The Indian belief, if developed, would have developed into a system of polytheism. Why pray to a benevolent God? Would not his goodness have taken care of things without the aid of human request?
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He is the Sun; she is the Moon. He is beneficent; but she is malignant, like the female demon of the Algonquins. They have a bark house, made like those of the Iroquois, at the end of the earth, and they often come to feasts and dances in the Indian villages. Jouskeha raises corn for himself, and makes plentiful harvests for mankind. Sometimes he is seen, thin as a skeleton, with a spike of shriveled corn in his hand, or greedily gnawing a human limb; and then the Indians know that a grievous famine awaits them. He constantly interposes between mankind and the malice of his wicked grandmother, whom, at times, he soundly cudgels. It was he who made lakes and streams: for once the earth was parched and barren, all the water being gathered under the armpit of a colossal frog; but Jouskeha pierced the armpit, and let out the water. No prayers were offered to him, his benevolent nature rendering them superfluous.
[Compare Brébeuf, as before cited, and Sagard, Voyage des Hurons, p. 228.]
The early writers call Jouskeha the creator of the world, and speak of him as corresponding to the vague Algonquin deity, Atahocan. Another deity appears in Iroquois mythology, with equal claims to be regarded as supreme. He is called Areskoui, or Agreskoui, and his most prominent attributes are those of a god of war. He was often invoked, and the flesh of animals and of captive enemies was burned in his honor. [Father Jogues saw a female prisoner burned to Areskoui, and two bears offered to him to atone for the sin of not burning more captives. — Lettre de Jogues, 6 Aug., 1643.] Like Jouskeha, he was identified with the sun; and he is perhaps to be regarded as the same being, under different attributes. Among the Iroquois proper, or Five Nations, there was also a divinity called Tarenyowagon, or Teharonhiawagon,  whose place and character it is very difficult to determine. In some traditions he appears as the son of Jouskeha. He had a prodigious influence; for it was he who spoke to men in dreams. The Five Nations recognized still another superhuman personage, — plainly a deified chief or hero. This was Taounyawatha, or Hiawatha, said to be a divinely appointed messenger, who made his abode on earth for the political and social instruction of the chosen race, and whose counterpart is to be found in the traditions of the Peruvians, Mexicans, and other primitive nations. 
[1 Le Mercier, Relation, 1670, 66; Dablon, Relation, 1671, 17. Compare Cusick, Megapolensis, and Vanderdonck. Some writers identify Tarenyowagon and Hiawatha. Vanderdonck assumes that Areskoui is the Devil, and Tarenyowagon is God. Thus Indian notions are often interpreted by the light of preconceived ideas.]
[2 For the tradition of Hiawatha, see Clark, History of Onondaga, I. 21. It will also be found in Schoolcraft’s Notes on the Iroquois, and in his History, Condition, and Prospects of Indian Tribes.
The Iroquois name for God is Hawenniio, sometimes written Owayneo; but this use of the word is wholly due to the missionaries. Hawenniio is an Iroquois verb, and means, “he rules, he is master”. There is no Iroquois word which, in its primitive meaning, can be interpreted, the Great Spirit, or God. On this subject, see Études Philologiques sur quelques Langues Sauvages (Montreal, 1866), where will also be found a curious exposure of a few of Schoolcraft’s ridiculous blunders in this connection.]
Close examination makes it evident that the primitive Indian’s idea of a Supreme Being was a conception no higher than might have been expected. The moment he began to contemplate this object of his faith, and sought to clothe it with attributes, it became finite, and commonly ridiculous. The Creator of the World stood on the level of a barbarous and degraded humanity, while a natural tendency became apparent to look beyond him to other powers sharing his dominion. The Indian belief, if developed, would have developed into a system of polytheism.
[Some of the early writers could discover no trace of belief in a supreme spirit of any kind. Perrot, after a life spent among the Indians, ignores such an idea. Allouez emphatically denies that it existed among the tribes of Lake Superior. (Relation, 1667, 11.) He adds, however, that the Sacs and Foxes believed in a great génie, who lived not far from the French settlements. — Ibid., 21.]
In the primitive Indian’s conception of a God the idea of moral good has no part. His deity does not dispense justice for this world or the next, but leaves mankind under the power of subordinate spirits, who fill and control the universe. Nor is the good and evil of these inferior beings a moral good and evil. The good spirit is the spirit that gives good luck, and ministers to the necessities and desires of mankind: the evil spirit is simply a malicious agent of disease, death, and mischance.
In no Indian language could the early missionaries find a word to express the idea of God. Manitou and Oki meant anything endowed with supernatural powers, from a snake-skin, or a greasy Indian conjurer, up to Manabozho and Jouskeha. The priests were forced to use a circumlocution, — “The Great Chief of Men,” or “He who lives in the Sky.” [See “Divers Sentimens,” appended to the Relation of 1635, § 27; and also many other passages of early missionaries.] Yet it should seem that the idea of a supreme controlling spirit might naturally arise from the peculiar character of Indian belief. The idea that each race of animals has its archetype or chief would easily suggest the existence of a supreme chief of the spirits or of the human race, — a conception imperfectly shadowed forth in Manabozho. The Jesuit missionaries seized this advantage. “If each sort of animal has its king,” they urged, “so, too, have men; and as man is above all the animals, so is the spirit that rules over men the master of all the other spirits.” The Indian mind readily accepted the idea, and tribes in no sense Christian quickly rose to the belief in one controlling spirit. The Great Spirit became a distinct existence, a pervading power in the universe, and a dispenser of justice. Many tribes now pray to him, though still clinging obstinately to their ancient superstitions; and with some, as the heathen portion of the modern Iroquois, he is clothed with attributes of moral good.
