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Home > Fundamentals of Tibetan Buddhism > Level 5: Analysis of the Mind and Reality > Affirmations, Negations, and Denumerable and Nondenumerable Ultimate Phenomena

Affirmations, Negations, and Denumerable and Nondenumerable Ultimate Phenomena

Alexander Berzin
January 2002, revised July 2006

Existents and Nonexistents

Existents (yod-pa) are defined in Buddhism as what are validly knowable (shes-bya).

Nonexistents (med-pa) are what cannot be validly known, conventionally (tha-snyad) or ultimately (mthar-thug). The word turtle-hair exists, made by combining the words turtle and hair, and can be validly known. Nevertheless, “turtle-hair” cannot be validly known, because there is no such thing. In other words, we may conceptualize “turtle-hair,” but the conceptualization does not refer to anything existent.

Affirmation Phenomena and Negation Phenomena

Existents include affirmation phenomena (sgrub-pa, affirmingly known phenomenon, affirmation) and negation phenomena (dgag-pa, negatingly known phenomenon, negation, refutation).

An affirmation phenomenon is an item, or a truth about an item, defined in terms of the establishment (sgrub-pa) of something, without an object to be negated (dgag-bya, object to be refuted) being explicitly precluded by the sounds that express it.An example of an affirmation phenomenon is “apple.” The sounds that express the word “apple” do not negate anything.

A negation phenomenon is an item, or a truth about an item, defined in terms of the exclusion of something else (gzhan-sel, elimination of other), in which an object to be negated is explicitly precluded by the conceptual cognition that cognizes the phenomenon. An example of a negation phenomenon is “ not an apple.” In order to conceptualize “not an apple,” one needs previously to have known “apple” (the object to be negated here).

[For more detail, see: Gelug Definitions of Affirmation and Negation Phenomena.]

Implicative and Nonimplicative Negation Phenomena

Items that fulfill the above definition of being a negation phenomena are of two types, implicative and nonimplicative.

An implicative negation phenomenon (ma-yin dgag, affirming negation) is an exclusion of something else in which, after the sounds of the words that exclude the object to be negated have negated that object, they leave behind in their wake, explicitly or implicitly, something else. Consider the example, “a table without a tablecloth.” Once the sounds of the words “a table without a tablecloth” have excluded “a tablecloth” (the object to be negated here), they explicitly leave behind “a table.”

A nonimplicative negation phenomenon (med-dgag, nonaffirming negation) is an exclusion of something else in which, after the sounds of the words that exclude the object to be negated have negated that object, they do not leave behind in their wake, explicitly or implicitly, something else. Consider the example, “the absence of a tablecloth” or “there is no tablecloth.” Once the sounds of the words “the absence of a tablecloth” or “there is no tablecloth” have excluded “a tablecloth” (the object to be negated here), they do not explicitly or implicitly leave behind anything.

There are two types of nonimplicative negation phenomenon: the nonimplicative negation of something existent and the nonimplicative negation of something totally nonexistent. An example of the former is “the absence of a tablecloth”; an example of the latter is “the absence of turtle-hair.” Even though a tablecloth may be absent here, it could be present elsewhere. However, when it is the case that turtle-hair is absent here, it cannot be present anywhere else either, since turtle-hair has never existed, doesn’t exist now, and never will exist.

There are also two types of nonimplicative negation of something totally nonexistent: the nonimplicative negation of a totally nonexistent item and the nonimplicative negation of a totally nonexistent mode of existence. An example of the former is “the absence of turtle-hair”; an example of the latter is “the absence of impossible existence.”

Each Indian school of Buddhist tenets asserts voidness (stong-pa-nyid, emptiness) as a nonimplicative negation of a totally nonexistent mode of existence, but defines the impossible mode of existence differently.

