Q: Does Advaita believe in reincarnation?
A: To answer simply, Advaita is not based on any single soul – there is no soul and not-soul at that ultimate understanding – there is only one non-dual sat chit and ananda. Existence-consciousness-ananda cannot be divided. If one sees divisions they are only apparent and not real. If one takes the apparent as real, then all others factors become as real.
Jiiva (soul) itself is a notion and when that notion is taken as real – all other problems become as real as jiiva. Hence reincarnation and transmigration of soul are all real in that frame of reference.
Look at this way: gold, iron and copper look different if these difference as taken as real. They can exist in different forms – now as ring, now as bangle, now as chain, now as bracelet – gold undergoing transmigration or reincarnation into different forms.
If one understands that all are nothing but electrons, protons, neutrons etc., then from that perspective gold, iron, copper are just bunches of electrons, protons and neutrons – which themselves are nothing but energy-states.
I can understand as a scientist they are all one – yet I can transact in the world taking gold as different from iron and copper. Transactions are done at one level while understanding is at the ultimate level – there is no confusion if one understands correctly. I know that the sun neither rises nor sets but I can still appreciate the beauty of sunrise and sunset.
That is advaita in spite of dvaita – that is no incarnation in spite of reincarnation. Karma (action) is at the transactional level. At the absolute level I realize that I am never a kartRRi (doer). That is Advaita. Advaita in spite of dvaita.
Q: But if reincarnation is not real at the ultimate level, what happens to dharma and ethics?
A: All dharma and adharma operate at the transaction level only. They are as real as jiiva and Isvara. Everything is included in that One – which is real from the absolute point.
When we say ‘I am’, ‘I’ stands for the consciousness aspect and ‘am’ stands for the existence aspect. When we say I am this, there is the confusion of identification of the subject I am with the object ‘this’. That is due to error ,which is due to the ignorance of not knowing that ‘I am’. Right now ‘I am a jiiva’ is the notional understanding while I am Brahman is the vision of my self according to the Upanishads. That true I am has to realized or recognized.
The body is only a vehicle or instrument required to exhaust my vAsana-s. Essentially, vAsana-s decide the type of body required – man or woman, white, brown or black skin etc. I, the jiiva, gravitate towards the environment that is conducive to my vAsana-s. Hence they are called ‘kAraNa shariira’ or causal body.
Hence what birth I take next depends on the most powerful vasana-s that are ready to germinate next. There is my total bank account of karma (saMchita karma), of which I brought into this life only those that can be exhausted (prArabdha karma) and, if in the process I make new ones (AgAmin karma), which cannot be exhausted in this life, these are deposited to my account. Until all vasanas get neutralized, I will continue taking births in one form or the other. By yoga or sAdhanA, I neutralize the vAsanas. When I realize who I am – I am not this, not this etc. (since I am the subject that can never be an object ‘this’) – I recognize that I am that sat chit ananda and then there is no more ownership of any karma. All are transcended in that knowledge of who I am.
As long as I think I am a jiiva, these notions are regarded as facts and Brahman does not come into picture I am Brahman is only realised from the state of absolute knowledge. Until this is recognized as a fact and not merely as a thought, jiiva-hood is there and vAsana-s operate. So karma and its kShaya (dominion) are there as long as you are there to question, since the questioning is done by a jiva.
As long as I am dreaming that I am being chased by a tiger, that dream tiger is as real as the one who is being chased. I have to run away as fast as I can to save myself from that tiger. Only when I am awakened to the higher state of consciousness, are the tiger and the one whom the tiger is chasing, as well as the forest and the ground upon which I am running, all resolved into my own mind.
The dreamer thinks that the dream world is real until he is awakened to a higher state where there is only one mind that projects the world of plurality. The plurality is real as long as dream lasts. The problem in your questions is that you want to place one leg in the waking state and one leg in the dream state and then question the validity of each from the other reference point. Any question from the Brahman viewpoint whilst still sitting at the jiiva position is like a dreamer asking about the waking mind. The waking mind is one Advaita. The plurality of the dream world is from the viewpoint of a dreamer who thinks he is different from the tiger and the trees in the forest.