Krishna now strengthens the foundational knowledge about our identity with some axiomatic principles.
For the temporary [material body] (asato), there is (vidyate) no (na) real existence (bhāvo) and for the eternal [soul] (sataḥ), there is (vidyate) no (na) cessation in existence (abhāvo). Indeed (tv), the seers of the truth (tattva-darśibhiḥ) have arrived at both (ubhayor api) of these (anayos) conclusions (antas) by their vision (dṛṣṭo). (BG 2.16) Krishna elaborates on each of these two conclusions in the following two verses – one pertaining to the eternal soul (BG 2.17) and the other pertaining to the perishing body (BG 2.18).
We should know (tu viddhi) that that (tad) which (yena) pervades (tatam) all (sarvam) this [body] (idaṁ) to be indestructible (avināśi). No one (na kaścit) can (arhati) cause (kartum) destruction (vināśam) of that (asya) imperishable soul (avyayasya). (BG 2.17) That which pervades the body is consciousness. So, the imperishable soul is the seat of our consciousness.
These (ime) bodies (dehā) of the indestructible (anāśino), immeasurable (prameyasya), and eternal (nityasya) embodied soul (śarīriṇaḥ) are said to (uktāḥ) surely end (antavanta). Therefore (tasmād), Arjuna (bhārata) should fight (yudhyasva). (BG 2.18)
In summary, the perishable body cannot be saved while the eternal soul, which gives rise to consciousness within the body, cannot be destroyed. Therefore, while navigating our journey within the temporary material body and in the temporary material world, we should nurture that which is eternal. In other words, we should not neglect the needs of the soul, which is our essential nature.