Arianism developed around 320, in Alexandria Egypt concerning the person of Christ and is named after Arius of Alexandar. For his doctrinal teaching he was exiled to Illyria in 325 after the first ecumenical council at Nicaea condemned his teaching as heresy. It was the greatest of heresies within the early church that developed a significant following. Some say, it almost took over the church.
Arius taught that only God the Father was eternal and too pure and infinite to appear on the earth. Therefore, God produced Christ the Son out of nothing as the first and greatest creation. The Son is then the one who created the universe. Because the Son relationship of the Son to the Father is not one of nature, it is, therefore, adoptive. God adopted Christ as the Son. Though Christ was a creation, because of his great position and authority, he was to be worshipped and even looked upon as God. Some Arians even held that the Holy Spirit was the first and greatest creation of the Son.
At Jesus' incarnation, the Arians asserted that the divine quality of the Son, the Logos, took the place of the human and spiritual aspect of Jesus, thereby denying the full and complete incarnation of God the Son, second person of the Trinity.
In asserting that Christ the Son, as a created thing, was to be worshipped, the Arians were advocating idolatry.

Gnosticism traces its roots back just after the beginning of the Christian Church. Some researchers state that evidence of its existence even predates Christianity. Whichever the case, the error of gnosticism had affected the culture and church of the time and possibly even a earned a mention in 1 John 4.
The word "gnosticism" comes from the Greek word "gnosis" which means "knowledge." There were many groups that were Gnostic and it isn't possible to easily describe the nuances of each variant of Gnostic doctrines. However, generally speaking, Gnosticism taught that salvation is achieved through special knowledge (gnosis). This knowledge usually dealt with the individual's relationship to the transcendent Being.
A more detailed Gnostic theology is as follows. The unknowable God was far too pure and perfect to have anything to do with the material universe which was considered evil. Therefore, God generated lesser divinities, or emenations. One of these emanations, Wisdom desired to know the unknowable God. Out of this erring desire the demiurge an evil god was formed and it was this evil god that created the universe. He along with archons kept the mortals in bondage in material matter and tried to prevent the pure spirit souls from ascending back to god after the death of the physical bodies. Since, according to the Gnostics, matter is evil, deliverance from material form was attainable only through special knowledge revealed by special Gnostic teachers. Christ was the divine redeemer who descended from the spiritual realm to reveal the knowledge necessary for this redemption. In conclusion, Gnosticism is dualistic. That is, it teaches there is a good and evil, spirit and matter, light and dark, etc. dualism in the universe.
What we know about Gnosticism is gained from the writings of Irenaeus, Hippolytus, Tertullian, Origen, and some later manuscripts discovered in the eighteenth century such as the "Codex Askew, Codex Bruce, the Berlin Gnostic Codes and, most recently, the Nag Hammadi collection."1 Nag Hammadi is a town in Upper Egypt near ancient Chenoboskion and 13 codices discovered were discovered about 1945.
The danger of gnosticism is easily apparent. It denies the incarnation of God as the Son. In so doing, it denies the true efficacy of the atonement since, if Jesus is not God, He could not atone for all of mankind and we would still be lost in our sins.
There is debate whether or not this is a Christian heresy or simply an independent development. The evidence seems to point to the later. Nevertheless, the Gnostics laid claim to Jesus as a great teacher of theirs and as such requires some attention. It is possible that 1 John was written against some of the errors that Gnosticism promoted.

Pelagianism derives its name from Pelagius who lived in the 5th century A.D. and was a teacher in Rome, though he was British by birth. It is a heresy dealing with the nature of man. Pelagius, whose family name was Morgan, taught that people had the ability to fulfill the commands of God by exercising the freedom of human will apart from the grace of God. In other words, a person's free will is totally capable of choosing God and/or to do good or bad without the aid of Divine intervention. Pelagianism teaches that man's nature is basically good. Thus it denies original sin, the doctrine that we have inherited a sinful nature from Adam. He said that Adam only hurt himself when he fell and all of his descendents were not affected by Adam's sin. Pelagius taught that a person is born with the same purity and moral abilities as Adam was when he was first made by God. He taught that people can choose God by the exercise of their free will and rational thought. God's grace, then, is merely an aid to help individuals come to Him.
Pelagianism fails to understand man's nature and weakness. We are by nature sinners (Eph. 2:3; Psalm 51:5). We all have sinned because sin entered the world through Adam: "Therefore, just as sin entered the world through one man, and death through sin, and in this way death came to all men, because all sinned" (Rom. 5:12, NIV). Furthermore, Romans 3:10-12 says, “There is none righteous, not even one; 11 There is none who understands, There is none who seeks for God; 12 All have turned aside, together they have become useless; There is none who does good, There is not even one.” Therefore, we are unable to do God's will (Rom. 6:16; 7:14). We were affected by the fall of Adam, contrary to what Pelagius taught.

