chain of illusory objects in conventional reality through a dialectical application of the argument in the prelude. In order to go beyond this chain into the noumenal reality or ultimate truth, we cannot employ any ordinary sensory activity, but must use Intellectual Intuition which allows us to have direct access to the absolute totality of Spirit that lies beyond the chain and ultimately justifies it. For Murti, this process must be dialectical, so that we never fall into the error of espousing some view, because doing so would collapse us into either circularity or insufficient reason and hence invalidate the chain of inferences leading to it. Instead, we can only be lead by the dialectical process into directly experiencing the way that this absolute totality of Spirit is outside of our usual categories of classification and hence justifies the chain while remaining immune to the collapse.

For now, we will leave aside the errors Murti has made by interpreting Mâdhyamika in this way and grant his point that the they share with Kant a goal of finding limits to reason. Nevertheless, as we shall see Priest point out, there are serious problems lurking in for any attempt at creating a Kantian definition of the limits of reason in this manner.

5. Priest

5.1 Kant and the problem of expressibility

Graham Priest’s Beyond the Limits of Thought is an intriguing compendium of various historical situations in which philosophy has run up against the limits of reason, and also, in Priest’s view, the existence of true contradictions. Returning to Kant, we explained that he held that the noumenal is beyond phenomenal experience. Indeed, the noumenal cannot even be spoken of according to the usual a priori categories such as existence or causality. He explains Kant’s view on page 81:

The reason that we cannot have knowledge of noumena is precisely that we cannot even make statements about them: any (meaningful) statement about them would have to apply the categories, and so is impossible.

However, Priest feels that Kant is here contradicting himself. The fact is that Kant does apply the categories in speaking of noumena, repeatedly, and any attempt to purge the instances of such from Kant as minor aberrations from his usual method is doomed to fail, because the entire premise of noumena is contradictory. From pages 81–83:

When Kant says noumena may be supposed to exist (A253=B309) he deploys the Category of existence; when he says they are not in time, he deploys the Category of negation. Even the statement that Categories cannot be applied to noumena deploys the Categories of possibility and negation! … Let me emphasize again: this is not a contradiction of the kind of which one finds so many in the Critique: a result of carelessness or of changes of view; it is a contradiction which is occasioned by the very objects of the theory.

Priest’s insights here capture the central project of the Critique: to offload all of the contradictions entailed in taking the usual objects of experience as things in themselves by moving noumena into their own realm, where, after stripping them of time and space and the categories of judgments, Kant hopes they will become powerless to cause any further problems for Reason. Unfortunately, the project still collides with the dreaded contradiction when one sees that even if noumena could be partitioned off from the world of experience, it nevertheless entails a contradiction, because if it is possible for the noumenal world to influence the phenomenal, then the noumenal is exhibiting causality of a phenomenal nature and thus is pulled down to the same level and subject to the same limitations as phenomenon.

5.2 Murti and the problems of expressibility and self-reference

Murti is also vulnerable on this point. He does however anticipate the problem, and in the section, “Is shûnyatâ a theory?” he protests that it is not, because, “Criticism of theories is no theory” (161). He goes on to explain on 162,

To analyze a proposition is not to make another proposition. If that were the case, we cannot make any universal statement. For, the statement about the nature of all propositions will, on this contention, be itself a proposition… Likewise, the self-conscious awareness of all points of view, or Reason as such, cannot itself be a view. Hence the true universal cannot be a view-point (a dṛṣṭi); and conversely all points of view are particular, not universal.

