The Vedanta Sutras, commentary by Sankaracharya (SBE34), tr. by George Thibaut  at sacred-texts.com
11. The 'two entered into the cave' (are the individual soul and the highest Self), for the two are (intelligent) Selfs (and therefore of the same nature), as it is seen (that numerals denote beings of the same nature).
In the same Kathavallî we read (I, 3, 1), 'There are the two drinking the reward of their works in the world, (i.e. the body,) entered into the cave, dwelling on the highest summit. Those who know Brahman call them shade and light; likewise those householders who perform the Trinâkiketa sacrifice.'
Here the doubt arises whether the mind (buddhi) and the individual soul are referred to, or the individual soul and the highest Self. If the mind and the individual soul, then the individual soul is here spoken of as different from the aggregate of the organs of action, (i.e. the body,) among which the mind occupies the first place. And a statement on this point is to be expected, as a question concerning it is asked in a preceding passage, viz. I, 1, 20, 'There is that doubt when a man is dead--some saying he is; others, he is not. This I should like to know taught by thee; this is the third of my boons.' If, on the other hand, the passage refers to the individual soul and the highest Self, then it intimates that the highest Self is different from the individual soul; and this also requires to be declared here, on account of the question contained in the passage (I, 2, 14), 'That which thou seest as different from religious duty and its contrary, from effect and cause, from the past and the future, tell me that.'
The doubt to which the passage gives rise having thus
been stated, a caviller starts the following objection: neither of the stated views can be maintained.--Why?--On account of the characteristic mark implied in the circumstance that the two are said to drink, i.e. to enjoy, the fruit of their works in the world. For this can apply to the intelligent individual soul only, not to the non-intelligent buddhi. And as the dual form 'drinking' (pibantau) shows that both are drinking, the view of the two being the buddhi and the individual soul is not tenable. For the same reason the other opinion also, viz. of the two being the individual soul and the highest Self, cannot be maintained; for drinking (i.e. the fruition of reward) cannot be predicated of the highest Self, on account of the mantra (Mu. Up. III, 1, 1), 'The other looks on without eating.'
These objections, we reply, are without any force. Just as we see that in phrases such as 'the men with the umbrella (lit. the umbrella-men) are walking,' the attribute of being furnished with an umbrella which properly speaking belongs to one man only is secondarily ascribed to many, so here two agents are spoken of as drinking because one of them is really drinking. Or else we may explain the passage by saying that, while the individual soul only drinks, the Lord also is said to drink because he makes the soul drink. On the other hand, we may also assume that the two are the buddhi and the individual soul, the instrument being figuratively spoken of as the agent--a figure of speech exemplified by phrases such as 'the fuel cooks (the food).' And in a chapter whose topic is the soul no two other beings can well be represented as enjoying rewards. Hence there is room for the doubt whether the two are the buddhi and the individual soul, or the individual soul and the highest Self.
Here the pûrvapakshin maintains that the former of the two stated views is the right one, because the two beings are qualified as 'entered into the cave.' Whether we understand by the cave the body or the heart, in either case the buddhi and the individual soul may be spoken of as 'entered into the cave.' Nor would it be appropriate, as long as another interpretation is possible, to assume
that a special place is here ascribed to the omnipresent Brahman. Moreover, the words 'in the world of their good deeds' show that the two do not pass beyond the sphere of the results of their good works. But the highest Self is not in the sphere of the results of either good or bad works; according to the scriptural passage, 'It does not grow larger by works nor does it grow smaller.' Further, the words 'shade and light' properly designate what is intelligent and what is non-intelligent, because the two are opposed to each other like light and shade. Hence we conclude that the buddhi and the individual soul are spoken of.
To this we make the following reply:--In the passage under discussion the individual soul (vigñânâtman) and the highest Self are spoken of, because these two, being both intelligent Selfs, are of the same nature. For we see that in ordinary life also, whenever a number is mentioned, beings of the same class are understood to be meant; when, for instance, the order is given, 'Look out for a second (i.e. a fellow) for this bull,' people look out for a second bull, not for a horse or a man. So here also, where the mention of the fruition of rewards enables us to determine that the individual soul is meant, we understand at once, when a second is required, that the highest Self has to be understood; for the highest Self is intelligent, and therefore of the same nature as the soul.--But has it not been said above that the highest Self cannot be meant here, on account of the text stating that it is placed in the cave?--Well, we reply, sruti as well as smriti speaks of the highest Self as placed in the cave. Compare, for instance (Ka. Up. I, 2, 12), 'The Ancient who is hidden in the cave, who dwells in the abyss;' Taitt. Up. II, 1, 'He who knows him hidden in the cave, in the highest ether;' and, 'Search for the Self entered into the cave.' That it is not contrary to reason to assign to the omnipresent Brahman a special locality, for the purpose of clearer perception, we have already demonstrated. The attribute of existing in the world of its good works, which properly belongs to one of the two only, viz. to the individual soul, may be assigned to both, analogously to the case of the men, one of whom carries an umbrella. Their being compared to light
and shade also is unobjectionable, because the qualities of belonging and not belonging to this transmigratory world are opposed to each other, like light and shade; the quality of belonging to it being due to Nescience, and the quality of not belonging to it being real. We therefore understand by the two 'entered into the cave,' the individual soul and the highest Self.--Another reason for this interpretation follows.