Atman and Brahman

 Advaita teaches that Atman/Self = subject = Brahman = True. 

anAtma = Object = Jagat = not True = appears to be true = illusion.

Ultimately Atmatva, Shivatva and even Advaitatva needs to be transcended as they point to qualities, to attain the unknowable / unthinkable nirguna, nirvishesha Brahman

Dvaita teaches that jIvAtman is not Brahman. In moksha the jiva attains it's own brahmatva or fullness / similar to parabrahman Vishnu.

Ishwara = Vishnu = Brahman = svatantra = independent truth.

Jiva = Atman = Infinite varieties = Paratantra = dependent truth (on Brahman).

Jada = Jagat = anAtma = Infinite varieties = Paratantra = dependent truth (on Brahman).

Interestingly Advaita and Dvaita are both based on the absolute nature of Atman/Brahman and the world of jiva/jada as AbhAsa/pratibimba/reflection of Brahman.

According to Advaita, the world is unreal because it is a reflection of the Atman/Brahman which is the original. But it also accepts that Atman/Brahman is the adhishTAna or the support for the jagat as a reflection. Just like the rope is the support or ground for the superimposed snake on the same. Jiva (as the self identified with the body) has no identification apart from the body which is the upAdhi. So when the upAdhi of body, which is a product of karma is gone the jiva merges with Brahman just like the space in the pot merges with the outer space or the reflection merges with the original. This merger is only apparent as it is already that.

But Dvaita argues that the world of multiplicity, as a reflection or dependent entity is dependently real,  as the jIva/Atma, as the upAdhi or medium is always real. The Jiva/Atma himself is a pratibimba or reflection of Brahman who is the original or Bimba. The jiva/Atma svaroopa is the upAdhi or medium also, like a mirror, in which Brahman is reflected as the antaryAmi. Every jiva has a svaroopa deha. So jiva svaroopa in Dvaita is essentially the body, in which Brahman is reflected. This makes it similar to Advaita with the only difference that the jiva svaroopa/body is dependently real.

V.Advaita teaches that Atman/chit and AnAtman/Achit and Brahman/nArAyaNa are different and real, but inseparably one like the body and soul. Identification of Atman/AnAtman culminates in Brahman just like identification of body like deva, man, women, human, animal and so on culminates in the indwelling soul.

Interestingly the body can also be taken as a reflection of the Atman/Brahman as the Self -  as it has properties that is opposed to the Atman. So this is compatible with Advaita and Dvaita where the world is taken to be vivarta / pratibimba respectively.

Atman and Brahman are two different words and so obviously with different meanings. So there cannot be any equation between them. But vedas teach the oneness of everything (sarvam) with Brahman and also the oneness of Atman (Self) with Brahman. 

This equation or identification between the two different words with different meanings is done based on the rule called sAmAnAdhikaraNyam in Sanskrit.

Advaita uses - bAdhAyAm sAmAnAdhikaraNyam where the attributes of jiva/embodied self and Ishwara/universal Self are removed to arrive at the pure impersonal conscious Self that is common between them.

V.Advaita uses - (Atma-Shareera) sAmAnAdhikaraNyam where Brahman alone is identified through all the many jiva and jada entities. 

Dvaita identifies every jiva/Atman and jada/anAtman and Ishwara Vishnu, separately. So all identifications are direct and so no sAmAnAdhikaraNyam is used. But still, Brahman is accepted to be known through every name/form - sarvanAma vAchya and sarvarUpavEdya. Also as Brahman is everywhere and indwelling in all as the antaryAmi - inner self, identification of every particular jiva/jada/name/form must culminate in Brahman who is everywhere. 

So for all practical purposes as long as one is embodied, the relation of Self and body between Brahman and the world must be valid in all views.

Reconciliation:

Every word has a meaning. Atman is a word with a meaning. So also is Brahman. Atman means the self. It is identified with whatever name/form it takes. If the jiva/self is in a stone it is a stone. If it is an animal's body it is an animal. In a human body it is human and in a devata's body it is a devata.

These identification keep changing depending on the body but atman is unchanging. Brahman is that which is everywhere, infinite. So, Atman whether it is embodied or not will always be in Brahman. Therefore it can be identified WITH Brahman at any point of time. It should be noted here that it is NOT Brahman also because the word and meaning are different. Atman is limited by anAtman and vice versa. But Brahman is unlimited or bhUmA and is everywhere. So the Vedic scripture declares Everything is Brahman - Sarvam khalvidam Brahma and this Atma is Brahma - ayamAtma Brahma.

Atman and anAtma are opposed to each other. But Brahman is un-opposed as all opposites are cognized in it. So it is essentially the sarvAtmA - the Self of all or paramAtmA which is in the Atman as well as in anAtma/prakriti. The jiva/Atma has to recognize and exist in this sarvAtma Brahman. Only then it will be a brahmachAri - brahmaNi charati - one who exists/moves in Brahman. In other words, the Self should expand beyond the body to include everything. Only then it becomes truely selfless bigger self or mahAtmA.

The Brahman that is indwelling in the Atman is the supreme AtmA - paramAtma. The same Brahman that is in prakriti / everything, takes the name Sarva. When that universal AtmA is identified everything is identified at once.

It should be noted that in Advaita, identity is only based on the lakshyArtha - indicative truth. Difference in literal truth or vAchyArtha is accepted though it comes under mithya or vyavahAra. So tattvamasi (you are that) and " atattvamasi / tvamtadadheenosi" (you are not that and you are dependent on that) both gets satisfied from the point of view of the embodied jivAtman.

Tatvamasi helps to identify  - nirguna brahman - the unknowable. Atattvamasi helps to establish the difference between saguna brahman and jiva - vAchyArtha - literal truth - leading to elimination of asura bhAva or I am God mentality. 

Objection:

This creates two Brahman with opposite qualities (one in the Atman as nirguna ) and the other in anAtma prakriti as saguna. 

Answer: Yes, but still that is not a problem. Brahman that is in the Atman is Truth/jnAna/Amrutha and Brahman that is in anAtma / jagat / prakriti / everything is Mruthyu / Dharma which is its own glory. Jiva or the entity going through pleasure and pain is stuck between these two forms of Brahman. When the jiva engages in dharma which is nothing but selfless service to the Brahman manifesting as jagat then both forms of Brahman gets aligned and there will be limitless Ananda. On the other hand when the jiva due to identification with the limited body acts in a selfish manner then the One Brahman gets divided into jnAna and agnAna leading to endless binding in pleasure and pain (sukha and duhkha in samsara).

The essence of sanAtana dharma is to continuously unite the Atman/Purusha with paramAtman who pervades anAtma/Prakrithi. This is nothing but continuous identification of the Self (Atman) with Everything (Sarva). Only then total selflessness or Brahmatva can arise. As Brahman is ananta or endless, Moksha or attainment of Brahman is a endless tapasya. That is why Ishwara who is nitya mukta is always shown to be engaged in tapasya.

Here is another food for thought:

Atman becomes Brahman / unlimited, only when one does not see any difference between oneself and everything else. Everything is in the Atman and the Atman is in everything. This is true Advaita where there will be no difference between nirguna Atma roopi Brahman and saguna Vishwa/Sarva roopi Brahman!

Namaste

Suresh