Objects To Be Negated, Bases for Negation, and Objects Left Behind in the Wake of a Negation

One must differentiate an object to be negated from its basis for negation (dgag-gzhi) – the item devoid of the object to be negated. For “a table without a tablecloth,” the object to be negated is “a tablecloth” and the basis for the negation is “the table.” For “the absence of a tablecloth on the table,” the object to be negated is “a tablecloth on the table” and the basis for the negation is “the table.” For “a turtle without turtle-hair,” the object to be negated is “turtle-hair” and the basis for the negation is “the turtle.” For “the absence of the impossible existence of a tablecloth,” the object to be negated is “the impossible existence of a tablecloth” and the basis for the negation is “a tablecloth.”

One must also be clear about what is an object left behind in the wake of a negation (bkag-shul), like an oil slick left behind in the wake of a moving motorboat. Nonimplicative negation phenomena do not leave anything behind in the wake of their negations; implicative ones do.

For example, in a nonimplicative negation of an impossible mode of existence, such as “the absence of the impossible existence of a tablecloth,” nothing is left behind in the wake of the negation, not even the basis for the negation, namely “a tablecloth.” Note that here the object to be negated is “the impossible existence of a tablecloth.” Even in the case of “the absence of the impossible existence of a tablecloth on the table,” nothing is left in the wake of the negation. There, the “table” is merely the location of the basis for the negation, which in this case is “a tablecloth on the table.”

In the case of the implicative negation “a tablecloth devoid of impossible existence,” “a tablecloth” is the object left behind in the wake of the negation. In this case, “a tablecloth” is also the basis for the negation.

Denumerable and Nondenumerable Ultimate Phenomena

In the context of Madhyamaka in general, ultimate phenomena (don-dam-pa) refer to voidnesses, which are of two types:

  • denumerable ultimate phenomena (rnam-grangs-pa’i don-dam),

  • nondenumerable ultimate phenomena (rnam-grangs ma-yin-pa’i don-dam).

Denumerable ultimate phenomena are voidnesses that are validly cognized conceptually. They are “denumerable” in the sense that they can be counted among what appears to minds validly cognizing phenomena through mentally labeling them with words and concepts.

Nondenumerable ultimate phenomena are voidnesses that are validly cognized nonconceptually. They are “nondenumerable” in the sense that they cannot be counted among what appears to minds validly cognizing phenomena through mentally labeling them with words and concepts.

Gelug Svatantrika Assertion

According to the Gelug explanation of the assertions of the Svatantrika division of Madhyamaka, the superficial truth (kun-rdzob bden-pa, relative truth, conventional truth) of anything refers to its appearance – the appearance of what it is. The deepest truth (don-dam bden-pa, ultimate truth) of anything refers to its voidness of truly established existence (bden-par grub-pa, true existence) – in other words, how it exists. This voidness, whether cognized conceptually or nonconceptually, is the nonimplicative negation of truly established existence: it is the type of negation that merely negates that there is any such thing.

From the point of view of superficial truth, phenomena have existence established by their self-nature (rang-bzhin-gyis grub-pa). This means that when valid cognition scrutinizes the superficial truth of something, it finds, on the side of the scrutinized phenomena, the referent “thing” (btags-don) corresponding to the name or label for the phenomenon. This is equivalent to saying that phenomena have their existence established by individual defining characteristic marks (rang-mtshan-gyis grub-pa), which are findable on the side of the phenomena. However, these individual defining characteristic marks lack, on their own, the power to establish the existence of phenomena. They can only do so in conjunction with mental labeling. Thus, from the point of view of deepest truth, no phenomenon exists independently from being what the word or label for it refers to. In other words, no phenomenon has truly established existence – existence established truly from the side of the phenomenon, independently of mental labeling.

When voidness is cognized conceptually, its superficial truth appears. This means that an individual characteristic mark, findable on the side of the nonimplicative negation phenomenon voidness of true existence, appears to the mind that conceptually cognizes this voidness. On the basis of this findable mark, the conceptual mind cognizes the voidness by mentally labeling it through the meaning/object category (don-spyi, meaning universal) voidness of true existence. Such a voidness, with an individual defining characteristic mark findable on its own side, is a denumerable ultimate phenomenon. It can be counted among what appears to minds validly cognizing phenomena through mentally labeling them with words and concepts.

