The Vedanta Sutras, commentary by Sankaracharya (SBE34), tr. by George Thibaut  at sacred-texts.com
17. And as the (atomic theory) is not accepted (by any authoritative persons) it is to be disregarded altogether.
While the theory of the pradhâna being the cause of the world has been accepted by some adherents of the Veda--as, for instance, Manu--with a view to the doctrines of the effect existing in the cause already, and so on, the atomic doctrine has not been accepted by any persons of authority in any of its parts, and therefore is to be disregarded entirely by all those who take their stand on the Veda.
There are, moreover, other objections to the Vaiseshika doctrine.--The Vaiseshikas assume six categories, which constitute the subject-matter of their system, viz. substance, quality, action, generality, particularity, and inherence. These six categories they maintain to be absolutely different from each other, and to have different characteristics;
just as a man, a horse, a hare differ from one another. Side by side with this assumption they make another which contradicts the former one, viz. that quality, action, &c. have the attribute of depending on substance. But that is altogether inappropriate; for just as ordinary things, such as animals, grass, trees, and the like, being absolutely different from each other do not depend on each other, so the qualities, &c. also being absolutely different from substance, cannot depend on the latter. Or else let the qualities, &c. depend on substance; then it follows that, as they are present where substance is present, and absent where it is absent, substance only exists, and, according to its various forms, becomes the object of different terms and conceptions (such as quality, action, &c.); just as Devadatta, for instance, according to the conditions in which he finds himself is the object of various conceptions and names. But this latter alternative would involve the acceptation of the Sânkhya doctrine 1 and the abandonment of the Vaiseshika standpoint.--But (the Vaiseshika may say) smoke also is different from fire and yet it is dependent on it.--True, we reply; but we ascertain the difference of smoke and fire from the fact of their being apperceived in separation. Substance and quality, on the other hand, are not so apperceived; for when we are conscious of a white blanket, or a red cow, or a blue lotus, the substance is in each case cognised by means of the quality; the latter therefore has its Self in the substance. The same reasoning applies to action, generality, particularity, and inherence.
If you (the Vaiseshika) say that qualities, actions, &c. (although not non-different from substances) may yet depend on the latter because substances and qualities stand in the relation of one not being able to exist without the other (ayutasiddhi 2); we point out that things which are
ayutasiddha must either be non-separate in place, or non-separate in time, or non-separate in nature, and that none of these alternatives agrees with Vaiseshika principles. For the first alternative contradicts your own assumptions according to which the cloth originating from the threads occupies the place of the threads only, not that of the cloth, while the qualities of the cloth, such as its white colour, occupy the place of the cloth only, not that of the threads. So the Vaiseshika-sûtras say (I, 1, 10), 'Substances originate another substance and qualities another quality.' The threads which constitute the causal substance originate the effected substance, viz. the cloth, and the qualities of the threads, such as white colour, &c., produce in the cloth new corresponding qualities. But this doctrine is clearly contradicted by the assumption of substance and quality being non-separate in place--If, in the second place, you explain ayutasiddhatva as non-separation in time, it follows also that, for instance, the right and the left horn of a cow would be ayutasiddha.--And if, finally, you explain it to mean 'non-separation in character,' it is impossible to make any further distinction between the substance and the quality, as then quality is conceived as being identical with substance.
Moreover, the distinction which the Vaiseshikas make between conjunction (samyoga) as being the connexion of things which can exist separately, and inherence (samavâya) as being the connexion of things which are incapable of separate existence is futile, since the cause which exists before the effect 1 cannot be said to be incapable of separate existence. Perhaps the Vaiseshika will say that his definition refers to one of the two terms only, so that samavâya is the connexion, with the cause, of the effect which is incapable of separate existence. But this also is of no avail; for as a connexion requires two terms, the effect as long as it has not yet entered into being cannot be connected with the cause. And it would be equally unavailing to say that the effect enters into the connexion after it has begun to exist; for if the Vaiseshika admits that the effect
may exist previous to its connexion with the cause, it is no longer ayutasiddha (incapable of separate existence), and thereby the principle that between effect and cause conjunction and disjunction do not take place is violated. 1 And 2 just as conjunction, and not samavâya, is the connexion in which every effected substance as soon as it has been produced stands with the all-pervading substances as ether, &c.--although no motion has taken place on the part of the effected substance--so also the connexion of the effect with the cause will be conjunction merely, not samavâya.
Nor is there any proof for the existence of any connexion, samavâya or samyoga, apart from the things which it connects. If it should be maintained that samyoga and samavâya have such an existence because we observe that there are names and ideas of them in addition to the names and ideas of the things connected, we point out that one and the same thing may be the subject of several names and ideas if it is considered in its relations to what lies without it. Devadatta although being one only forms the object of many different names and notions according as he is considered in himself or in his relations to others; thus he is thought and spoken of as man, Brâhmana learned in the Veda, generous, boy, young man, old man, father, son, grandson, brother, son-in-law. &c. So, again, one and the same stroke is, according to the place it is connected with, spoken of and conceived as meaning either ten, or hundred, or thousand, &c. Analogously, two connected things are not only conceived and denoted as connected things, but in addition constitute the object of the ideas and terms 'conjunction' or 'inherence' which however do not prove
themselves to be separate entities.--Things standing thus, the non-existence of separate entities (conjunction, &c.), which entities would have to be established on the ground of perception, follows from the fact of their non- perception.
