Trinitarian Heresies
All heresies with respect to the Trinity may be reduced to the one great heresy of mixing the eternal and the temporal.
— Cornelius Van Til
Throughout Christian history, various heresies have arisen concerning the nature of the Trinity—the doctrine that God exists as three persons in one essence. As of late, however, there has been a lot of hubbub going on about the Trinity and how to understand the relationship between Father, Son, and Spirit. Certainly, all the answers will not be solved here, but I thought this might be a helpful bit of information to put in front of you to assist the church in staying away from past errors. These errors continue today, albeit sometimes under different names, so you must know what the heresies proclaim so that whether it is called Subordinationism or ESS (Eternal Subordination of the Son) you will know what is being said.
Modalism
This school of thought taught that the three persons of the Trinity operate as different “modes” of the Godhead. Adherents believed that the Father, Son, and Holy Spirit are not distinct personalities, but different modes of God's self-revelation. A typical modalist approach is to regard God as the Father in creation, the Son in redemption, and the Spirit in sanctification. In other words, God manifests himself as Father, Son, and Spirit in different eras, to perform different tasks, and accomplish different goals, but never as triune.
Nestorianism
Nestorianism, associated with Nestorius, separates the divine and human natures of Christ to the extent that it implies Jesus was two distinct persons rather than one person with two natures.
Monophysitism
Those holding this position argue that Jesus has only one nature (a divine-human nature), denying the distinctness of His divine and human natures.
Subordinationism
Subordinationism teaches an inherent hierarchical subordination within the Trinity, suggesting that one person is subordinate in essence (ontology) or attributes to another.
Eunomianism
Eunomianism, associated with Eunomius, asserts that the Son is of a different essence than the Father, challenging the Nicene Creed's affirmation of consubstantiality.
Patripassianism
This belief stems from Modalism and believes that the Father, not the Son of God, actually suffered on the cross and died.
Sabellianism
God is one person with three names: Father, Son, and Holy Spirit.
Tritheism
Tritheism confesses the Father, Son, and Holy Spirit as three independent divine beings; three separate beings forming three separate gods but who nevertheless share in the 'same substance'. This is a common mistake because of a misunderstanding of the use of the term 'persons' in defining the Trinity.
Arianism
This belief teaches that the preexistent Christ was the first and greatest of God’s creatures but denied his fully divine status. The Arian controversy was of major importance and was crucial in the development of our understanding of Christology. During the fourth century, this idea was addressed in the Nicene Creed.
Docetism
This viewpoint taught that Jesus Christ was a purely divine being who only had the “appearance” of being human, but did not really have a body. Regarding his suffering, some versions taught that Jesus’ divinity abandoned or left him upon the cross while others claimed that he only appeared to suffer (much like he only appeared to be human). This belief is the result of Gnosticism
Gnosticism
Adherents to this philosophical worldview stress that special knowledge is needed to attain salvation. It also maintains that matter is entirely evil and spirit is good. Because matter is evil, human souls, in a sense, are trapped in a material world; trapped in a material body. Therefore, gnostics must deny that Jesus is God in the flesh because evil is bad and spirit is good.
Ebionitism
Adherents to this view taught that while Jesus was endowed with particular charismatic gifts that distinguished him from other humans he was nonetheless merely and purely human, i.e. not divine. He was only the Son of God due to having been “adopted” by God. This belief also taught the necessity of keeping the Jewish law.
Macedonianism
This is a denial of the full divinity or personality of the Holy Spirit. A belief that the Holy Spirit is a created being.
Adoptionism
This position taught that Jesus was born as a complete and total human and was only later given powers and “adopted” – either at his baptism or at his resurrection – by God in a special (divine) way.
Partialism
Propagators of this position taught that the Father, Son, and Holy Spirit are merely components of the one God. This led them to believe that each of the persons of the Trinity is only part of God, only becoming fully God when they come together. An example of this would be the stomach, arms, and legs, which are each part of the body, but only constitute an actual body when they are all together.