The Vedanta Sutras, commentary by Sankaracharya (SBE34), tr. by George Thibaut  at sacred-texts.com
25. And on account of remembrance.
The philosopher who maintains that all things are momentary only would have to extend that doctrine to the perceiving person (upalabdhri) also; that is, however, not possible, on account of the remembrance which is consequent on the original perception. That remembrance can take place only if it belongs to the same person who previously made the perception; for we observe that what one man has experienced is not remembered by another man. How, indeed, could there arise the conscious state expressed in the sentences, 'I saw that thing, and now I see this thing,' if the seeing person were not in both cases the same? That the consciousness of recognition takes place only in the case of the observing and remembering subject being one, is a matter known to every one; for if there were, in the two cases, different subjects, the state of consciousness arising in the mind of the remembering person would be, 'I remember; another person made the observation.' But no such state of consciousness does arise.--When, on the other hand, such a state of consciousness does arise, then everybody knows that the person who made the original observation, and the person who remembers, are different persons, and then the state of consciousness is expressed as follows, 'I remember that that other person saw that and that.'--
[paragraph continues] In the case under discussion, however, the Vainâsika himself--whose state of consciousness is, 'I saw that and that'--knows that there is one thinking subject only to which the original perception as well as the remembrance belongs, and does not think of denying that the past perception belonged to himself, not any more than he denies that fire is hot and gives light.
As thus one agent is connected with the two moments of perception and subsequent remembrance, the Vainâsika has necessarily to abandon the doctrine of universal momentariness. And if he further recognises all his subsequent successive cognitions, up to his last breath, to belong to one and the same subject, and in addition cannot but attribute all his past cognitions, from the moment of his birth, to the same Self, how can he maintain, without being ashamed of himself, that everything has a momentary existence only? Should he maintain that the recognition (of the subject as one and the same) takes place on account of the similarity (of the different self-cognitions; each, however, being momentary only), we reply that the cognition of similarity is based on two things, and that for that reason the advocate of universal momentariness who denies the existence of one (permanent) subject able mentally to grasp the two similar things simply talks deceitful nonsense when asserting that recognition is founded on similarity. Should he admit, on the other hand, that there is one mind grasping the similarity of two successive momentary existences, he would thereby admit that one entity endures for two moments and thus contradict the tenet of universal momentariness.--Should it be said that the cognition 'this is similar to that' is a different (new) cognition, not dependent on the apperception of the earlier and later momentary existences, we refute this by the remark that the fact of different terms--viz. 'this' and 'that'--being used points to the existence of different things (which the mind grasps in a judgment of similarity). If the mental act of which similarity is the object were an altogether new act (not concerned with the two separate similar entities), the expression 'this is similar to that'
would be devoid of meaning; we should in that case rather speak of 'similarity' only.--Whenever (to add a general reflexion) something perfectly well known from ordinary experience is not admitted by philosophers, they may indeed establish their own view and demolish the contrary opinion by means of words, but they thereby neither convince others nor even themselves. Whatever has been ascertained to be such and such must also be represented as such and such; attempts to represent it as something else prove nothing but the vain talkativeness of those who make those attempts. Nor can the hypothesis of mere similarity being cognised account for ordinary empirical life and thought; for (in recognising a thing) we are conscious of it being that which we were formerly conscious of, not of it being merely similar to that. We admit that sometimes with regard to an external thing a doubt may arise whether it is that or merely is similar to that; for mistakes may be made concerning what lies outside our minds. But the conscious subject never has any doubt whether it is itself or only similar to itself; it rather is distinctly conscious that it is one and the same subject which yesterday had a certain sensation and to-day remembers that sensation.--For this reason also the doctrine of the Nihilists is to be rejected.