When voidness is cognized nonconceptually, its superficial truth does not appear. No findable individual characteristic mark appears. All that appears is a absolute absence of truly established existence.

Mental labeling occurs only with conceptual cognition. Thus, the voidness that is cognized nonconceptually is a nondenumerable ultimate phenomenon. It cannot be counted among what appears to minds validly cognizing phenomena through mentally labeling them with words and concepts.

In short, Gelug Svatantrika asserts that “denumerable” and “nondenumerable voidnesses” – if we may coin these two terms – are the same voidnesses. The only difference is that the mind that conceptually cognizes denumerable voidness cognizes the superficial truth of voidness, which has existence established by a findable individual characteristic mark; while the mind that nonconceptually cognizes nondenumerable voidness cognizes the deepest truth of voidness.

Sakya and Nyingma Madhyamaka Assertion

According to the explanation of Madhyamaka by many of masters from the Sakya and Nyingma traditions of Tibetan Buddhism, denumerable and nondenumerable voidnesses are different voidnesses.

Denumerable voidness is simply the nonimplicative negation phenomenon the absolute absence of truly established existence. Nondenumerable voidness is the voidness that is beyond words and concepts (brjod-dang rtog-pa-las ‘das-pa).

According to Sakya and Nyingma Madhyamaka, “negation phenomenon” is merely a conceptual category (spyi, universal), merely a mental fabrication (spros-pa, mental construct). As such, negation phenomena, including voidness as a negation phenomenon, can only be validly cognized conceptually. This means that when validly cognized conceptually, the mind not only makes negation phenomena appear to be truly existent, it also grasps for them actually to exist in that impossible manner. More precisely, the mind that conceptually validly cognizes voidness makes an appearance of a truly existent absolute absence of true existence and grasps for that absence to exist in this manner. Because of these points, voidness, as a nonimplicative negation phenomenon, can only be validly cognized conceptually.

To gain nonconceptual cognition of voidness, one must go beyond cognizing voidness through words and concepts. Therefore, the voidness validly cognized nonconceptually (nondenumerable voidness) is not the same voidness as the voidness validly cognized conceptually (denumerable voidness). Nondenumerable voidness is a voidness that is beyond the conceptual category of a negation phenomenon.

In fact, nondenumerable voidness is beyond all conceptual categories of affirmation or negation phenomena, or both, or neither. In other words, it is beyond the conceptual categories of the four extremes: (1) an affirmation of true existence, (2) a negation of true existence, (3) from the point of view of superficial truth, an affirmation of true existence and from the point of view of deepest truth, a negation of true existence, or (4) neither an affirmation nor a negation of true existence.

Gelug Prasangika Assertion

According to the Gelug explanation of the Prasangika Madhyamaka assertions, denumerable and nondenumerable voidnesses are the same voidness. Both are voidness as the nonimplicative negation of truly established existence – similar to the Gelug Svatantrika assertion. Gelug Prasangika also agrees with Svatantrika, here, that valid conceptual cognition of denumerable voidness cognizes the superficial truth of voidness and that this superficial truth appears to have its existence established by a findable individual defining characteristic mark. However, unlike the Gelug Svatantrika assertion, Prasangika asserts that even when scrutinized from the point of view of superficial truth, no such characteristic mark can be found. Voidness of truly established existence is equivalent to voidness of existence established by individual defining characteristic marks.

Thus, although denumerable voidness appears to be truly existent and nondenumerable voidness does not appear to be truly existent; nevertheless, both denumerable and nondenumerable voidnesses exist in exactly the same manner.