(In studying the writers of the last and of the present century, it is to be remembered that their observations were made upon savages who had been for generations in contact, immediate or otherwise, with the doctrines of Christianity. Many observers have interpreted the religious ideas of the Indians after preconceived ideas of their own; and it may safely be affirmed that an Indian will respond with a grunt of acquiescence to any question whatever touching his spiritual state. Loskiel and the simple-minded Heckewelder write from a missionary point of view; Adair, to support a theory of descent from the Jews; the worthy theologian, Jarvis, to maintain his dogma, that all religious ideas of the heathen world are perversions of revelation; and so, in a greater or less degree, of many others. By far the most close and accurate observers of Indian superstition were the French and Italian Jesuits of the first half of the seventeenth century. Their opportunities were unrivalled; and they used them in a spirit of faithful inquiry, accumulating facts, and leaving theory to their successors. Of recent American writers, no one has given so much attention to the subject as Mr. Schoolcraft; but, in view of his opportunities and his zeal, his results are most unsatisfactory. The work in six large quarto volumes, History, Condition, and Prospects of Indian Tribes, published by Government under his editorship, includes the substance of most of his previous writings. It is a singularly crude and illiterate production, stuffed with blunders and contradictions, giving evidence on every page of a striking unfitness either for historical or philosophical inquiry, and taxing to the utmost the patience of those who would extract what is valuable in it from its oceans of pedantic verbiage.)
The primitive Indian believed in the immortality of the soul,  but he did not always believe in a state of future reward and punishment. Nor, when such a belief existed, was the good to be rewarded a moral good, or the evil to be punished a moral evil. Skilful hunters, brave warriors, men of influence and consideration, went, after death, to the happy hunting-ground; while the slothful, the cowardly, and the weak were doomed to eat serpents and ashes in dreary regions of mist and darkness. In the general belief, however, there was but one land of shades for all alike. The spirits, in form and feature as they had been in life, wended their way through dark forests to the villages of the dead, subsisting on bark and rotten wood. On arriving, they sat all day in the crouching posture of the sick, and, when night came, hunted the shades of animals, with the shades of bows and arrows, among the shades of trees and rocks: for all things, animate and inanimate, were alike immortal, and all passed together to the gloomy country of the dead.
[1 The exceptions are exceedingly rare. Father Gravier says that a Peoria Indian once told him that there was no future life. It would be difficult to find another instance of the kind.]
The belief respecting the land of souls varied greatly in different tribes and different individuals. Among the Hurons there were those who held that departed spirits pursued their journey through the sky, along the Milky Way, while the souls of dogs took another route, by certain constellations, known as the “Way of the Dogs.” [Sagard, Voyage des Hurons, 233.]
At intervals of ten or twelve years, the Hurons, the Neutrals, and other kindred tribes, were accustomed to collect the bones of their dead, and deposit them, with great ceremony, in a common place of burial. The whole nation was sometimes assembled at this solemnity; and hundreds of corpses, brought from their temporary resting-places, were inhumed in one capacious pit. From this hour the immortality of their souls began. They took wing, as some affirmed, in the shape of pigeons; while the greater number declared that they journeyed on foot, and in their own likeness, to the land of shades, bearing with them the ghosts of the wampum-belts, beaver-skins, bows, arrows, pipes, kettles, beads, and rings buried with them in the common grave. (The practice of burying treasures with the dead is not peculiar to the North American aborigines. Thus, the London Times of Oct. 25, 1885, describing the funeral rites of Lord Palmerston, says: “And as the words, ‘Dust to dust, ashes to ashes,’ were pronounced, the chief mourner, as a last precious offering to the dead, threw into the grave several diamond and gold rings.”) But as the spirits of the old and of children are too feeble for the march, they are forced to stay behind, lingering near their earthly villages, where the living often hear the shutting of their invisible cabin-doors, and the weak voices of the disembodied children driving birds from their corn-fields. [Brébeuf, Relation des Hurons, 1636, 99 (Cramoisy).] An endless variety of incoherent fancies is connected with the Indian idea of a future life. They commonly owe their origin to dreams, often to the dreams of those in extreme sickness, who, on awaking, supposed that they had visited the other world, and related to the wondering bystanders what they had seen.
– The Jesuits in North America in the Seventeenth Century Introduction by Francis Parkman
The below is from Francis Parkman’s Introduction.
If, at times, it may seem that range has been allowed to fancy, it is so in appearance only; since the minutest details of narrative or description rest on authentic documents or on personal observation.
Faithfulness to the truth of history involves far more than a research, however patient and scrupulous, into special facts. Such facts may be detailed with the most minute exactness, and yet the narrative, taken as a whole, may be unmeaning or untrue. The narrator must seek to imbue himself with the life and spirit of the time. He must study events in their bearings near and remote; in the character, habits, and manners of those who took part in them, he must himself be, as it were, a sharer or a spectator of the action he describes.
With respect to that special research which, if inadequate, is still in the most emphatic sense indispensable, it has been the writer’s aim to exhaust the existing material of every subject treated. While it would be folly to claim success in such an attempt, he has reason to hope that, so far at least as relates to the present volume, nothing of much importance has escaped him. With respect to the general preparation just alluded to, he has long been too fond of his theme to neglect any means within his reach of making his conception of it distinct and true.