The most notorious of the three points is the problem of how it happens that new qualities may be produced in earthy substances when they are exposed to heat. Although four types of qualities are said to be produced through heating---color, taste, aroma, and feel---the standard examination of the problem focuses on the change of color that occurs when a clay pot is fired in the kiln. A black pot goes in and a red one comes out; the Nyaya school (in what is called the pithara-paka-vada, "doctrine of the heating of the pot") maintains simply that the heat changes the color of the pot from black to red by penetrating down to the level of the molecules, while the Vaisesika (in what is called the pilu-paka-vada, "doctrine of the heating of the atoms") insists, for reasons offered below, that the heat dismantles the black pot into its constituent atoms, destroys the black color of those atoms, and produces red color in them, after which the newly red atoms are recombined to form a red pot of the same shape as the previous black one. The passage translated below is a famous presentation of this strange theory, culminating in the Vaisesikas' trademark procedure of counting, moment by moment, the precise number of steps required in a scrupulous account of every detail of causation involved in the problem at hand.
In this case the counting of moments is complicated by considerations involving the second of the three points of difference, the problem of the ways in which disjunction between substances can come about. For both the Nyaya school and the Vaisesika school, the term "disjunction" (vibhaga) refers to the state of being spatially separated, which is analyzed as a quality, rather than to the act of becoming separated, which is analyzed as a motion. Neither should be confused with the destruction of contact between substances, which is analyzed as yet another event. It is characteristic of the painstaking linear approach of the Vaisesikas that each of these three is given a step of its own in the causal sequence, so that the motion which removes one substance from another is the cause of the subsequent disjunction between them, which in turn is the cause of the subsequent destruction of the contact between them, which in turn paves the way for a fourth event (and thus a fourth moment in the sequence), that of the contact of the substance with a new location.
This much is accepted by the Nyaya school as well, and both schools can agree that when a person withdraws a hand that had been leaning against a tree, the motion of the hand is the cause of the hand's subsequent state of disjunction from the tree. But what about the disjunction of the person's body from the tree? The Nyaya school is content to say that this is caused by the same motion (although in its "New" version, armed with a metalanguage of limitors and describers, the school returns to the problem of whole and part that is involved here), while the Vaisesikas consider this too simple, since the motion of a part is not the motion of the whole, as a turning wheel demonstrates. They insist that in such circumstances one disjunction (e.g., body from tree) may have to be viewed as caused by another disjunction (e.g., hand from tree).
The third point of disagreement between the two schools is not directly referred to in the passage translated here, and involves the problem of how the quality of number arises in a substance. Both schools recognize that the fact of an object's being part of a group of two objects or part of a group of three objects is associated with an enumerating cognition on the part of an observer. The Nyaya school says that this cognition serves to manifest a number already present, while the Vaisesika school insists that the enumerating cognition actually brings into being the quality of number in the substances so enumerated. At first glance the Vaisesika view may seem the simpler, but the element of causation leads to greater complexity on the level of counting the individual moments required.
The passage translated below is from a particularly skillful treatise on the views of the Vaisesika school, the Kiranavali of Udayana (11th century). For all its originality, this text is formally a commentary on another very original work, the Padarthadharmasangraha or Prasastapadabhasya of Prasastapada (5th century), which in turn is ostensibly a commentary on the Vaisesika Sutras themselves. I have translated from the Sanskrit text as edited by Jitendra S. Jetly in Prasastapadabhasyam: With the Commentary "Kiranavali" of Udayanacarya, Gaekwad's Oriental Series, No. 154 (Baroda: Oriental Institute, 1971), pp. 121--124 (= section 128 in Prasastapada).
In reading the passage, keep in mind that what is meant by the destruction of a molecule is not the obliteration of its matter but the dismantling of its parts, and that what is meant by disjunction is not the process of separating substances but the state of their separation.
