nasato vidyate bhavo
nabhavo vidyate satah
ubhayor api drsto ’ntas
tv anayos tattva-darshibhih
Those who are seers of the truth have concluded that of the nonexistent [the material body] there is no endurance and of the eternal [the soul] there is no change. This they have concluded by studying the nature of both.
Commentary by Srila Prabhupada
There is no endurance of the changing body. That the body is changing every moment by the actions and reactions of the different cells is admitted by modern medical science; and thus growth and old age are taking place in the body. But the spirit soul exists permanently, remaining the same despite all changes of the body and the mind. That is the difference between matter and spirit. By nature, the body is ever changing, and the soul is eternal. This conclusion is established by all classes of seers of the truth, both impersonalist and personalist. In the Vishnu Purana (2.12.38) it is stated that Vishnu and His abodes all have self-illuminated spiritual existence (jyotimsi vishnur bhuvanani vishnuh). The words existent and nonexistent refer only to spirit and matter. That is the version of all seers of truth.
This is the beginning of the instruction by the Lord to the living entities who are bewildered by the influence of ignorance. Removal of ignorance involves the reestablishment of the eternal relationship between the worshiper and the worshipable and the consequent understanding of the difference between the part-and-parcel living entities and the Supreme Personality of Godhead. One can understand the nature of the Supreme by thorough study of oneself, the difference between oneself and the Supreme being understood as the relationship between the part and the whole. In the Vedanta-sutras, as well as in the Srimad-Bhagavatam, the Supreme has been accepted as the origin of all emanations. Such emanations are experienced by superior and inferior natural sequences. The living entities belong to the superior nature, as it will be revealed in the Seventh Chapter. Although there is no difference between the energy and the energetic, the energetic is accepted as the Supreme, and energy or nature is accepted as the subordinate. The living entities, therefore, are always subordinate to the Supreme Lord, as in the case of the master and the servant, or the teacher and the taught. Such clear knowledge is impossible to understand under the spell of ignorance, and to drive away such ignorance the Lord teaches the Bhagavad-gita for the enlightenment of all living entities for all time.
Commentary by Sri Visvanatha Cakravarti Thakur
This verse describes the results for those who have attained the level of discrimination. Actually as sruti says, the soul is not attached to matter: asango hi ayam purusah. (Brhad Aranyaka Upanisad 4.3.15) Thus, the jiva does not have a relationship with the subtle or gross bodies and its products such as lamentation and bewilderment. This relationship is caused by ignorance. This is explained in this verse.
There is no existence (bhavah) of the body (asatah), the shelter of lamentation and bewilderment, because of its opposite nature to the soul, in which these do not exist. And there is no destruction of the jiva with its real form (satah). The conclusion (antah) about both of these—the body and the soul – is seen by the seers of truth. By this, there will be no lamentation or bewilderment arising from seeing body and things related to the body because of the eternal, indestructible soul in Bhisma and others of the opposing party as well as you and your allies. How can Bhisma and others be destroyed, and why do you lament for them?