The Vedanta Sutras, commentary by Sankaracharya (SBE34), tr. by George Thibaut  at sacred-texts.com
30. And on account of the equality of names and forms there is no contradiction (to the eternity of the word of the Veda) in the renovation (of the world); as is seen from Sruti and Smriti.
If--the pûrvapakshin resumes--the individual gods and so on did, like the individual animals, originate and pass away in an unbroken succession so that there would be no break of the course of practical existence including denominations, things denominated and agents denominating; the connexion (between word and thing) would be eternal, and the objection as to a contradiction with reference to the word (raised in Sûtra 27) would thereby be refuted. But if, as Sruti and Smriti declare, the whole threefold
world periodically divests itself of name and form, and is entirely dissolved (at the end of a kalpa), and is after that produced anew; how can the contradiction be considered to have been removed?
To this we reply: 'On account of the sameness of name and form.'--Even then the beginninglessness of the world will have to be admitted (a point which the teacher will prove later on: II, 1, 36). And in the beginningless samsâra we have to look on the (relative) beginning, and the dissolution connected with a new kalpa in the same light in which we look on the sleeping and waking states, which, although in them according to Scripture (a kind of) dissolution and origination take place, do not give rise to any contradiction, since in the later waking state (subsequent to the state of sleep) the practical existence is carried on just as in the former one. That in the sleeping and the waking states dissolution and origination take place is stated Kaush. Up. III, 3, 'When a man being asleep sees no dream whatever he becomes one with that prâna alone. Then speech goes to him with all names, the eye with all forms, the ear with all sounds, the mind with all thoughts. And when he awakes then, as from a burning fire, sparks proceed in all directions, thus from that Self the prânas proceed, each towards its place; from the prânas the gods, from the gods the worlds.'
Well, the pûrvapakshin resumes, it may be that no contradiction arises in the case of sleep, as during the sleep of one person the practical existence of other persons suffers no interruption, and as the sleeping person himself when waking from sleep may resume the very same form of practical existence which was his previously to his sleep. The case of a mahâpralaya (i. e. a general annihilation of the world) is however a different one, as then the entire current of practical existence is interrupted, and the form of existence of a previous kalpa can be resumed in a subsequent kalpa no more than an individual can resume that form of existence which it enjoyed in a former birth.
This objection, we reply, is not valid. For although a mahâpralaya does cut short the entire current of practical
existence, yet, by the favour of the highest Lord, the Lords (îsvara), such as Hiranyagarbha and so on, may continue the same form of existence which belonged to them in the preceding kalpa. Although ordinary animated beings do not, as we see, resume that form of existence which belonged to them in a former birth; still we cannot judge of the Lords as we do of ordinary beings. For as in the series of beings which descends from man to blades of grass a successive diminution of knowledge, power, and so on, is observed--although they all have the common attribute of being animated--so in the ascending series extending from man up to Hiranyagarbha, a gradually increasing manifestation of knowledge, power, &c. takes place; a circumstance which Sruti and Smriti mention in many places, and which it is impossible to deny. On that account it may very well be the case that the Lords, such as Hiranyagarbha and so on, who in a past kalpa were distinguished by superior knowledge and power of action, and who again appear in the present kalpa, do, if favoured by the highest Lord, continue (in the present kalpa) the same kind of existence which they enjoyed in the preceding kalpa; just as a man who rises from sleep continues the same form of existence which he enjoyed previously to his sleep. Thus Scripture also declares, 'He who first creates Brahman (Hiranyagarbha) and delivers the Vedas to him, to that God who is the light of his own thoughts, I, seeking for release, go for refuge' (Svet. Up. VI, 18). Saunaka and others moreover declare (in the Anukramanîs of the Veda) that the ten books (of the Rig-veda) were seen by Madhukkhandas and other rishis. 1And, similarly, Smriti tells us, for every Veda, of men of exalted mental vision (rishis) who 'saw' the subdivisions of their respective Vedas, such as kândas and so on. Scripture also declares that the performance of the sacrificial action by means of the mantra is to be preceded by the knowledge of the rishi and so on, 'He who makes another person sacrifice or read by means of a mantra of which he