But surely criticism is a theory — the theory that the criticized theory is incorrect. Against this, Murti claims that universal propositions are not views, hence neither is the universal criticism of shûnyatâ. However, ordinarily, we will call any proposition that can be referred to and predicated meaningfully a view, and surely, it is at least sometimes possible to make reference to universal judgments. For example, we can say without contradiction, “the universal judgment that everything — be it a thing, a word, a concept, this sentence, or anything else — is actually a banana is a false universal judgment.” Being universal was no protection for that judgment from being quite demonstrably false. (Even a radical monist would have to admit the properties usually imputed in a banana — being real, yellow, edible, a fruit, and differing from non-material things — are not present in a proposition, though the monist may suppose that the bananas which we actually experience are secretly the same as everything else.) Therefore, if false universal judgments are not made inexpressible by their self-reference, then it seems likely that a true universal judgment is also theoretically possible. But if true universal judgments are possible then they must also constitute a view, since we can say determinately, “this universal judgment is true.” Murti might here offer the following line of objection, “the previously given example universal judgment is clearly false, and thus it counts as a view. However, there is another class of universal judgments which, due to epistemic limits, cannot be determined as true or false. These universal judgments are not views.” Alas, his last statement sinks him. If Murti’s objection is true, then the statement “these universal judgments are not views” is itself epistemically available to us. In other words, if he has a meaningful and valid argument, we should be able to affirm it. But, if his argument is valid, then it is possible to refer to those universal-judgments-which-are-not-views in a meaningful way, and if this is possible, then those universal judgments are views after all, since they still can be used to predicated meaningfully, even if we lack the ability to predicate as regards the truth or falsehood of their content. “1.) It is true that shûnyatâ is not a view. 2.) If an understanding is not a view, we cannot make meaningful assertions about it. 3.) Contradiction from assumptions one and two.” Thus, reductio has turned against Murti.

If we examine Murti’s motivations, we can see that he wants to say, “All views are wrong, and this is not a view.” He wants to avoid saying, “All views are wrong except this one,” because to allow an exception like this is too ad hoc. Any opponent would of course affirm just the same thing, only redirect the reference of “this view” to her own view. By adding the rider, “and this is not a view,” what he is really attempting to show is that his view is a special view, not subject to the usual limitations, and only his view is able to be treated in this way. The addition makes his view uniquely non-substitutable, since while on final consideration we may not accept that shûnyatâ is not a view, the claim is not a completely implausible, as it would be if one were to claim that, say, “atomic theory is not a view.” The same motivation comes into play whenever we use the Principle of Sufficient Reason. There is no reason we could not propose that the Principle of Sufficient Reason is incorrect, and the correct principle is that everything has a higher explanation, except for whatever thing our particular theory considers to be ultimate (be it God or string theory or whatever). However, to do so is blatantly ad hoc and begging the question, because we first determined that the proposed ultimate thing must exist at all on the basis of the Principle of Sufficient Reason, but now we have changed that foundational principle in order to ensure it stops at our ultimate thing. Thus, Murti’s attempt to escape this sort of difficulty by finding a special kind of view that is uniquely suited to non-refutation is not misguided, just failed.

It may be objected that Murti is wise to posit that a universal statement cannot refer to itself because allowing indiscriminate self-reference engenders the Curry paradox and the like. However, the attempt to limit the scope of self-reference to specific areas, as in a type system, is not a viable metaphysical proposition, though it may be a useful technique mathematically. The reason is that any sufficiently complex type system is inherently limited by Gödel’s paradox to being either contradictory or incomplete. If Murti were to claim, “it is true that there is no self-reference at the ultimate level,” then this is a contradiction for the ultimate level describes itself as being without self-reference. If he were to claim that this can be considered to be the case but it is not explicitly stated at the ultimate level so as to avoid contradiction, then the ultimate level is incomplete. (An incomplete system is one that cannot fully describe itself.) While this may be fine for mathematics, in which the higher system (like the language of the textbook) describes the lower system (the metamathematical system described in the textbook) which in describes still lower systems (ordinary arithmetic), we cannot suppose reality to be incomplete at the highest ontological level without conceding in advance that there are no ultimate explanations, only penultimate explanations. In a type system, you can say there is no meaning in asking for the value of a self-referential formulation within a given type, but one can always construct a higher type in order to refer to the lower formula. If there is no self-reference on the ultimate level, then there is always another level beyond the ultimate level which informs us of this truth, and the ultimate is not ultimate after all. Indeed, we find there must be an infinite regress of pseudo-ultimate systems. However, this is precisely what Murti was trying to avoid by positing that the ultimate level is not a view.

The inability of the ultimate theory to be ultimate can be understood on the analogy of the inability of parts of a body to be a body (or parts of a term paper, a whole term paper). Just as a physical whole is not the same as parts, so too a totality of criticism does not emerge from a myriad of criticisms. Each individual criticism may conventionally hold, like the parts of the body, but a totality needs to possess certain properties which it can never get from its parts. An ultimate theory must possess the property of ultimateness, but if none of the steps making up the ultimate theory possess such a property, it is natural to wonder from what the property can be taken to emerge. This line of reasoning can also be taken in the opposite direction, to show the emptiness of the elements that make up a complete view. If an ultimate view posits that there is no finality, as Mâdhyamika does, then it may be asked if any of the components of their reasoning possess finality. This is why Candrakîrti writes in Madhyamakavatara 6:176,

The logical objections of contiguity and so forth would be applicable to us only if we were to maintain that the nature of the reasoning — that which gives rise to the understanding of what is proved — and the nature of that which is actually understood — that which is proved — were inherently existent. But we assert that they have no inherent existence. Therefore, the objections our critics make against us are utterly in vain.

