The Vedanta Sutras, commentary by Sankaracharya (SBE34), tr. by George Thibaut  at sacred-texts.com
28. The non-existence (of external things) cannot be maintained, on account of (our) consciousness (of them).
There having been brought forward, in what precedes, the various objections which lie against the doctrine of the reality of the external world (in the Bauddha sense), such as the impossibility of accounting for the existence of aggregates, &c., we are now confronted by those Bauddhas who maintain that only cognitions (or ideas, vigñâna) exist.--The doctrine of the reality of the external world was indeed propounded by Buddha conforming himself to the mental state of some of his disciples whom he perceived to be attached to external things; but it does not represent his own true view according to which cognitions alone are real.
According to this latter doctrine the process, whose constituting members are the act of knowledge, the object of knowledge, and the result of knowledge 1, is an altogether internal one, existing in so far only as it is connected with the mind (buddhi). Even if external things existed, that process could not take place but in connexion with the mind. If, the Bauddhas say, you ask how it is known that that entire process is internal and that no outward things exist apart from consciousness, we reply that we base our
doctrine on the impossibility of external things. For if external things are admitted, they must be either atoms or aggregates of atoms such as posts and the like. But atoms cannot be comprehended under the ideas of posts and the like, it being impossible for cognition to represent (things as minute as) atoms. Nor, again, can the outward things be aggregates of atoms such as pillars and the like, because those aggregates can neither be defined as different nor as non-different from the atoms 1.--In the same way we can show that the external things are not universals and so on 2.
Moreover, the cognitions--which are of a uniform nature only in so far as they are states of consciousness--undergo, according to their objects, successive modifications, so that there is presented to the mind now the idea of a post, now the idea of a wall, now the idea of a jar, and so on. Now this is not possible without some distinction on the part of the ideas themselves, and hence we must necessarily admit that the ideas have the same forms as their objects. But if we make this admission, from which it follows that the form of the objects is determined by the ideas, the hypothesis of the existence of external things becomes altogether gratuitous. From the fact, moreover, of our always being conscious of the act of knowledge and the object of knowledge simultaneously it follows that the two are in reality identical. When we are conscious of the one we are conscious of the other also; and that would not happen if the two were essentially distinct, as in that case there would be nothing to prevent our being conscious of one apart from the other. For this reason also we maintain that there are no outward things.--
[paragraph continues] Perception is to be considered as similar to a dream and the like. The ideas present to our minds during a dream, a magical illusion, a mirage and so on, appear in the twofold form of subject and object, although there is all the while no external object; hence we conclude that the ideas of posts and the like which occur in our waking state are likewise independent of external objects; for they also are simply ideas.--If we be asked how, in the absence of external things, we account for the actual variety of ideas, we reply that that variety is to be explained from the impressions left by previous ideas 1. In the beginningless samsâra ideas and mental impressions succeed each other as causes and effects, just as the plant springs from the seed and seeds are again produced from the plant, and there exists therefore a sufficient reason for the variety of ideas actually experienced. That the variety of ideas is solely due to the impressions left on the mind by past ideas follows, moreover, from the following affirmative and negative judgments: we both (the Vedântins as well as the Bauddhas) admit that in dreams, &c. there presents itself a variety of ideas which arise from mental impressions, without any external object; we (the Bauddhas) do not admit that any variety of ideas can arise from external objects, without mental impressions.--Thus we are again led to conclude that no outward things exist.
To all this we (the Vedântins) make the following reply.--The non-existence of external things cannot be maintained because we are conscious of external things. In every act of perception we are conscious of some external thing corresponding to the idea, whether it be a post or a wall or a piece of cloth or a jar, and that of which we are conscious cannot but exist. Why should we pay attention to the words of a man who, while conscious of an outward thing through its approximation to his senses, affirms that he is conscious of no outward thing, and that no such thing exists,
any more than we listen to a man who while he is eating and experiencing the feeling of satisfaction avers that he does not eat and does not feel satisfied?--If the Bauddha should reply that he does not affirm that he is conscious of no object but only that he is conscious of no object apart from the act of consciousness, we answer that he may indeed make any arbitrary statement he likes, but that he has no arguments to prove what he says. That the outward thing exists apart from consciousness, has necessarily to be accepted on the ground of the nature of consciousness itself. Nobody when perceiving a post or a wall is conscious of his perception only, but all men are conscious of posts and walls and the like as objects of their perceptions. That such is the consciousness of all men, appears also from the fact that even those who contest the existence of external things bear witness to their existence when they say that what is an internal object of cognition appears like something external. For they practically accept the general consciousness, which testifies to the existence of an external world, and being at the same time anxious to refute it they speak of the external things as 'like something external.' If they did not themselves at the bottom acknowledge the existence of the external world, how could they use the expression 'like something external?' No one says, 'Vishnumitra appears like the son of a barren mother.' If we accept the truth as it is given to us in our consciousness, we must admit that the object of perception appears to us as something external, not like something external.--But--the Bauddha may reply--we conclude that the object of perception is only like something external because external things are impossible.--This conclusion we rejoin is improper, since the possibility or impossibility of things is to be determined only on the ground of the operation or non-operation of the means of right knowledge; while on the other hand, the operation and non-operation of the means of right knowledge are not to be made dependent on preconceived possibilities or impossibilities. Possible is whatever is apprehended by perception or some other means of proof; impossible is what is not so apprehended. Now the external things are,
according to their nature, apprehended by all the instruments of knowledge; how then can you maintain that they are not possible, on the ground of such idle dilemmas as that about their difference or non-difference from atoms?--Nor, again, does the non-existence of objects follow from the fact of the ideas having the same form as the objects; for if there were no objects the ideas could not have the forms of the objects, and the objects are actually apprehended as external.--For the same reason (i.e. because the distinction of thing and idea is given in consciousness) the invariable concomitance of idea and thing has to be considered as proving only that the thing constitutes the means of the idea, not that the two are identical. Moreover, when we are conscious first of a pot and then of a piece of cloth, consciousness remains the same in the two acts while what varies are merely the distinctive attributes of consciousness; just as when we see at first a black and then a white cow, the distinction of the two perceptions is due to the varying blackness and whiteness while the generic character of the cow remains the same. The difference of the one permanent factor (from the two--or more--varying factors) is proved throughout by the two varying factors, and vice versâ the difference of the latter (from the permanent factor) by the presence of the one (permanent factor). Therefore thing and idea are distinct. The same view is to be held with regard to the perception and the remembrance of a jar; there also the perception and the remembrance only are distinct while the jar is one and the same; in the same way as when conscious of the smell of milk and the taste of milk we are conscious of the smell and taste as different things but of the milk itself as one only.
