Anyone who knows proximately this self– this enjoyer of the fruits of works, the supporter of life, etc. – as the Lord of the past and the future, does not want to save the self just because of that knowledge. This indeed is that.

Here, the self (atman) is defined as the ‘enjoyer of the fruits of works’, ie, who exists under the law of karma, being rewarded for good deeds and punished for bad. Also it is defined as the ‘supporter of life’, ie, it is this soul which supports life including consciousness, sense organs, etc. and they are not self contained but need the soul for being ‘alive’. The self or atman here is hence neither the consciousness nor Brahman, because it is defined separately from both, the description ‘enjoyer of the fruits of works’ separates it from Brahman and ‘supporter of life’ separates it from the body and consciousness. Then it is said, this soul or atman is the ‘Lord of the past and the future’, here Brahman is defined, since it is from Brahman that the soul originated from and it is to Brahman that the soul will go to. Hence, we should know this self as Brahman itself.
2.1.6:

He sees this very aforesaid Brahman who sees the First Born (Hiranyagarbha) – born before the elements from Consciousness (Brahman) – as existing in the cavity of the heart in the midst of the body and senses, after having entered here.

Here, the soul is called Hiranyagarbha, the first born. There is a story in the Upanishads about the origin of the world, in which the principle or deity called Hiranyagarbha was the first to originate from Brahman. It is said here that this Hiranyagarbha forms our souls. Thus our souls are different from direct Brahman. But in many other sutras as we have seen, Brahman itself is described as existing in the heart and there is no intervening principle.
2.1.12:

The Being (Purusa), of the size of a thumb, resides in the body. Knowing him as the ruler of the past and the future, one does not want, by virtue of that knowledge, to save the Self. This indeed is that.

Here, our soul or Hiranyagarbha is called by the name Purusa when it exists in the human body.
2.1.15:

O Gautama, as pure water poured on pure water becomes verily the same, so also does become the self of the man of knowledge who is given to deliberation on the Self.

Here, two levels are described, the self of man or Hiranyagarbha, and Brahman, and it is said that on meditation the self of man becomes as clear as Brahman and merges into the same without any difference.
In this way, this important section of the Upanishads shows that our soul is non–different from Brahman.
My reading of this is that the sages tried to reconcile reincarnation with Advaita. Advaita works more naturally if there are only two levels, the body–mind and Brahman lodged in the heart. But for reincarnation, a separate soul which can exist apart from the body–mind so that it can take up body after body needs to be defined. Defining a separate soul in this way goes against Advaita. Hence, while the first section defines the soul as an independent entity, independent from individual consciousness, this second section is an attempt to explain reincarnation through Advaita, by repeatedly stressing that, although there may be an individual soul in the heart, this soul is in reality Brahman itself, and it is non–different.
However, in my opinion, this attempt does not work and leads to logical inconsistencies. If the soul enjoys the fruits of works, goes through repeated births, etc. it has to be separate from Brahman, at least as long as it is going through the cycle. Hence it is independent, not just from our consciousness, but from Brahman also. This gives us three levels of existence.
If we say that it is Brahman itself which is lodged in our hearts, and there is no separate soul and instead our individual consciousness is all that exists and is our atman, then Advaita works naturally and forms a logical whole. The problem for traditional Advaita is that reincarnation cannot be supported with this explanation.
But for our modern times, we are under no constraint of having to accept traditional ideas, we can dispense with reincarnation also, and this lets us accept a clear and logical Advaita philosophy.
Also, in most other parts of the Upanishads as we have seen, a separate soul is not defined and instead Brahman itself is said to be lodged in the hearts, and this makes it clear that this is the original purport of the Upanishads. Hence such a logical Advaita philosophy has support from a greater part of the Upanishads than the theories that explain reincarnation.

Taittriya Upanishad

1.6.1:

In the space that is there in this heart, is this Person who is realizable through knowledge, and who is immortal and effulgent...

