Totally Pervasive, Mutually Exclusive and Dichotomous Sets of Objects
Two sets of objects may be totally pervasive (don-gcig) or mutually exclusive (‘gal -ba).
Two sets are totally pervasive if every element in set A is also a member of set B, and vice versa – for example, the sets of stars and suns. All stars are suns and all suns are stars.
Two sets are mutually exclusive is they do not share any common locus (gzhi-mthun). A common locus is an item that is a member of both sets. The sets of ways of cognizing an object (shes-pa) and of forms of physical phenomena (gzugs) are mutually exclusive. There is no phenomenon that is both.
Two mutually exclusive sets may or may not constitute a dichotomy (dngos-‘gal). They form a dichotomy if all existent phenomena must be in either one or the other mutually exclusive set.
For example, the sets of static (permanent) and nonstatic (impermanent) phenomena are mutually exclusive and dichotomous. All existent phenomena must be either static or nonstatic, and nothing exists that is both. The sets of ways of cognizing an object and of forms of physical phenomena are mutually exclusive, but not dichotomous. Phenomena exist that are members of neither one nor the other set – for example, abstractions.
Trilemmas and Tetralemmas
Two sets may also constitute a trilemma (mu-gsum) or a tetralemma (mu-bzhi).
The relationship between two sets is a trilemma if there are three possibilities. There are phenomena that are members of
- Both set A and set B
- Neither set A nor set B
- Only set A, but not set B.
There are no phenomena that are members of set B that are not also members of set A. In other words, all elements of set B are also members of set A, but not all elements of set A are elements of set B.
Consider the relationship between the sets of mammals and animals. Something may be both a mammal and an animal – for example, a dog. Something may be neither a mammal nor an animal – for example, a rock. Something may be only an animal, but not a mammal – for example, a snake. Nothing exists, however, that is only a mammal, but not also an animal. In other words, all mammals are animals, but not all animals are mammals.
The relationship between two sets is a tetralemma if there are four possibilities. There are phenomena that are members of
- Both set A and set B
- Neither set A not set B
- Only set A, but not set B
- Only set B, but not set A.
Consider the relationship between the sets of our relatives and our friends. There are four possibilities. Someone may be both a relative and a friend, a relative but not a friend, a friend but not a relative, or neither a friend nor a relative.
Same Essential Nature
Two things are of the same essential nature (ngo-bo gcig, one by nature) if they are two facts about the same attribute (rnam-pa) of a phenomenon. In other words, they are two facts about the same attribute of the same phenomenon perceived from two different, yet valid points of view.
A classic example is the two truths (bden-pa gnyis, two levels of truth) about something, as defined by the various Mahayana schools. According to the common assertion shared by the divisions of Madhyamaka, for example, they are:
- The appearance of an object as “this” or “ that,”
- The mode of existence of the appearance.
The former is the superficial truth (kun-rdzob bden-pa, relative truth, conventional truth) about the object, and the latter is the deepest truth (don-dam bden-pa, ultimate truth) about it. Both truths are facts about the same attribute of an object, in this case its appearance. The two facts simply describe the appearance from different points of view: what it appears as and how it exists as that.
For example, an apple appears to be red. Its appearance as red is devoid of existing in impossible ways. The appearance of the apple as red and the void nature of that appearance are two facts about the same attribute of the apple: its color. On the other hand, the facts that the color of an apple is red and that its taste is sour may both be true. However, they are not facts about the same attribute of the apple. One concerns the appearance of the apple; the other concerns its taste. The apple’s color and taste do not share the same essential nature.
Two facts about the same attribute of an object are always inseparable (dbyer-med). One cannot be the case without the other also being true.
For example, an apple cannot appear as red without that appearance being void by nature. This does not mean, however, that when we cognize or understand one of the facts, we cognize or understand the other. When we cognize or understand that the apple appears to us as red, we do not necessarily cognize or understand the void nature of the appearance.
On the other hand, two sides of a coin may be inseparable, but they are not two facts about the appearance of the coin. They are merely two aspects of that appearance. When we look at a coin from one side or the other, we see two different aspects of the appearance of the coin. Two facts about the appearance of a coin, however, do not derive from looking at the coin from two different physical viewpoints. They derive from considering the appearance of the coin from two different cognitive points of view.
Mutually Exclusive or Totally Pervasive Facts
Two inseparable facts about the same attribute of an object may be mutually exclusive (‘gal-ba) or totally pervasive (don-gcig).
Two facts about something are mutually exclusive if they have totally different meanings. The color and the taste of an apple, for instance, are two different facts about the fruit, although not two facts about the same attribute of the fruit Here, it is obvious that the color of the apple does not mean its taste, and vice versa. The two facts are mutually exclusive. Similarly, the two truths about something are different facts about the same attribute of an object that are mutually exclusive. The appearance of an apple as red – as opposed to its appearance as green – does not mean the void nature of that appearance, and vice versa. The two facts do not have the same meaning.
