I have read in Buddhist text, Buddhism is about "Bhāva" and not "Ātman".
What is the difference between "Bhāva" and "Ātman"?
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Both have their places in Buddhist thought/practice.
First, the definitions:
Here are a couple of relevant quotes:
In Buddhist thought, bhāva denotes the continuity of life and death, including reincarnation, and the maturation arising therefrom. (source)
So, bhāva could be described as the "seamlessness of existence".
Although the Buddha argued that no permanent, unchanging "self" can be found, some Buddhist schools, sutras and tantras present the notion of an atman or permanent "Self", although mostly referring to an Absolute and not to a personal self. (source)
And atta is about the person in the moment; though as mentioned above, it's really more about a higher level conceptual "self".
In Buddhist thought, the opposite of atta (anatta) is a generally more significant concept:
In Buddhism, the term anattā refers to the perception of "not-self", recommended as one of the seven beneficial perceptions, which along with the perception of dukkha and impermanence is also formally classified among the three marks of existence. (source)
I hope this helps!
They are more or less the same. Well, different aspects of the same mistaken view.
Atman (literally "spirit", "breath") refers to the soul (the entity, the identity) that reincarnates and/or the little boss inside our brain who decides what to do.
Modern cognitive science is mostly on board with anatta. There is no soul, there is no single command center in the brain.
Bhava (literally "being", "existence") refers to the deeply ingrained experience of individual existence: "I am this thing here - and that stuff over there is the rest of the world". "I'm in here looking at the world through the holes in the eyes." It is a habit to self-identify with the point of view located inside a living organism. If you are the living organism then obviously when the organism dies you die.
Because the habit of bhava goes very deep, it remains the unspoken assumption behind our lives, regardless of our theoretical understanding of physics and brain. Theoretical understanding is separate, experiential assumption is separate. Maybe if memetics matures one day we will have a better model to supersede bhava. As long as we don't self-identify with the memes...
Anyhow, the reason Buddhism is interested in abandoning Atman/Bhava is not because non-dualism is the panacea (although it does reduce conflicts caused by egoistic behavior and suffering caused by wrong expectations) - but largely because Buddhism is interested in going beyond naive reification of all and any models, including that of non-dualism.
The word 'Bhava' as used in the Paticca Samuppada means Becoming. The Buddha explains that due to Vedana (feelings), one may out of Avijja (ignorance) generate Tanha (craving) which leads to Upadana (clinging) which in turn leads to Bhava.
Now the same Vedana, out of Panna (wisdom), can lead to freedom from Bhava and take one to Nibbana. When the feelings arise, if one watches their impermanence and remains equanimous, one understands that craving for that feeling is futile. This generates wisdom.
Coming to Atman, the Sanskrit word simply means 'self' or 'ego'. The Buddha taught the teaching of Anatta, the Pali for Anatman, which means non-self. It means that there is nothing in this structure of Body-Mind to be called self. Everything is impermanent and hence not suitable to clinging
Atman - View there is a Soul or Entity. Here the belief is there either controllable, non changing entity. (Entity view.)
Bhava - Becoming or creating further existences. This is a process under which your next moment is create through the rolling of the Dependent Origination (DO). This is like a stochastic process. (Process view.)
In simple terms the general tendency is the look at a being as an Entity but actually there is a Process (Bhava) which does not properties you associate with and Entity (Atman).