Here also, the person in the heart is Brahman and not a soul like Purusa or Hiranyagarbha.
2.1.1:

‘...Brahman is truth, knowledge, and infinite, he who knows that Brahman as existing in the intellect which is lodged in the supreme space in the heart, enjoys, in identification with the all–knowing Brahman, all desirable things simultaneously.’

Here also, it is said that it is Brahman itself which exists as the intellect or consciousness in the heart (since the ancients believed that our consciousness was lodged in the heart). Once we know this Brahman which exists as our intellect, that is, once we know our consciousness, to be that Brahman which is truth, knowledge and infinite, we will enjoy all desirable things simultaneously.
The sutras from 2.1.1 to 2.5.1 are also important are also important for their description of the constitution of the human body.
They describe in evocative language how the body is made up of five sheets, from the outer to the inner. The outermost sheath is that of food, the next is prana or vital force, the next is mind, fourth is intellect, and fifth is bliss.
2.1.1

...From food was born man. That man, such as he is, is surely a product of the essence of food. Of him this indeed is the head; this is the southern side; this is the northern side; this is the self; this is the stabilizing tail.

2.2.1

As compared with this self made of the essence of food, as said before, there is another inner self which is amade of air. By that is this one filled. That self which is this, is also verily of the human form. Its human form takes after the human form of that earlier one. Of this, prana is indeed the head, Vyana is the right side, apana is the left side, space is the self, the earth is the tail that stabilizes.

2.3.1

...Of the preceding physical one, this one, indeed, is the embodied self. As compared with this vital body, there is another internal self constituted by the mind. By that one is this one filled up. That self which is this, is also of a human shape. The human shape of this mental body takes after the human shape of that vital body. Of that mental body, the Yajur –mantras are the head. The rik–mantras are the right side, the Sama–mantras are the left side, the brahmana portion is the self, the mantras seen by the Atharvangiras are the stabilizing tail..

2.4.1

...Of the preceding vital one, this mental one is verily the embodied self. As compared with this mental body, there is another internal self constituted by the valid knowledge. By that one is this one filled up. This one, as aforesaid,has verily a human shape. It is humanly shaped in accordance with the hman shape of the earlier one. Of him, faith is verily the head. Righteousness is the right side, truth is the left side, concentration is the self, Mahat is the stabilizing tail..

2.5.1

Of that preceding (mental) one, this (cognitive) one is verily the embodied self. As compared with this cognitive body, there is another internal self constituted by bliss. By that one is this one filled up. This one, as aforesaid, has verily a human shape. It is humanly shaped in accordance with the human shape of the earlier one. Of him joy is verily the head; enjoyment is the right side; hilarity is the left side; bliss is the self. Brahman is the tail that stabilizes.

Food of course is the gross material body. The second sheath of vital force or prana means the energy in the body. The third sheath of the mind consists of our thoughts and sensations. The fourth sheath, translated here as intellect or ‘valid knowledge‘, means the discriminating part of our consciousness (the word used is vigyanam). The mind and the intellect together constitue our consciousness. The fifth sheath of bliss signifies the pure consciousess. The natural state of our consciousness is said to be bliss, and it is only because our minds are drawn outwards that we do not exist in bliss. Hence these three inner sheaths together form our consciousness.
Then it is said, of the sheath of bliss, Brahman is the tail. This means that Brahman is the support of our entire existence, from the consciousness to the vital force to the material body. These five sheaths together constitute our identity. There is no mention of a soul here apart from the mind, intellect and bliss. Hence this is very important for modern Advaita and lends support to its logic.END=NAM MO SAKYAMUNI BUDDHA.( 3 TIMES ).WORLD VIETNAMESE BUDDHIST ORDER=VIETNAMESE BUDDHIST NUN=GOLDEN LOTUS MONASTERY=THE EIGHTFOLD PATH.THICH CHAN TANH.THE MIND OF ENLIGHTMENT.AUSTRALIA,SYDNEY.7/1/2015.