Please don't take offense at what I'm about to write -
I think one of the problems with this discussion, and many discussions in forums like this where the most subtle aspects of Buddhist thought are discussed, we depart from the tried and true texts and instead proceed with our own interpretations, bouncing them off one another in a didactic pattern until we are all painted into the corner of the idiosyncrasies of our respective views. I was surprised it took until Astus on the second page of this discussion to ground the discussion in actual textual teachings.
With that said - someone early in this thread mentioned that Tathagatagarbha Sutras say some really provoking things - like this passage from the Mahaparinirvana Sutra that is pertinent to the title of this thread:
From Chapter 3 of the Mahayana Mahaparinirvana Sutra. If you have never been exposed to this sutra before, you may experience some gaskets popping in your head:
tl;dr version: Buddha says "I taught you Anatman because you guys had all kinds of crazy ideas about Atman, and rather than try to point out the myriad ways you screwed it up, I just taught you Anatman. Now, since you have learned Anatman and all those crazy ideas have been purged from your mind, I'm going to teach you about the True Atman."
O you Bhiksus! Do not abide in the thought of the non-Eternal, Suffering, non-Self, and the not-Pure and be in the situation of those people who take stones, bits of wood, and gravel to be the true gem. You must study well the Way, how to act, wherever you go, and "meditate on the Self, the Eternal, Bliss, and the Pure". Know that the outer forms of the four items which you have learnt up to now are inversions and that anyone who desires to practise the Way should act like the wise man who deftly gets hold of the gem. This refers to the so-called thought of Self, and that of the Eternal, Bliss, and Pure."
Then all the bhiksus said to the Buddha: "O World-Honoured One! You, the Buddha, said before that all things have no Self, that we should practise this and that, when practised, the thought of Self goes away, and that once the thought of Self is done away with, one does away with arrogance and that, arrogance once done away with, one gains Nirvana. Thus did you say "How might we understand this?"
The Buddha said to all the bhiksus: "Well said, well said! You ask this question and intend to dispel your doubt. Imagine: there is a king, who is dull-witted. He has little wisdom. And there is a doctor, who is obstinate. But the King does not know this and pays him a salary. This doctor uses the products of milk to cure all illnesses. Also, he does not know where the illnesses come from. He may be versed in the medicine of milk, but for him there exists no difference between a cold and a fever. He prescribes milk for all illnesses. This King was unaware that this doctor was ignorant of the pleasing and non-pleasing, the good and bad aspects of milk. But there was a Doctor who knew eight different treatments for illnesses and who was able to cure all diseases. This Doctor was versed in prescription and medicines and had come from a far-off place. And the King's doctor did not know how to ask and learn. He was rash and haughty. So the learned Doctor cordially invited the King's doctor and looked up to him [as an expedient] as his master and asked of him the secret of treatment. He said to the King's doctor: "I now invite you and make you my teacher. Please be good enough to teach me." The King's doctor said: "If you serve me for 48 years, I will teach you the art of medicine. " Then, at these words, the learned Doctor said: "I shall do as you tell me. I shall do my best and run errands." Then the King's doctor, taking the learned Doctor along with him, went to see the King. At this, the visiting Doctor explained to the King the various ways of treatment and even other things. He said: "Please know, O great King! Know well! This Dharma is like this and you will well cure illnesses." On hearing this, the King recognised the ignorance and lack of knowledge of his own doctor. He at once drove him out of the country. And he respected the new Doctor all the more. Then the new Doctor said to himself: "It is now time to teach the King." He said to the King: "O great King! If you truly love me, please make me a promise!" The King replied: "I shall give you, should you desire it, even my right hand or any part of my body." The new Doctor said: "You may give me all statuses, but I myself do not wish to have much. What I desire you to do for me is to proclaim to the people of every corner of your land that henceforth they are not to use the milk medicine, which the former doctor told them to use. Why not? Because much harm and poisonous results arise [from it]. Any person who still takes this medicine should be beheaded. If the milk medicine is not used, there will be no untimely deaths; all will go in peace. That is why I ask this of you." Then the King said: "What you ask me to do is a trifle. I shall at once issue an order and see to it that anyone who is ill does no take milk as a medicine. Any person who does will be beheaded." At this, the learned Doctor made several kinds of medicine, which tasted pungent, butter, salty, sweet, and sour. With these, treatment was given, and there was no case in which illness could not be cured.
"After some time, the King himself became ill, and the Doctor was called in. The King said: "I am now ill. How am I to be cured?" The Doctor thought about the illness of the King and saw that the milk medicine was good [here]. So he said to the King: "What you are now suffering from can very well be cured by milk. What I said before about the milk medicine was not true. If you take it now, you will be cured. You are now suffering from a fever. It is right that you should take milk." Then the King said to the Doctor: "Are you mad? Is it a fever? And you say that if I take milk, it will cure me? Before, you said it was poison. Now you tell me to take it. How is this? Do you mean to cheat me? What the former doctor said was good, [yet] you despised it and said that it was poison, and you made me drive him away. Now you say that it well cures illness. From you you say, the former doctor ought to excel you."