The ultimate truth is itself empty of inherent existence, hence there is no need for Murti to try defend it as not a view in order to protect it from Mâdhyamika reductive analysis. The Mâdhyamika readily acknowledges that the application of their system to itself would destroy it.

5.3 Priest on Nâgârjuna and the problem of expressibility

This problem of a universal judgment being subject to itself and thus undermining itself is a real problem for both philosophy and logic. Priest’s book deal with numerous examples in which a self-referential proposition is created by some means, such as diagonal argument in math or simple demonstratives in the Liar paradox. Priest’s conclusion, drawn from the numerous examples in his book, is that only by adopting some form of paraconsistent logic can we avoid the Scylla of paradoxical self-reference and Charybdis of logical explosion (which is the result of arguments in the form (∀x) (a & ~a → x)). Limitations of time and space prevent us from detailing the full argument here. Instead we turn to Priest’s view of the chief patriarch of the Mâdhyamika, Nâgârjuna. (The relevant chapter of Beyond the Limits of Thought was co-authored by Jay Garfield, but for convenience, we will continue to write “Priest’s argument…”)

First, Priest addresses the question of whether Nâgârjuna really did want to say, “all views are wrong,” and if so, how he overcame the implicit contradiction in doing so. He considers that perhaps Nâgârjuna only appears to be asserting views but is actually merely negating the views of others without asserting any of his own as Murti suggests. However, the textual evidence is against Murti, as Nâgârjuna can be see to openly claim the fact of dependent origination, etc. Another interpretation might have Nâgârjuna merely uttering words that just so happen to cause us to abandon our views without these words meaning anything to Nâgârjuna himself, but Priest finds no evidence supporting this interpretation. Another interpretation might hold that Nâgârjuna’s assertions, where they exist, are merely conventional assertions which he ultimately renounces. This too Priest rejects on the grounds that an ultimate assertion is an assertion about what is left after analysis, and Nâgârjuna and his commentators are in complete agreement that what is left is nothing. This must be an assertion about the ultimate. On page 263, Priest concludes,

There is, then, no escape. Nâgârjuna’s view is contradictory. The contradiction is clearly a paradox of expressibility. Nâgârjuna succeeds in saying the unsayable… As Siderits ((1989), p. 231) has put it, “The ultimate truth is that there is no ultimate truth.”

(Note that Siderits does not agree with Priest and Garfield’s interpretation of his slogan.)

5.4 Priest on Nâgârjuna’s ontology

Next, examining Nâgârjuna’s ontology, Priest rejects Murti’s Kantian view of the ultimate/conventional distinction on the grounds that,

The emptiness of emptiness means that ultimate reality cannot be thought of as a Kantian noumenal realm. For ultimate reality is just as empty as conventional reality. Ultimate reality is hence only conventionally real! (256)

Kant and Murti want to partition out a realm where the usual rules do not apply to save it from contradiction, but the Mâdhyamikas expressly allow that the ultimate realm is subject to the same limitations as the conventional. However, just positing the emptiness of everything is not without its difficulties. If emptiness cashes out to meaning, “without an essential nature,” then we may claim that everything lacks a nature. However if everything lacks a nature, then we may say that everything shares a nature, the nature of emptiness. Thus, everything both has and does not have a nature, namely emptiness.

There is an additional problem with positing the emptiness of emptiness. We may inquire about whether things just happen to be without essential properties or if it is impossible for anything to be without essential properties. The many arguments of Nâgârjuna are clearly meant to show it is impossible for things to have essential properties. Priest quotes Candrakîrti’s commentary, “Things are not without characteristics through characteristiclessness; to be a thing is to be without a defining characteristic” (266). Clearly this is a contradiction if we take “having an essence” to mean the necessary possession of some property. Nâgârjuna and Candrakîrti are arguing that things both do not have essential characteristics and that things do have the essential characteristic of lacking characteristics.