does not know the rishi, the metre, the divinity, and the Brâhmana, runs against a post, falls into a pit 1, &c. &c., therefore one must know all those matters for each mantra' (Ârsheya Brâhmana, first section).--Moreover, religious duty is enjoined and its opposite is forbidden, in order that the animate beings may obtain pleasure and escape pain. Desire and aversion have for their objects pleasure and pain, known either from experience or from Scripture, and do not aim at anything of a different nature. As therefore each new creation is (nothing but) the result of the religious merit and demerit (of the animated beings of the preceding creation), it is produced with a nature resembling that of the preceding creation. Thus Smriti also declares, 'To whatever actions certain of these (animated beings) had turned in a former creation, to the same they turn when created again and again. Whether those actions were harmful or harmless, gentle or cruel, right or wrong, true or untrue, influenced by them they proceed; hence a certain person delights in actions of a certain kind.'--Moreover, this world when being dissolved (in a mahâpralaya) is dissolved to that extent only that the potentiality (sakti) of the world remains, and (when it is produced again) it is produced from the root of that potentiality; otherwise we should have to admit an effect without a cause. Nor have we the right to assume potentialities of different kind (for the different periods of the world). Hence, although the series of worlds from the earth upwards, and the series of different classes of animate beings such as gods, animals, and men, and the different conditions based on caste, âsrama, religious duty and fruit (of works), although all these we say are again and again interrupted and thereupon produced anew; we yet have to understand that they are, in the beginningless samsara, subject to a certain determinateness analogous to the determinateness governing the connexion between the senses and their objects. For it is impossible to imagine that the relation of senses and sense-objects should be a different one in different creations, so
that, for instance, in some new creation a sixth sense and a corresponding sixth sense-object should manifest themselves. As, therefore, the phenomenal world is the same in all kalpas and as the Lords are able to continue their previous forms of existence, there manifest themselves, in each new creation, individuals bearing the same names and forms as the individuals of the preceding creations, and, owing to this equality of names and forms, the admitted periodical renovations of the world in the form of general pralayas and general creations do not conflict with the authoritativeness of the word of the Veda. The permanent identity of names and forms is declared in Sruti as well as Smriti; compare, for instance, Rik. Samh. X, 190, 3, 'As formerly the creator ordered sun and moon, and the sky, and the air, and the heavenly world;' which passage means that the highest Lord arranged at the beginning of the present kalpa the entire world with sun and moon, and so on, just as it had been arranged in the preceding kalpa. Compare also Taitt. Brâhm. III, 1, 4, 1, 'Agni desired: May I become the consumer of the food of the gods; for that end he offered a cake on eight potsherds to Agni and the Krittikâs.' This passage, which forms part of the injunction of the ishti to the Nakshatras, declares equality of name and form connecting the Agni who offered and the Agni to whom he offered 1.
Smriti also contains similar statements to be quoted here; so, for instance, 'Whatever were the names of the rishis and their powers to see the Vedas, the same the Unborn one again gives to them when they are produced afresh at the end of the night (the mahâpralaya). As the various signs of the seasons return in succession in their due time, thus the same beings again appear in the different yugas. And of whatever individuality the gods of the
past ages were, equal to them are the present gods in name and form.'
213:1 Which circumstance proves that exalted knowledge appertains not only to Hiranyagarbha, but to many beings.
214:1 Viz. naraka, the commentaries say.
215:1 Asmin kalpe sarveshâm prâninâm dâhapâkaprakâsakârî yo#yam agnir drisyate so#yam agnih pûrvasmin kalpe manushyah san devatvapadaprâpakam karmânushthâyâsmin kalpa etag ganma labdhavân atah pûrvasmin kalpe sa manushyo bhâvinîm samgñâm âsrityâgnir iti vyapadisyate.--Sâyana on the quoted passage.