The doctrine of the Trinity is a key doctrine of Christianity. It is a magnificent and mysterious insight into the nature of God. Briefly, the doctrine consists of the following three truths:
1. God is one.
2. God consists of three persons (Father, Son, and Holy Spirit).
3. Each of the three persons is fully God.
Throughout history, people have attempted to make sense of this reality by removing one or another of these three elements. Doing so makes the doctrine far easier to understand, but it also leads to major error and, taken far enough, heresy, since each of the three elements is necessary.
Tritheism denies that God is one. Perhaps the simplest (and most clearly wrong) way to clarify the idea of the Trinity is to state that there are actually three Gods. This is obviously unbiblical (e.g. Deut. 6:4) and has rarely if ever been proposed as a serious Christian doctrine. (There does seem to be a strong tendency in the modern evangelical church, however, to emphasize the three persons so heavily that in practice many Christians think and worship with tritheistic leanings.)
Modalism denies that God is three distinct persons. Modalism claims that God is one and appears to us in various ‘modes’ which are all different views of one divine Person. This is similar to thinking of a man as simultaneously a doctor, a husband, and a father, yet only one man. A strength of modalism is that it places strong emphasis on the oneness of God, an important truth emphasized throughout the Bible. However, modalism ignores the many occurrences of relationship between members of the Trinity, and so falls short of a fully adequate description of reality. (A good example of one of these occurrences is at the baptism of Christ, where the Father speaks approval of the Son as the Spirit settles on him in the form of a dove.)
Arianism denies the deity of the Son and the Spirit. Arianism (named after Arius, a bishop of Alexandria in the fourth century A.D.) claims that the Son was created by the Father before the rest of creation, and that neither the Son nor the Holy Spirit existed until then. It is centered around an understanding of “only-begotten” (and the phrase “first-born of all creation” in Col. 1:15) as referring to a process of birthing or creation. The true meaning of “begotten” with reference to the Son is not clearly understood. However, it is clear from other passages that the Son should not be considered less than fully divine. One of these passages is Rev. 22:13, in which Jesus calls himself “the Alpha and the Omega, the first and the last, the beginning and the end,” using the same formula with which the Father identifies himself in Rev. 1:8 and 21:6.