Nor, again 1, does the circumstance of the word and idea of connexion having for its object the things connected involve the connexion's permanent existence, since we have already shown above that one thing may, on account of its relations to other things, be conceived and denoted in different ways.
Further 2, conjunction cannot take place between the atoms, the soul, and the internal organ, because they have no parts; for we observe that conjunction takes place only of such substances as consist of parts. If the Vaiseshika should say that parts of the atoms, soul and mind may be assumed (in order to explain their alleged conjunction), we remark that the assumption of actually non-existing things would involve the result that anything might be established; for there is no restrictive rule that only such and such non-existing things--whether contradictory to reason or not--should be assumed and not any other, and assumptions depend on one's choice only and may be carried to any extent. If we once allow assumptions, there is no reason why there should not be assumed a further hundred or thousand things, in addition to the six categories assumed by the Vaiseshikas. Anybody might then assume anything, and we could neither stop a compassionate man from assuming that this transmigratory world which is the cause of so much misery to living beings is not to be, nor a malicious man from assuming that even the released souls are to enter on a new cycle of existences.
Further, it is not possible that a binary atomic compound, which consists of parts, should be connected with the simple indivisible atoms by an intimate connexion (samslesha) any more than they can thus be connected with ether; for between ether and earth, &c. there does not exist that kind of intimate connexion which exists, for instance, between wood and varnish 1.
Let it then be said (the Vaiseshika resumes) that the samavâya relation must be assumed, because otherwise the relation of that which abides and that which forms the abode--which relation actually exists between the effected substance and the causal substance--is not possible.--That would, we reply, involve the vice of mutual dependence; for only when the separateness of cause and effect is established, the relation of the abode and that which abides can be established; and only when the latter relation is established, the relation of separateness can be established. For the Vedântins acknowledge neither the separateness of cause and effect, nor their standing to each other in the relation of abode and thing abiding, since according to their doctrine the effect is only a certain state of the cause 2.--Moreover, as the atoms are limited (not of infinite extension), they must in reality consist of as many parts as we acknowledge regions of space 3, whether those be six or eight or ten, and consequently they cannot be permanent; conclusions contrary to the Vaiseshika doctrine of the indivisibility and permanency of the atoms.--If the Vaiseshika replies that those very parts which are owing to the existence of the different regions of space are his (indestructible)
atoms; we deny that because all things whatever, forming a series of substances of ever-increasing minuteness, are capable of dissolution, until the highest cause (Brahman) is reached. Earth--which is, in comparison with a binary compound, the grossest thing of all--undergoes decomposition; so do the substances following next which belong to the same class as earth; so does the binary compound; and so does, finally, the atom which (although the minutest thing of all) still belongs to the same general class (i.e. matter) with earth, &c. The objection (which the Vaiseshika might possibly raise here again) that things can be decomposed only by the separation of their parts 1, we have already disposed of above, where we pointed out that decomposition may take place in a manner analogous to the melting of ghee. Just as the hardness of ghee, gold, and the like, is destroyed in consequence of those substances being rendered liquid by their contact with fire, no separation of the parts taking place all the while; so the solid shape of the atoms also may be decomposed by their passing back into the indifferenced condition of the highest cause. In the same way the origination of effects also is brought about not merely in the way of conjunction of parts; for we see that milk, for instance, and water originate effects such as sour milk and ice without there taking place any conjunction of parts.
It thus appears that the atomic doctrine is supported by very weak arguments only, is opposed to those scriptural passages which declare the Lord to be the general cause, and is not accepted by any of the authorities taking their stand on Scripture, such as Manu and others. Hence it is to be altogether disregarded by highminded men who have a regard for their own spiritual welfare.
395:1 The Sânkhyas looking on everything (except the soul) as being the pradhâna in various forms.--There is no need of assuming with Govindânanda that by the Sânkhya of the text we have to understand the Vedânta.
395:2 Yayor dvayor madhya ekam avinasyad aparâsritam evâvatishthate tâv ayutasiddhau yathâvayavâvayavinau.
396:1 The connexion of cause and effect is of course samavâya.
397:1 If the effect can exist before having entered into connexion with the cause, the subsequent connexion of the two is no longer samavâya but samyoga; and that contradicts a fundamental Vaiseshika principle.
397:2 This clause replies to the objection that only those connexions which have been produced by previous motion are to be considered conjunctions.
398:1 A clause meant to preclude the assumption that the permanent existence of the things connected involves the permanent existence of the connexion.
398:2 It having been shown above that atoms cannot enter into samyoga with each other, it is shown now that samyoga of the soul with the atoms cannot be the cause of the motion of the latter, and that samyoga of soul and manas cannot be the cause of cognition.
399:1 Ekasambandhyâkarshane yatra sambandhyantarâkarshanam tatra samsleshah, sa tu sâvayavânâm gatukâshthâdînâm drishto na tu niravayavaih sâvayavânâm, ato dvyanukasya sâvayavasya niravayavena paramânunâ sa nopapadyate. Brahmavidyâbh.
399:2 In answer to the question how, in that case, the practically recognised relation of abode, &c. existing between the cause and the effect is accounted for.
399:3 For they must in that case have a northern end, an eastern end, &c.
400:1 And that on that account the atoms which he considers as the ultimate simple constituents of matter cannot be decomposed.