Two facts, on the other hand, are totally pervasive if they have the same meaning. An apple being nonstatic also means that it is an object affected by causes and conditions (‘dus-byas, conditioned phenomenon), and vice versa. The fact that an apple rots means that an apple is affected by the passage of time, and vice versa. Although we may only know one of the two mutually pervasive facts about an apple, our unawareness of one of the facts does not negate the other fact or that the two facts have the same meaning.
Identical or Different
Two facts about the same attribute of a phenomenon, even if totally pervasive, must not be identical (gcig); they must always be different (tha-dad) facts. Otherwise, they are the same fact and not two facts.
For example, two facts about the same attribute of a woman may be that she is a mother and that she is a mom. If a woman is a mother, she is necessarily a mom, and vice versa. The two facts have the same meaning and are synonyms (ming-gi rnam-grangs). However, they are different facts or true statements about the person, because the words “mother” and “mom” are different words.
Two facts or true statements are identical only if they are identical in all respects.
Same Essential Nature, but Different Conceptually Isolated Items
Two facts about the same attribute of a phenomenon, such as the two truths about something, share the same essential nature. They are not only two different facts, however; they can be specified as different conceptually isolated items (ldog-pa tha-dad, distinguishers, isolates).
The conceptually isolated item that specifies a validly knowable phenomenon in conceptual cognition is the mental exclusion (blo’i gzhan-sel) of everything that is other than that validly knowable phenomenon. In other words, it is what is left over after conceptually excluding everything that is not a certain item. It is a conceptual device for specifying something as fitting into a specific conceptual category (spyi, universal), such as one of the two truths and not any category other than that.
For example, a medical examination may specify a disease by the symptoms it finds. It may also specify the sickness by logically excluding what it is not, as indicated by the negative results of exhaustive tests. In medicine, knowing that a disease is not X or Y specifies that it must be Z, if Z is the only possibility left over. Here, however, the conceptually specified item does not explicitly indicate that the disease is Z. It merely specifies that it is not non-Z.
The mental exclusion of everything other than X, however, does not require the active process of excluding, one by one, every item that is non-X. A conceptual isolated item is merely a conceptual tag for specifying something as an individual validly knowable phenomenon.
Same Natal Source
Two items share the same natal source (rdzas-gcig, same natal substance) if they arise from the same source. They may or may not be inseparable.
For example, a clay pot and its belly arise from the same potter’s wheel as their natal source and are inseparable, as is the case with a flame and the heat of the flame arising from the same match.
Two clay pots, however, may come from the same potter’s wheel, but are not inseparable. Likewise, two rebirths may arise from the same karmic legacy (sa-bon, karmic seed, karmic tendency) as their shared natal source, but are not inseparable.
Obtaining Causes and Simultaneously Acting Conditions
An obtaining cause (nyer-len-gyi rgyu, material cause) is the item from which one obtains the result. It functions as the natal source (rdzas) giving rise to the result as its successor and ceases to exist simultaneously with the arising of its result.
If an item is the natal source of something, it may or may not also be its obtaining cause. For example, a seed is both a natal source and obtaining cause for a sprout. It ceases to exist with the production of the sprout. A potter’s wheel, on the other hand, is a natal source for a clay pot, but not an obtaining cause; whereas the unfired pot is both a natal source and an obtaining cause. The unfired pot ceases to exist with the production of the fired clay pot, the potter’s wheel does not.
An obtaining cause requires simultaneously acting conditions (lhan-cig byed-rkyen, accompanying condition) in order to give rise to its result. For example, a seed requires moisture, heat, and sunlight to give rise to a sprout.
Simultaneously Arising Causes
When two items exist simultaneously as the causes for each other – in the sense of each being indispensable for the existence of the other – and each arises from a different natal source, they are simultaneously arising causes (lhan-cig ‘byung-ba’i rgyu).
A common example is a vase and the earth particles of the vase. A vase cannot exist without its earth particles, and its earth particles cannot exist as earth particles of a vase without the vase they comprise existing at the same time. The natal source of the fired vase is the unfired vase; while the natal source of the earth particles of the vase are the earth particles of the clay.
Another example is a moment of primary consciousness (rnam-shes), such as eye consciousness, and its accompanying mental factors, such as feeling a level of happiness. For instance, in a moment of happily seeing our mother, the seeing of our mother and the feeling of happiness that accompanies seeing her simultaneously arise. Both are indispensable for the existence of the moment of happily seeing our mother. The natal source giving rise to the moment of seeing our mother is the karmic legacy of actions in previous lives that have ripened into being born as her child and meeting her now. The natal source giving rise to the feeling of happiness that accompanies that seeing is the karmic legacy of constructive actions we have done in the past.
In short, an item is not made from its natal source and obtaining cause, but is made of its simultaneously arising causes.
When we think of a hand through the conceptual category hand, as an example of an unaffected phenomenon other than voidness, the conceptual cognition arises from a karmic legacy as its natal source. As an unaffected static phenomenon, the conceptual category hand cannot arise from anything. Yet, the conceptual category hand is a component of the cognition.