One way out of the two apparent contradictions might be to argue like Kant and Murti that the properties of the ultimate are such that is possible to both have and to lack characteristics without entailing a contradiction. However, we have already seen the difficulty that this position entails. By saying, “emptiness is empty,” the Madhyamika is acknowledging that merely calling everything empty runs into the same sorts of contradictions that damned his substantialist opponents.

5.5 Nâgârjuna and paradox

Thus, there are multiple contradictions in Priest’s interpretation of Nâgârjuna. On the level of expression, he says what cannot be said, and on the level of ontology, everything shares the property of lacking properties. To resolve these conflicts, in a note on page 250 Priest signals his agreement with Tillemans’ 1999 “Is Nâgârjuna Logic Deviant or Classical?” in which it is argued that Nâgârjuna employs classical logic on the conventional level but paraconsistent logic on the ultimate level. Thus, in Priest’s interpretation, Nâgârjuna’s claim is that our mind naturally imputes external objects as the cause of our experience. This imputation is incorrect and moreover positively harmful, as it mires us in the cycle of existence bound by desire. In Priest’s interpretation, to escape this means to see experience as experience and nothing else:

Penetrating to the depths of being, we find ourselves back on the surface of things, and so discover that there is nothing, after all, beneath those deceptive surfaces. Moreover, what is deceptive about them is simply the fact that we take there to be ontological depths lurking just beneath. (226)

Following from this for Priest is the conclusion that experience if taken in itself is not harmful. Since only the reified experience of imputed objects is harmful, the ultimate truth is nothing but ordinary experience without such reifying:

Nâgârjuna demonstrates that the emptiness of emptiness permits the “collapse” of the distinctions between the two truths, revealing the empty to be simply the everyday, and so saves his ontology from a simple-minded dualism. (270)

Thus on Priest’s view, in terms of the possibilities of the first section, Nâgârjuna subscribes to possibility 3 (“there are no ultimate justifications”) on the conventional and ultimate levels by way of possibility 4 (“contradiction”) at the ultimate level. The one potential qualm with Priest’s view is that it comes dangerously close to ascribing a kind of empirical realism to Nâgârjuna in emphasizing that the everyday is the ultimate. Calling the everyday the ultimate might be interpreted to suggest that we are safe in relying on everyday senses, when, as was strongly emphasized before, this is far from the case. To the contrary, in the Tibetan version of Bodhicaryâvatâra 9:167, Shantideva longs to “reveal emptiness to those ruined by reification.” This is because while the ultimate collapses into the conventional level, this does not negate that fact that even on the conventional level, things are not what the consensus of experience seems to suggest. Again, while avoiding taking a position in the long running dispute about the nature of the conventional realm within Mâdhyamika, we note that even Svatantrika school will claim that the conventional realm can be broken into momentary dharmas and the like. Hence Bodhicaryâvatâra 9:8, “There is no fault in the conventional truth of the contemplatives,” that is those who subscribe to the Buddhist world view not the conventional truth of ordinary understanding. Nevertheless, outside of this potential misstep, Priest’s interpretation of Mâdhyamika is largely sound.

6. Conclusions

6.1 Mâdhyamika and the end of analysis

With this understanding in mind, we are now able to return to the question that originally engaged us: What are the implications of analysis of the sort conducted in the prelude? First of all, if the Mâdhyamika are right, analysis of this sort both has and does not have a stopping point. There is no stopping point in the sense that any object of analysis can be further analyzed into more basic points. This is helpful for the Mâdhyamika because if there were such a stopping point, the ultimate objects could potentially be objects for craving. There is a stopping point in the sense that it is possible to realize that there is no stopping point, and thus there is no need to conduct further analysis in order to find one. This also serves the Mâdhyamika goals, because if it were not possible to know that there is no stopping point for analysis, the mind would never be at rest, but instead it would continually analyze objects deeper and deeper in the hopes that a stopping point might later be found. The difficulty is that since there is a stopping point, the mind is tempted to reify emptiness itself into an object worthy of grasping. However, those who understand the emptiness of emptiness will properly refrain from doing so. This is why Shantideva says in Bodhicaryâvatâra 9:34, “When neither an entity nor a non-entity remains before the mind, then since there is no other possibility, having no objects, it becomes calm.” Thus, the contradiction is that one must cease analysis with the knowledge that there can be no cessation to analysis.

