Does Buddhism, other than Amidism, describe or explain entities like Amida, or any other "other power," or intra-psychic, in yer mind, other.
I did not mean to consider whether Buddhism is theistic or not.
Pigeonholing Buddhism into theistic or atheistic category betrays ignorance of the relationship between reality and its description.
Theistic concepts such as gods, souls, afterlife, other realms etc. are all descriptions referring to certain phenomena observable in the real life.
Most of these phenomena are of such nature that speaking about them in other terms is hard or impossible. So over the centuries humanity developed a kind of partially metaphorical / partially exaggerated / partially simplified vocabulary that we now know as "the supernatural" and "the metaphysical".
Then, on top of that useful if a little inaccurate vocabulary, a hundred generations of people overlaid their fairy tales and anecdotes. Then on top of this folklore came systematizers who wrote down the canons and catechisms. The mixture of these three layers is what we know as a religion.
When we talk about Buddhism, the conversation would get a lot more clear if we were to drop the two later layers and focus on the original set of ideas used to describe phenomena that don't have adequate representation in materialistic let alone scientific vocabularies.
I claim that ideas such as gods, spirits, other worlds, and other seemingly fictional elements are simplified descriptions or real things going on in the real world you and I live in. There's no room in this answer for going in details but at least I have made the claim.
If we suspend our judgment and assume (hypothetically) that my claim is grounded in reality, then we will have to say that the difference between theistic and non theistic Buddhism is moot. In fact we would have to say that what we know as traditional Buddhism is probably more complete while secular Buddhism artificially restricts itself to a subset of reality that is included in the modern materialistic description while leaving the other important phenomena out just because we are not aware of them and don't understand them enough to describe in our own words.
Buddha speaks that the power of mära (mära bala) is something we should strive to win against though practice of Buddhism.
Buddha has also said that he doesn't see anybody else who exercises power as the mära does.
However mära also dies. Even Arhat Moghalläna has been mära.
Mära is also explained by Buddha as things that perish.
Our eyes, ears, nose, tongue, body and mind, when specifically considered as "me", "mine" or "my soul", is said by mära to be belonging to him when answering a question by Buddha.
The only time I can think of mention of an 'other power', is perhaps in Zen's Gateless Gate book of Koan's where there is mention in #42 of a girl next to the Buddha. I think that this "girl" may be Amida (who is neutre) but it is only a guess.
There is so the bull in Zen's ten pictures of the bull. It is a sort of pair to self and dissappears when enlightenment is achieved.
There is officially no such thing as "atheistic Buddhism".
Yes, the Kamala Sutta does provide rhetorical ammunition to allow disbelief in some or all gods. Yes, the belief in Karma does provide a moral absolute that exists independently of the will of any Higher Power. Yes, the Buddhism does provide a Marcion-ist view of dispassion towards the physical cosmos, so one is not commanded to venerate a creator deity who reigns over a flawed universe.
Yes, Buddhism, especially Mahayana Buddhism, does tend to emphasize the god within, a sort of Spinoza pantheism. Yes, Buddhism gives ample leeway to interpret the gods, spirits, and heroic characters allegorically--including the Buddha himself. (Mahayana texts are largely the product of a Buddha who appears in meditative trances rather than the oral legends passed down from the historical, flesh-and-blood Shakyamuni Buddha.)
That so, "atheistic" Buddhism would be one that strongly denies even the possibility of gods and spirits, and rigorously demands empirical observation supporting every truth claim. "Atheistic" Buddhism did not exist from any historical accounts; it is a recent innovation. Modern atheist thinkers are using the permissiveness of agnostic Buddhism, Kalama-sutta Buddhism, to create an atheistic form of Buddhism.
Nothing wrong with that; atheists are allowed to be Buddhists, just like anybody else.
In DN 1 (below), we see something like a God, but here it refers to a being who delusionally thinks that he is the Supreme Creator, when in fact, he misinterpreted coincidental events as acts of his power.
"There comes a time, bhikkhus, when after the lapse of a long period this world contracts (disintegrates). While the world is contracting, beings for the most part are reborn in the Ābhassara Brahma-world. There they dwell, mind-made, feeding on rapture, self-luminous, moving through the air, abiding in glory. And they continue thus for a long, long period of time.
"But sooner or later, bhikkhus, after the lapse of a long period, there comes a time when this world begins to expand once again. While the world is expanding, an empty palace of Brahmā appears. Then a certain being, due to the exhaustion of his life-span or the exhaustion of his merit, passes away from the Ābhassara plane and re-arises in the empty palace of Brahmā. There he dwells, mind made, feeding on rapture, self-luminous, moving through the air, abiding in glory. And he continues thus for a long, long period of time.
"Then, as a result of dwelling there all alone for so long a time, there arises in him dissatisfaction and agitation, (and he yearns): 'Oh, that other beings might come to this place!' Just at that moment, due to the exhaustion of their life-span or the exhaustion of their merit, certain other beings pass away from the Ābhassara plane and re-arise in the palace of Brahmā, in companionship with him. There they dwell, mind-made, feeding on rapture, self-luminous, moving through the air, abiding in glory. And they continue thus for a long, long period of time.
"Thereupon the being who re-arose there first thinks to himself: 'I am Brahmā, the Great Brahmā, the Vanquisher, the Unvanquished, the Universal Seer, the Wielder of Power, the Lord, the Maker and Creator, the Supreme Being, the Ordainer, the Almighty, the Father of all that are and are to be. And these beings have been created by me. What is the reason? Because first I made the wish: "Oh, that other beings might come to this place!" And after I made this resolution, now these beings have come.'
"And the beings who re-arose there after him also think: 'This must be Brahmā, the Great Brahmā, the Vanquisher, the Unvanquished, the Universal Seer, the Wielder of Power, the Lord, the Maker and Creator, the Supreme Being, the Ordainer, the Almighty, the Father of all that are and are to be. And we have been created by him. What is the reason? Because we see that he was here first, and we appeared here after him.'
"Herein, bhikkhus, the being who re-arose there first possesses longer life, greater beauty, and greater authority than the beings who re-arose there after him.
"Now, bhikkhus, this comes to pass, that a certain being, after passing away from that plane, takes rebirth in this world. Having come to this world, he goes forth from home to homelessness. When he has gone forth, by means of ardor, endeavor, application, diligence, and right reflection, he attains to such a degree of mental concentration that with his mind thus concentrated he recollects his immediately preceding life, but none previous to that. He speaks thus: 'We were created by him, by Brahmā, the Great Brahmā, the Vanquisher, the Unvanquished, the Universal Seer, the Wielder of Power, the Lord, the Maker and Creator, the Supreme Being, the Ordainer, the Almighty, the Father of all that are and are to be. He is permanent, stable, eternal, not subject to change, and he will remain the same just like eternity itself. But we, who have been created by him and have come to this world, are impermanent, unstable, short-lived, doomed to perish.'
I'm not sure what you mean by "other" but there's a lot of doctrine like Upaddha Sutta (SN 45.2) in the Pali canon.
Don't say that, Ananda. Don't say that. Admirable friendship, admirable companionship, admirable camaraderie is actually the whole of the holy life.
It is in dependence on me as an admirable friend that beings subject to birth have gained release from birth, that beings subject to aging have gained release from aging, that beings subject to death have gained release from death, that beings subject to sorrow, lamentation, pain, distress, & despair have gained release from sorrow, lamentation, pain, distress, & despair.
For lay people too there is doctrine about social relations, with good friends or bad friends, parents, teachers, people you work with, and so on.
If the opposite of "other" is "self", then perhaps Buddhism in general is at least as much other-centred as self-centred.