Arius rejected the trinity as we know it. He rejected the coequality of Jesus to God. But Jesus is the begotten son of God according to Arius, the Logos, the primary being between God and the rest of creation, the only son, thus God's son is a god, just not coeternal with the father. Thats the idea of the Arian heresy.
The idea of the Trinity hadn't even seeped into the various sects, of which there were many, when Constantine accepted the Catholic Church as the religion of the Empire. In fact at Nicaea none of the bishops assembled promoted the Trinity. They were just deciding the nature of Jesus. If the Trinity included the holy spirit, you certainly would have expecting that they would have included it then.
It wasn't until decades later after Constantine had died (and that unbaptized pagan is the one that declared Jesus was God) that Emperor Theodosius convened the Council of Constantinople in 381 C. E. that put the holy spirit on the same standing of God and Jesus Christ. This was 56 years after the Council of Nicaea held in 325 C. E.
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To the post above yours about the NWT:
Many scholars have upheld the NWT as one of the most accurate of translations available. And Jehovah's Witnesses do not just use the NWT. In fact before 1950 the most common translation in English the JWs used was the KJV. I have a KJV printed by the Watchtower Society on my bookshelf. And Jehovah's Witnesses have printed and/or used dozens of other Bible translations:
As for Bible Canon:
17 The Roman Catholic Church claims responsibility for the decision as to which books should be included in the Bible canon, and reference is made to the Council of Carthage (397 C.E.), where a catalog of books was formulated. The opposite is true, however, because the canon, including the list of books making up the Christian Greek Scriptures, was already settled by then, that is, not by the decree of any council, but by the direction of God’s holy spirit—the same spirit that inspired the writing of those books in the first place. The testimony of later noninspired catalogers is valuable only as an acknowledgment of the Bible canon, which God’s spirit had authorized.
18
The Evidence of Early Catalogs. A glance at the accompanying chart reveals that a number of fourth-century catalogs of the Christian Scriptures, dated prior to the above-mentioned council, agree exactly with our present canon, and some others omit only Revelation. Before the end of the second century, there is universal acceptance of the four Gospels, Acts, and 12 of the apostle Paul’s letters. Only a few of the smaller writings were doubted in certain areas. Likely this was so because such writings were limited in their initial circulation for one reason or another and thus took longer to become accepted as canonical.
19 One of the most interesting early catalogs is the fragment discovered by L. A. Muratori in the Ambrosian Library, Milan, Italy, and published by him in 1740. Though the beginning is missing, its reference to Luke as the third Gospel indicates that it first mentioned Matthew and Mark. The Muratorian Fragment, which is in Latin, dates to the latter part of the second century C.E. It is a most interesting document, as the following partial translation shows: “The third book of the Gospel is that according to Luke. Luke, the well-known physician, wrote it in his own name . . . The fourth book of the Gospel is that of John, one of the disciples. . . . And so to the faith of believers there is no discord, even although different selections are given from the facts in the individual books of the Gospels, because in all [of them] under the one guiding Spirit all the things relative to his nativity, passion, resurrection, conversation with his disciples, and his twofold advent, the first in the humiliation arising from contempt, which took place, and the second in the glory of kingly power, which is yet to come, have been declared. What marvel is it, then, if John adduces so consistently in his epistles these several things, saying in person: ‘what we have seen with our eyes, and heard with our ears, and our hands have handled, those things we have written.’ For thus he professes to be not only an eyewitness but also a hearer and narrator of all the wonderful things of the Lord, in their order. Moreover, the acts of all the apostles are written in one book. Luke [so] comprised them for the most excellent Theophilus . . . Now the epistles of Paul, what they are, whence or for what reason they were sent, they themselves make clear to him who will understand. First of all he wrote at length to the Corinthians to prohibit the schism of heresy, then to the Galatians [against] circumcision, and to the Romans on the order of the Scriptures, intimating also that Christ is the chief matter in them—each of which it is necessary for us to discuss, seeing that the blessed Apostle Paul himself, following the example of his predecessor John, writes to no more than seven churches by name in the following order: to the Corinthians (first), to the Ephesians (second), to the Philippians (third), to the Colossians (fourth), to the Galatians (fifth), to the Thessalonians (sixth), to the Romans (seventh). But though he writes twice for the sake of correction to the Corinthians and the Thessalonians, that there is one church diffused throughout the whole earth is shown [?i.e., by this sevenfold writing]; and John also in the Apocalypse, though he writes to seven churches, yet speaks to all. But [he wrote] out of affection and love one to Philemon, and one to Titus, and two to Timothy; [and these] are held sacred in the honorable esteem of the Church. . . . Further, an epistle of Jude and two bearing the name of John are counted . . . We receive the apocalypses of John and Peter only, which [latter] some of us do not wish to be read in church.”—
The New Schaff-Herzog Encyclopedia of Religious Knowledge, 1956, Vol. VIII, page 56.
20 It is noted that toward the end of the Muratorian Fragment, mention is made of just two epistles of John. However, on this point the above-mentioned encyclopedia, page 55, notes that these two epistles of John “can only be the second and third, whose writer calls himself merely ‘the elder.’ Having already treated the first, though only incidentally, in connection with the Fourth Gospel, and there declared his unquestioning belief in its Johannine origin, the author felt able here to confine himself to the two smaller letters.” As to the apparent absence of any mention of Peter’s first epistle, this source continues: “The most probable hypothesis is that of the loss of a few words, perhaps a line, in which I Peter and the Apocalypse of John were named as received.” Therefore, from the standpoint of the Muratorian Fragment, this encyclopedia, on page 56, concludes: “The New Testament is regarded as definitely made up of the four Gospels, the Acts, thirteen epistles of Paul, the Apocalypse of John, probably three epistles of his, Jude, and probably I Peter, while the opposition to another of Peter’s writings was not yet silenced.”
21 Origen, about the year 230 C.E., accepted among the inspired Scriptures the books of Hebrews and James, both missing from the Muratorian Fragment. While he indicates that some doubted their canonical quality, this also shows that by this time, the canonicity of most of the Greek Scriptures was accepted, only a few doubting some of the less well-known epistles. Later, Athanasius, Jerome, and Augustine acknowledged the conclusions of earlier lists by defining as the canon the same 27 books that we now have.
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22 The majority of the catalogs in the chart are specific lists showing which books were accepted as canonical. Those of Irenaeus, Clement of Alexandria, Tertullian, and Origen are completed from the quotations they made, which reveal how they regarded the writings referred to. These are further supplemented from the records of the early historian Eusebius. However, the fact that these writers do not mention certain canonical writings does not argue against their canonicity. It is just that they did not happen to refer to them in their writings either by choice or because of the subjects under discussion. But why do we not find exact lists earlier than the Muratorian Fragment?
23 It was not until critics like Marcion came along in the middle of the second century C.E. that an issue arose as to which books Christians should accept. Marcion constructed his own canon to suit his doctrines, taking only certain of the apostle Paul’s letters and an expurgated form of the Gospel of Luke. This, together with the mass of apocryphal literature by then spreading throughout the world, was what led to statements by catalogers as to which books they accepted as canonical.
https://wol.jw.org/en/wol/d/r1/lp-e/1101990131#h=51