However, have the Mâdhyamika avoided the trap the Murti was attempting to avoid by asking, “Is shûnyatâ a theory?” The principle of recursive analysis lead the Mâdhyamika to renounce all views, but does such a renunciation constitute a view that is any different from, “All views are wrong except mine,” which anyone could endorse? Also, if the Mâdhyamika answer to this difficulty entails a contradiction, why should analysis cease where the Mâdhyamika suppose it does, rather than at some other contradiction, such as those lead to by the theories of substantialists?

The difference between Mâdhyamika views and the views of their opponents is that Mâdhyamika follow their principles past the limits of their implications before abandoning them, rather than begging off a contradiction sooner. Any theory can propose an ad hoc explanation right off the bat. We could just propose to explain that everything that happens is the will of some inscrutable spirit at step one and be done with it. However, a more useful explanation will always go deeper until there is no deeper left to go. Thus, we might attempt to beg off the contradictions inherent in thinking of the experience of objects as proof of objects as things in themselves by saying that since we have no epistemic access to things in themselves and neither can we even theoretically encounter objects in any manner other than through experience, things in themselves are a mystery and leaving it at that, but logical consistency demands that we dig deeper before allowing ourselves the luxury of recourse to the unknowable. Through the reductio ad absurdum argument, the Mâdhyamika demonstrates the intellectual laziness of the supposedly logical opponent who has ceased analysis before it turns on itself. Thus, the following exchange takes place in Bodhicaryâvatâra 9:109–110:

109. [Objection:] But if one analyzes by means of analysis which is itself analyzed, then there is an infinite regress, because that analysis can also be analyzed.

110. [Mâdhyamika:] When the object of analysis is analyzed, no basis for analysis is left. Since there is no basis, it does not arise, and that is called “nirvâna.”

The Mâdhyamika analyzes even past the point of absurdity, and thus nothing remains to be analyzed, and the mind is pacified.

6.2 The meaning of illusion and explanation

Next, what is it that Mâdhyamika analysis reveals? Yes, everything is an illusion, but what does that mean? First, it is worth defining illusion itself. Illusion is taking one’s experience to imply something that is not in fact the case. In the case of an ordinary illusion, I may, for example, see a train speeding toward the movie screen and react with fear. This is an incorrect reaction, because the train is not actually dangerous to me. My impression of the danger of a train coming towards me is an imputation that causes me to draw incorrect causal inferences. On the other hand, the fact that I am experiencing an image of a train coming toward me is not controverted by the explanation that the “train” is only an image of a train. The common lesson of Kant and the Mâdhyamika is that all of experiences are only the experience of appearances, not the direct experience of objects, which is logically impossible. Contra Magritte’s The Treachery Of Images, even a real pipe outside of a painting is not a pipe. It is only seeing, touching, feeling, and smelling a pipe. On the other hand, the causal inferences that one can draw from a painting of a pipe and the causal inferences one can draw from an ordinary pipe are quite different. A painting of a pipe cannot allow one to experience smoking, but an ordinary pipe can. Returning to the train example, if from the film of a train coming toward the screen one drew the conclusion that one’s life were in danger, this would be a mistake, but to draw the conclusion that the “life” of the girl tied to the tracks in the movie is in danger would be a correct inference. Similarly, this may not be a term paper, but it has the same causal efficacy as one, meaning that for conventional purposes and within certain limitations, it can be treated as such, though it is not. Thus, even illusions have their range of causal efficacy, it is just that this causal efficacy is not as wide as it may appear to one unaware of the illusion. As Candrakîrti says in Madhyamakavatara 6:175, “Even though a reflection is not true it can still establish whether or not one’s face is clean.” A wise man can use a mirror to wash his own face. The fool will wash the mirror.