Further, two ideas which occupy different moments of time and pass away as soon as they have become objects of consciousness cannot apprehend--or be apprehended by--each other. From this it follows that certain doctrines forming part of the Bauddha system cannot be upheld; so the doctrine that ideas are different from each other; the doctrine that everything is momentary, void, &c.; the doctrine of the distinction of individuals and classes; the
doctrine that a former idea leaves an impression giving rise to a later idea; the doctrine of the distinction, owing to the influence of Nescience, of the attributes of existence and non-existence; the doctrine of bondage and release (depending on absence and presence of right knowledge) 1.
Further, if you say that we are conscious of the idea, you must admit that we are also conscious of the external thing. And if you rejoin that we are conscious of the idea on its own account because it is of a luminous nature like a lamp, while the external thing is not so; we reply that by maintaining the idea to be illuminated by itself you make yourself guilty of an absurdity no less than if you said that fire burns itself. And at the same time you refuse to accept the common and altogether rational opinion that we are conscious of the external thing by means of the idea different from the thing! Indeed a proof of extraordinary philosophic insight!--It cannot, moreover, be asserted in any way that the idea apart from the thing is the object of our consciousness; for it is absurd to speak of a thing as the object of its own activity. Possibly you (the Bauddha) will rejoin that, if the idea is to be apprehended by something different from it, that something also must be apprehended by something different and so on ad infinitum. And, moreover, you will perhaps object that as each cognition is of an essentially illuminating nature like a lamp, the assumption of a further cognition is uncalled for; for as they are both equally illuminating the one cannot give light to the other.--But both these objections are unfounded. As the idea only is apprehended, and there is consequently no necessity to assume something to apprehend the Self which witnesses the idea (is conscious of the idea), there results no regressus ad infinitum. And the witnessing Self and the idea are of an essentially different nature, and may therefore stand to each other in the relation of knowing subject and object known. The existence of the witnessing
[paragraph continues] Self is self-proved and cannot therefore be denied.--Moreover, if you maintain that the idea, lamplike, manifests itself without standing in need of a further principle to illuminate it, you maintain thereby that ideas exist which are not apprehended by any of the means of knowledge, and which are without a knowing being; which is no better than to assert that a thousand lamps burning inside some impenetrable mass of rocks manifest themselves. And if you should maintain that thereby we admit your doctrine, since it follows from what we have said that the idea itself implies consciousness; we reply that, as observation shows, the lamp in order to become manifest requires some other intellectual agent furnished with instruments such as the eye, and that therefore the idea also, as equally being a thing to be illuminated, becomes manifest only through an ulterior intelligent principle. And if you finally object that we, when advancing the witnessing Self as self-proved, merely express in other words the Bauddha tenet that the idea is self-manifested, we refute you by remarking that your ideas have the attributes of originating, passing away, being manifold, and so on (while our Self is one and permanent).--We thus have proved that an idea, like a lamp, requires an ulterior intelligent principle to render it manifest.
418:1 According to the vigñânavâdin the cognition specialised by its various contents, such as, for instance, the idea of blue colour is the object of knowledge; the cognition in so far as it is consciousness (avabhâsa) is the result of knowledge; the cognition in so far as it is power is mâna, knowledge; in so far as it is the abode of that power it is pramâtri, knowing subject.
419:1 If they are said to be different from the atoms they can no longer be considered as composed of atoms; if they are non-different from atoms they cannot be the cause of the mental representations of gross non-atomic bodies.
419:2 Avayavâvayavirûpo vâhyo#rtho nâsti ken mâ bhûd gâtivyaktyâdirûpas tu syâd ity âsankyâha evam iti. Gâtyâdînâm vyaktyâdînâm kâtyantabhinnatve svâtantryaprasangâd atyantâbhinnatve tadvadevâtadbhâvâd bhinnâbhinnatvasya viruddhatvâd avayavâvayavibhedavag gâtivyaktyâdibhedo#pi nâstîty arthah.
420:1 Vâsanâ, above translated by mental impression, strictly means any member of the infinite series of ideas which precedes the present actual idea.
423:1 For all these doctrines depend on the comparison of ideas which is not possible unless there be a permanent knowing subject in addition to the transitory ideas.