The idea is this. Since heat is such a light thing its velocity and its impact are so great that the motion it produces knocks out of place the previous arrangement of a composite substance and brings its parts into a different arrangement. Otherwise how could such (composite substances) as milk and water swell up when they are boiled, once the heat has penetrated into the intervals (between their parts)? If (you reply that) this is because of the weak contact (between the parts in such fluids), (we say) no, because the same (swelling) is observed in (firmer and more compact substances) such as rice grains as well. And because even the hardest (substances), such as gems and diamonds, explode when heated. If (you reply that) this is because of the intensity of the contact with heat, (we say) what does "intensity" mean? If (your answer is that it means) being repeated many times, (we say) no, because if the preliminary (application of heat) is not effective, what use is repeated application? (It is of no use,) because there can be no accumulation on the part of sequential items that are momentary by nature. Therefore we view it as reasonable to suppose that just as in the body (of a human being), for example, a change that is not noticed day by day may be perceived as obvious after the interval of some time, so also in something like the heating of a pot (a gross change may occur through minute events not noticed in themselves). This refutes the notion that the destruction of the previous substance is proven through certain facts: that we recognize (the pot as being the same as before), that we see it (abiding) in all the stages (of its being fired), that other objects of clay placed above it (when the items to be fired are stacked in the kiln) are held up (rather than crashing down because the supporting pot is destroyed), and that there is no change in such (characteristics) as its external shape, its number, its size, and the lines, scratches, or other identifying marks upon it. (The notion is refuted) because it is possible (for there to be a new pot even though in most respects it seems to be the same pot as before), just as, for example, a pot that has had three or four tiny particles scraped away by being pierced with a needle (is no longer the same pot as before). In spite of this the Mimamsakas are impudent enough to claim that (substances) such as a pot are never really destroyed at all. They deserve our pity. For once the atoms have ceased to exist the molecules must necessary be destroyed; otherwise it would follow that effects would be permanent. And upon their destruction the tiny particles (made up of molecules) would necessarily be destroyed, and upon their destruction, their effects (would be destroyed), and so on by this same sequence down to the general destruction of the end products; because otherwise it would follow that effects persist even after they have lost their substratum. Even if a few of the parts are destroyed, (you might argue,) the remaining parts could provide a substratum for the effect. They could not, (we reply,) because a substance that possesses a size capable of being filled out by a given number of parts simply will not fit within a reduced number (of parts). If (you propose that) there will be a shrinking in size, as in a cloth that is folded up, (we reply that) there could not be; for (in the case of a cloth before and after folding) there is no difference between the two, since the lack of difference is a property of the substance. (This is so) because no destruction (of the previous size without the destruction of the underlying substance is possible), since the size abides as long as the substance exists, and can be destroyed only when the underlying substance is destroyed. If (you propose) that it will also be subject to destruction upon the removal or destruction of some parts of its substratum, (we say) no, because it is wishful thinking to suppose that upon the removal or destruction of parts the whole will not be destroyed but its size will be destroyed. If (you insist on your theory) because of our recognizing the whole (as being the same as before), then why is it that we cannot recognize its size (as being the same as before) when only a few tiny parts have been removed? But enough of this torment.
Now, students will wish to know how many moments it takes, starting with the destruction of the molecules (of the old pot), for (the new) molecules to be produced and to come to possess color. In order to clarify the mind of students, the sequence involved is (summarized) as follows:
The sequence as given above is in accordance with the view that both (a) the disjunction that destroys the contact (between parts) that constructs the (composite) substance and (b) the disjunction that does not destroy (the constructing contact, viz., the disjunction of a part from its previous location in space rather than from its contact with another part) are caused by (a single) motion. On the view that the disjunction (caused by the motion) causes the destruction of the previous contact (of part with part), and thereupon arise both the destruction of the (composite) substance and a disjunction (of the parts from their previous location in space) caused (not by the original motion but) by (the first) disjunction, there will be (not nine but) ten moments, as follows:
And so what we learn from all of this is that the special qualities of a composite (substance) last as long as the substance lasts, and that they can be produced by heating only at the level of atoms. This should be viewed as logical support for the same points that I made in discussing the soul: that (qualities of the soul) such as pleasure cannot belong to the body (which is a composite substance), because they do not last as long as it lasts, nor can they belong to (the mind, which is) an atomic thing, because they are perceptible.
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