The one difference between Mâdhyamika analysis and the usual explanation of an illusion is that explanation is predicated on the real existence of something deeper that explains the illusion. For example, in our prelude, we left behind the-experience-of-reading-a-term-paper as the real which remains after analysis. The Mâdhyamika thesis is that analysis can always be applied recursively until there can be nothing deeper that escapes analysis, for the reasons given earlier. Thus, even the deep explanation of the-experience-of-reading-a-term-paper is vulnerable to further reduction. Deeper explanations in general come in two types: those that replace the previous explanation and those that merely subsume them. Newton’s gravity replaced Aristotle’s entirely, only to be completely replaced in turn by Einstein’s (though Newton’s gravity lives on as a convenient means of estimating). On the other hand, learning that subtraction can be generalized as the addition of negative numbers does not invalidate the use of ordinary subtraction, and the discover of higher realms of non-Euclidean geometry does not preclude relying on the same inferences within an explicitly Euclidean context. For Mâdhyamika, the conventional result of analysis is that which causes us to revise our estimation of the causal efficacy of things in experience. For example, I may think of myself as a person with a soul, but if analysis reveals that I am empty of self then this has direct application in the estimation of my causal efficacy. On the other hand, though on the ultimate level the result of analysis is finding that there is no ultimate ground for being, this has no direct impact on our estimation of the causal efficacy of objects in the world. The only impact this discovery has is on my process of analysis itself. (That is, my analysis can cease, since there is no ultimate being to discover.) Conventional analysis reveals what we do not have here and now; ultimate analysis reveals what we do not have and cannot hope for.

6.3 Implications

Starting from an entirely different perspective, Rescher comes to similar conclusions about the problem of ultimate analysis from a scientific perspective. Any ultimate analysis must be subject to itself as well, no matter what difficulties this entails:

We clearly cannot provide a scientific explanation for the whole system of science in terms of something that falls outside: it would not be the whole system if anything fell outside it. Explanatory self-subsumption is infeasible at the level of facts and laws. But at the systemic level it is a conditional necessity: if the system can be explained at all, that explanation must fall within it. As long as we operate on scientific principles, we canot get outside the framework of our completed explanatory system: to explain the system in terms of X would simply be to enlarge it to include X itself. The quest for a system-external foundation for the scientific rationalization of the system is ultimately senseless. (88–89)

Since we cannot go posit anything outside of the explanatory system itself, the system becomes an interdependent one whose value is judged based on its systematic unity as a whole:

Thus, we have here a wholly different approach to explanation; one that takes systematization itself as the key, relying not on subsumptive inference but on systemic coordrination. (85)

The issue of legitimation is thus settled in terms of a cyclic interdependence and self-supportiveness. The idea of explanatory stratification is misleading: no neat linear order of fundamentality obtains among nature’s facts of laws. (90)

Thus even from a scientific perspective something like dependent origination is necessary (“cyclic interdependence”), though of course Rescher’s proposal is nowhere near as sweeping as the Mâdhyamika, in part because he is considering justification from a scientific basis that takes external objects for granted rather than an epistemic one that questions their very possibility. What is the meaning of Mâdhyamika-style ultimate analysis? In conclusion, we can say that the illusory nature of objects under analysis implies that there are no ultimate justifications, though this comes by way of contradiction on the ultimate level, since the interdependence of things might otherwise be taken as such a justification. In terms of conventional reality, objects must be analyzed in terms of their conventional efficaciousness. Even on this level, however, we will find that the external objects which reason compels us to impute are not ever to be found in actual experience. Thus, Kant and Murti were on the right track with their dialectic method, but they stopped short of the full implications of their method by withholding a deeper realm from analysis. Priest’s interpretation of Nâgârjuna and his paradoxes is mostly correct, although his emphasis on the identity of the conventional and ultimate realms comes dangerously close to endorsing our common sense notions of the world, which Nâgârjuna would not do. Illusions are ordinarily divided into a real perception which causes a falsely inferred cause but is actually caused by a real cause, but in the case of universal illusion, we can say that there is no real cause nor can there be, though it is a contradiction to do so.

7. References

Candrakîrti. A Guide to the Middle Way. (Madhyamakavatara.) Translated by Stephen Batchelor from Geshe Rabten’s Echoes of Voidness. Wisdom Publications, pp. 82 and 84, 1984.

Kant, Immanuel. Critique of Pure Reason. Translated by Werner S. Pluhar. Hackett Publishing Co. Indianapolis. Originals 1781, 1787. Translation 1996.

Murti, T. R. V. The Central Philosophy of Buddhism. Second edition. Bradford and Dickens. London. 1955, 1960.

Priest, Graham. Beyond the Limits of Thought. Second edition. Oxford University Press. 1995, 2002.

Rescher, Nicholas. Nature and Understanding: The Metaphysics and Methods of Science. Oxford University Press. 2001.

Shantideva. A Guide to the Bodhisattva Way of Life. (Bodhicaryâvatâra.) Translated by Vesena Wallace and B. Allan Wallace. Snow Lion Publications, Ithica. 1997.