"Then the learned Doctor said to the King: "O King! Do not say this, please. A worm eats on [a piece of] wood and [the shape of] a letter comes out. This worm does not know anything of letters. A wise person sees this. But he does not say that this worm understands letters. And he is not overcome by surprise. O great King! Please know: so was it also with the former doctor. To all illnesses he gave medicine made from milk. This is as in the case of the worm that eats on wood, as a result of which a form like a letter emerges. The former doctor did not know how to distinguish between the pleasing and non-pleasing aspects, the good and the bad." Then the King wanted to know: "What do you mean he did not know?" The guest Doctor answered the King: "This milk medicine is harmful, but it is also a manna." "How can you say that this milk is manna?" "If you milking cow has not taken the lees, the slippery grass and the wheat refuse, and if the calf fares well, and if the cow was not grazed too high up on the land or in a low and wet place, if the cow is given pure water and not made to run or made to live among the bulls, and if feeding is done regularly, and if the place it lives in is fit, the milk gained from such a cow well does away with all illnesses. This can well be called the manna of medicine. Any other milk is poison."
"On hearing this, the King praised the great Doctor: "Well said, well said, O great Doctor! Today, for the first time in my life, I know of the pleasing and non-pleasing, that which is good and not good in the milk medicine. Taking this, I am now well. I shall at once proclaim to the people that they may well take the milk medicine." On hearing this, the people of the country, angry and resentful, said: "The great King is now caught by a devil. Is he mad? He cheats us and makes us take milk." All the people, angry and resentful, came to the King. The King said to them: "Be not angry, and have no resentment. To take milk or not to take it all comes from the science of medicine. I am not to blame." At this, the great King and the people all jumped for joy. They all the more respected and honoured the Doctor, and made offerings to him. That is how all the people took the milk medicine and regained their health.
"Know, O you Bhiksus! The same is the case with the Tathagata, the Alms-deserving, the All-Enlightened-One, the Unsurpassed Best Trainer, the Teacher-of-Heaven-and-Earth, the Buddha-World-Honoured One. He comes as a great Doctor and subdues all tirthikas and bad doctors. In the presence of kings and all people, he says: "I shall become the King of doctors and subdue tirthikas." Thus we say: "There is no self, no man, no being, no life, no nurturing, no knowing, none that does, and none that receives." O Bhiksus! Know that what the tirthikas say is like the case of a worm that eats upon [a piece of] wood, from which, by chance, there appears what looks like a letter. Because of this, the Tathagata teaches and says no-self. This is to adjust beings and because he is aware of the occasion. Such non-self is, as occasion arises, spoken of, and it is [also] said that there is the Self. This is as in the case of the learned Doctor, who knows well the medicinal and non-medicinal qualities of milk. It is not as with common mortals, who might measure the size of their own self. Common mortals and the ignorant may measure the size of their own self and say, 'It is like the size of a thumb, like a mustard seed, or like the size of a mote.' When the Tathagata speaks of Self, in no case are things thus. That is why he says: 'All things have no Self.'
Even though he has said that all phenomena [dharmas] are devoid of the Self, it is not that they are completely/ truly devoid of the Self. What is this Self? Any phenomenon [dharma] that is true [satya], real [tattva], eternal [nitya], sovereign/ autonomous/ self-governing [aisvarya], and whose ground/ foundation is unchanging [asraya-aviparinama], is termed 'the Self' [atman]. This is as in the case of the great Doctor who well understands the milk medicine. The same is the case with the Tathagata. For the sake of beings, he says "there is the Self in all things" O you the four classes! Learn Dharma thus!"
Now, to ameliorate some of the frustration some of you may be experiencing at this moment, this passage has been interpreted, at least in the East Asian Lotus Tradition founded by Zhiyi, a Tathagatagarbha school of Buddhism, through the lens of Nagarjuna's Tetralemma -
There is X
There is no X
There both is X and no X
There is neither X nor no X
(x=whatever dharma you need to understand)
True Self (one way to describe the Eternal Buddha's achievement)(or Tathagatagarbha, or Buddha Nature) is neither Atman (in the conventional, ignorant sense) nor Anatman.
What we are dealing with is that technically ungraspable remainder after Nagarjuna's sunyata analysis has been fully performed - it is not nothing - it stubbornly won't go away and just let us dissolve into nihilism, but defies us by being impervious to any conception, let alone name, we try to put to it, necessarily falling short of equating with it. It is non-arising; it is imperishable also. What do?
In my take, Tathagatagarbha Buddhism basically said, "OK. Taking this Sunyata thing so far leaves us a bunch of mutes, staring at each other, or often just staring into Sunyata, with nothing to say. Anytime someone says something, there is a chorus of 'SUNYATA!' 'ANATMAN' 'MUUUUUUUUUUUU!' We need to be able to talk to further explore the implications of this teaching. We will posit a conventional name for this empty, ineffable, inexpressible, inconceivable 'full-middle' so that we can continue examination of what it means to be enlightened. Agreed? OK, now..." Permanent, Eternal, Tathagatagarbha, BuddhaNature, 諸法実相 (True Apect of all Dharmas)... etc.