"Panditāh, people who know the knowledge of the self don't grief", implies that self-knowledge is the solution for sorrow which represents samsārah (life of becoming). Due to mix-up between what is real me - ātmā and non-me - anātmā, this confusion become the basis of our sorrow. Therefore ātmā-anātmā-vivekah - analysis of differences between self and non-self is to be done. Arjuna' s sorrow is about the death of his kins, from that starting point, we did a brief negation of the physical body, senses and mind. They are not real me, because anything which I can identify is not me. Objectifier can never be the same entity as the objectified.
Q: If I am not the body, senses and mind, who am I? Am I the total ignorance or nothingness, just like in deep sleep, where there is no awareness of myself and others?
A: Some using deep sleep state to ascertain the ignorance nature of the self, but in Vedānta, deep sleep is an experience to establish the nature of awareness. The method is called avasthātrayaśāksi - witness of three states of experience, one of the methods of analysis about ātmā - self and anātmā - non-self. Anything which is inherent to me is my nature alone, just like the nature of water is liquid, it never ceases away from water. In the same time, if anything is incidental to me means it is not nature to me, just like the waviness in the water can come incidentally, it is not there all the time, therefore waviness is not nature of water.
We have three states of experience, jagrad - waking state, svapna - dream state, and susupti - deep sleep state. In the waking state, I identify with this physical body, mind and sense, anything within these activities is taking to be me alone. But physical body and senses are negated during dream state. Even in the dream we still carry our body and senses, but they are not the same one in waking state, they are purely projection of mind alone. Which can be negated is anātma - other than me, therefore physical body and senses are not me. But "I" who objectifies my body and senses in the waking state, continue as the same one who witnesses my dream state. In the dream state, mind is the major player, entire dream world is the manifestation of mind alone. But the very same mind also being negated when I fall in to the deep sleep state. Therefore I am not the mind. The same “I” who witness the dream, continue witness the deep sleep state. Therefore “I” the witness who survive in waking, dream and deep sleep state is the real self.
Q: If you said that I witness the deep sleep state, why I don't recall anything? Nothing I experienced there, how can you say that I was there to witness? That "I" might drop off also like the others.
A: In the deep sleep state neither senses are working like in waking state, nor mind is projecting like in dream state. Total non-experience is there, not because I wasn't there to experience, but because there is no activity for one to aware anything was there. Deep sleep state is just like me in the pitch-dark room, even my eyes are open and I know very well there is no defect with my eyes, I still couldn't see anything. I couldn't see anything doesn't mean I was not there to see. Sight doesn't take place because there is no external light falls on them. In the same manner during deep sleep state, I experienced nothingness because there is no other object nor objectifier other than me. The objectifier here is working as light to light up any object (bring the object become exist for me to experience). To light up the gross object we need senses to know their existence. To light up the senses, our mind is the light. To light up the mind, I the awareness is the light. And who light up the awareness? Awareness is cit-svarupah, of the nature of self-effulgence/self-illumine/self-evident, it is ātmā , and this ātmā is me.
Lets analyze on our experience itself. Do we know that we had a good sleep after waking up? We do. If I was not there, I will not know either I had a good sleep or not, and I don't even know that I don't know anything. When we are talking about total ignorance, means we don't even know we are ignorance. When I am ignorance about certain language like javanese, I know that I don't know that language. The absent of the knowledge of the language is aware by me. I the awareness was there lights up even the ignorance. In the same time I know nothing was there in the deep sleep state, because my nature which is awareness even light up the absent of anātma. And because I awareness was the only one there in the deep sleep, therefore I experience nothing but myself. This self is self-illumine, doesn't need other illuminator to prove its existence.
The same self which pass through waking, dream and deep sleep state also pass through childhood, youth and old age, even migrates from one body to another, is the self which is never change and never die. And why we are grieving for the self which is never die? When we said something is never die, we will refer it as eternal. We think eternal means having a long, long life. But it is not that the entity has born but never die. Anything which is born, will die. Birth is the marking of something was not there and become there; from un-manifest to manifest. This process is involved in the time. Anything that is time-bound, will change and we cannot stop it, because the nature of the time is to keep on changing. And the changing of physical body is having six-folds - sadvikārah, they are: asti - exist, jāyate - born, vardhate - grows, viparinamate - changes, apaksīyate - degenerates, and vinaśyati - perishes. Therefore the body which is anātma, will perishes, but the self - ātmā, will continue to be.
Therefore when we say self is eternal means there is no time where the self never exist. Non-existence - abhāva is not there for ātmā at all. From the analysis of three states of experience, we understand that there is no time for the self not to be exist, but non-self comes and goes in different states. This we were seeing from individual angle. When we are seeing from the total angle - universe, ātmā was there before the manifestation and will be there after the resolution of the world. It is supported by one of the sentence of Chandogya Upanishad, “It is said that before this creation there was only one thing, the sat-vastu, which was non-dual, one without a second, undifferentiated. Nothing else was there. From that sat-vastu, Brahman alone, everything has come and is non-separate from it. Nothing exist apart from sat.”
Let us understand what is the meaning of sat and asat. Sat is what exists independent of anything else and asat means something that does not exist independently. What doesn't exist independently? This is a pot made from clay. It came from clay and will go back to clay. Clay is the cause - kārana and pot is the product - kārya. A product doesn't exist independently apart from its cause. Therefore this pot cannot exist independently from clay. Pot is asat, therefore there is no real entity called pot apart from clay. Pot is just name and form (with its function). I even can say that this pot is not real, because the weight of the pot is the weight of clay, the temperature of the pot is temperature of clay, and the smell of the pot is smell of clay. Therefore this name and form "pot" is just an idea with its function which doesn't have independent existence. This is called asat. The entire creation itself is asat, because it depends on sat-vastu to exist.