Note that Gelug does not assert that any validly knowable phenomenon is beyond words and concepts in the non-Gelug sense that it cannot be validly cognized conceptually. According to Gelug, if something exists, it is validly knowable by conceptual cognition. This does not mean, however, that if something exists, it is validly knowable only by conceptual cognition. Many phenomena are also validly knowable by nonconceptual cognition. However, there are only two possibilities: phenomena validly knowable by

  • only conceptual cognition, such as categories,

  • both conceptual and nonconceptual cognition, such as a vase, anger, or voidness as an absolute absence.

There are no validly knowable phenomena that

  • can be validly cognized only by nonconceptual cognition, or

  • cannot be validly cognized either by conceptual or nonconceptual cognition.

Gelug Prasangika defines validly knowable phenomena, in fact, in terms of the conceptual cognition of them. Validly knowable phenomena are merely what the words and concepts for them refer to, validly labeled (imputed) on bases for labeling (gdag-gzhi, bases for imputation). Although the act of mental labeling occurs only with conceptual cognition; nevertheless, all existent phenomena, whether cognized conceptually or nonconceptually, have their existence established merely in terms of the mental labels for them.

According to Gelug Prasangika, since the referent objects (btags-chos) of words and concepts cannot be found as some sort of referent “things” (btags-don), either conventionally or ultimately, we cannot specify what a word or concept refers to by pointing to it. We can only specify what a word or concept refers to by the exclusion of something else – namely, by the exclusion of everything else that is not what the word or concept refers to, and this is purely a conceptual construct. In other words, we can only specify validly knowable phenomena in terms of conceptually isolated items (ldog-pa, distinguishers, isolates), validly knowable only by conceptual cognition. The conceptually isolated item an apple is that object or set of objects that is excluded from the set of everything “not an apple” (the set of “everything other than an apple”). Thus, the conceptually specified item an apple reduces to “nothing other than an apple.” The “exclusion of something else,” however, does not mean actively excluding everything “not an apple,” one by one. It is merely an operation of logic.

Since everything validly knowable must be specifiable, Gelug asserts that everything knowable must be validly knowable by conceptual cognition, even deepest truths.

Furthermore, even if denumerable voidness, as the nonimplicative negation of a totally nonexistent mode of existence, does not leave any object behind in the wake of its negation, this does not mean that the view of denumerable voidness reduces to the extreme of nihilism, as some advocates of nondenumerable voidness would assert. The nonimplicative negation does not negate the basis for its negation (conventional objects, such as apples and tablecloths), only its object to be negated (impossible modes of existence of conventional objects).

Karma Kagyu Madhyamaka Assertion

From the time of the Eight Karmapa (Kar-ma-pa Mi-bskyod rdo-rje), the Karma Kagyu tradition, for the most part, accepts the Gelug interpretation of the Svatantrika and Prasangika presentations of denumerable and nondenumerable voidnesses. Karma Kagyu, however, emphasizes that denumerable voidness is the nonimplicative negation (absolute absence) merely of the first of the four extremes: truly established existence. Nondenumerable voidness is the nonimplicative negation of all four extremes.

Karma Kagyu asserts nondenumerable voidness as a voidness beyond words and concepts only in its presentation of Maha-Madhyamaka and its other-voidness (gzhan-stong) view. In this view, voidness beyond words and concepts is not an ontological state, but rather is a level of mind.

Kadam Sources of the Above Views

The two streams of interpretation of nondenumerable voidness being either beyond words and concepts or a nonimplicative negation phenomenon trace in Tibet from two of the early masters of the Kadam tradition.

The earlier of the two was Ngog Lotsawa (rNgog Lo-tsa-ba Blo-ldan shes-rab). He propagated the tradition that nondenumerable voidness is beyond words and concepts. He explained that it is not fit to be either the direct object (dngos-yul) or even the conceptually implied object (zhen-yul) of words or concepts.

The later of the two was Chapa (Phyva-pa Chos-kyi seng-ge). He taught that nondenumerable voidness is a nonimplicative negation and is fit to be the conceptually implied object of words and concepts.