Six powers of the Buddha by which he claims leadership, has confidence in addressing any group, and rolls on the wheel of Dhamma.
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Index to available translations: AN 6.64
The key to getting the real feel for this sutta is in understanding the term 'yathābhūta' 'suchas-it lives.'
Hare: 'knows as fact';
Bhk. Bodhi: 'understands as it really is';
Bhk. Thissaro: 'as actually present'.
PED: bhūta grown, become; born, produced; nature as the result of becoming.
I suggest 'such as it is/was'.
We only need the 'really, in fact, actually' because we do not believe the statement on it's face. This emphasis is not in the term itself.
And this is the point of this sutta, that is that in three sets of six heavily emphasized statements the Buddha is saying that the powers he is claiming for himself here are things he sees in the same way as any other phenomenon observable in the world is seen.
That is why this is called a 'Lion's Roar'; it is a public declaration of some virtue in one's self for the sake of eliminating doubt.
Like the Lion's roar as it leaves it's den in the evening to go out into the jungle to take the evening air, it is a strong reminder to creatures large and small as to what they are dealing with and to make themselves safe.
In our world where the lie is so commonplace that we no longer believe anything, it is hard to see that in Gotama's time, where even most criminals if asked if they committed a crime would admit it for shame at lying, to make a false asertion, or even a self-deceptive asertion (saying something that is not true), so many times in succession without going crazy on the spot would be a virtual impossibility.
This sutta, and those of this type, are close relatives to the magic command/wish/demand made by an 'act of truth'; 'Let lightening strike me dead if such and such is not the truth, or let my people go.' ... usually requiring the public revelation of some deep personal secret.
See MN 12, and AN 4.8.
One of the powers as translated here is that the Buddha: ...knows the stain, purity and emergence in musing, deliverance and concentration attainments." This (italicized phrase) is, in the Pali: jhāna-vimokkha-samādhi-samāpattinaɱ. Does this mean, in stead: "jhāna-deliverance-samādhi-attainments" — one compound term? ("jhāna-release-serenity-attainment"), a single idea, not three?
The problems in attaining, clarification of, and emergence from a state of release in serenity attained through jhāna?
If not, what is the implied distinction between 'jhāna' and 'samādhi'?
See also in this regard: MN 12.
Bhks. Ñanamoli/Bodhi have this there as here, 3 ideas. Bhk. Bodhi's note there apparently relying on commentary ignores 'samādhi' and explains the releases as liberations (the vimokkha, 'releases' include the four immaterial jhanas and the attainment of the ending of sense-perception and sense-experience) and samāpatti as 'the attainments': of jhāna, the four immaterial attainments and the cessation of perception and vedana. In any case, this translated as three concepts amounts to a heap of confusion.
Another interesting thing to note in this sutta (ignoring Hare's translation of samādhi as 'concentration') is the statement that these powers, which include the three 'visions' associated with Arahantship, are attained only by those who have (or who 'are') 'samādhi.'
Depending on how one understands this term this can be problematic. Samādhi defined as the four jhānas, (but the term is not 'sammā samādhi') is saying that the four jhānas are necessary for arahantship. Defined as serenity, only the highest form of which is the four jhānas, and the three modes of which are ambitionlessness, signlessness and emptiness, attainment of the four jhānas, or all four, might not be absolutely required. The first jhāna would certainly qualify as samādhi or serenity.