A heresy concerning the nature of God. It is derived from two brothers of the surname Sozinni who lived in the 1500's in Poland. Socinianism denies the doctrine of the Trinity claiming it denies the simplicity of God's unity. Instead, God is a single person with the Holy Spirit as the power of God. Since it emphasizes the unity of God, there could be no divine and human union in a single person as Christ. Therefore, Socinianism denies the incarnation and deity of Christ as well as Christ's pre-existence. It teaches that Jesus was only a man. However, as is separate from the unitarians, it taught that Jesus was a deified man and was to be adored as such. Nevertheless, since Jesus is not divine by nature, His sacrifice was not efficacious; that is, it did not result in the redemption of people who would trust in it. Instead it was an example of self sacrifice. The followers of Socinianism also rejected infant baptism, hell, and taught the annihilation of the wicked. The Bible was authoritative but was only properly understood through rationalism.
Of course, this system of belief is wrong since it denies the doctrine of the Trinity and deity of Christ.

Docetism was an error with several variations concerning the nature of Christ. Generally, it taught that Jesus only appeared to have a body, that he was not really incarnate, (Greek, "dokeo" = "to seem"). This error developed out of the dualistic philosophy which viewed matter as inherently evil, that God could not be associated with matter, and that God, being perfect and infinite, could not suffer. Therefore, God as the word, could not have become flesh per John 1:1,14, "In the beginning was the Word, and the Word was with God, and the Word was God...And the Word became flesh, and dwelt among us.. " This denial of a true incarnation meant that Jesus did not truly suffer on the cross and that He did not rise from the dead.
The basic principle of Docetism was refuted by the Apostle John in 1 John 4:2-3. "By this you know the Spirit of God: every spirit that confesses that Jesus Christ has come in the flesh is from God; 3and every spirit that does not confess Jesus is not from God; and this is the spirit of the antichrist, of which you have heard that it is coming, and now it is already in the world." Also, 2 John 7, "For many deceivers have gone out into the world, those who do not acknowledge Jesus Christ as coming in the flesh. This is the deceiver and the antichrist."
Ignatius of Antioch (died 98/117) and Irenaeus (115-190), and Hippolatus (170-235) wrote against the error in the early part of the second century.
Docetism was condemned at the Council of Chalcedon in 451.

"Kenosis" is derived from the Greek word "kenoo" which means "to empty." It is used in Phil. 2:7. The text of Phil. 2:5-8 is worth recording here.

"Have this attitude in yourselves which was also in Christ Jesus, 6who, although He existed in the form of God, did not regard equality with God a thing to be grasped, 7but emptied Himself, taking the form of a bond-servant, and being made in the likeness of men. 8And being found in appearance as a man, He humbled Himself by becoming obedient to the point of death, even death on a cross," (Phil. 2:5-8).

The kenosis theory states that Jesus gave up some of His divine attributes while He was a man here on earth. These attributes were omniscience, omnipresence, and omnipotence. Christ did this voluntarily so that He could function as a man in order to fulfill the work of redemption. This view was first introduced in the late 1800s in Germany with Gottfried Thomasius (1802-75), a Lutheran theologian.
Phil. 2:5-8 does not teach that Jesus gave up any of His divine attributes since it says nothing of those attributes. Instead, it is speaking of His humility that moved him, according to the will of the Father, to leave His majestic state in heaven and enter into the humble position of human nature.
There is, however, a problem the orthodox must deal with that the Kenosis theory seems to more adequately address. Take Mark 13:32 for example. In it, Jesus said, "But of that day or hour no one knows, not even the angels in heaven, nor the Son, but the Father alone." If Jesus knew all things, as is implied in His divine nature, then why did He not know the day or hour of His own return. The answer is that Jesus cooperated with the limitations of humanity and voluntarily did not exercise His attribute of omniscience. He still was divine but was moving and living completely as a man.
The Kenosis theory is a dangerous doctrine because if it were true then it would mean that Jesus was not fully divine. If Jesus was not fully divine, then His atoning work would not be sufficient to atone for the sins of the world.
The correct doctrine is the Hypostatic Union, that Jesus is both fully God and fully man (Col. 2:9) and did not give up any divine attributes while as a man on earth.

Modalism is probably the most common theological error concerning the nature of God. It is a denial of the Trinity which states that God is a single person who, throughout biblical history, has revealed Himself in three modes, or forms. Thus, God is a single person who first manifested himself in the mode of the Father in Old Testament times. At the incarnation, the mode was the Son. After Jesus' ascension, the mode is the Holy Spirit. These modes are consecutive and never simultaneous. In other words, the Father, the Son, and the Holy Spirit never all exist at the same time, only one after another. Modalism denies the distinctiveness of the three persons in the Trinity even though it retains the divinity of Christ.
Present day groups that hold to forms of this error are the United Pentecostal and United Apostolic Churches. They deny the Trinity, teach that the name of God is Jesus, and require baptism for salvation. These modalist churches often accuse Trinitarians of teaching three gods. This is not what the Trinity is. The correct teaching of the Trinity is one God in three eternal coexistent persons: The Father, the Son, and the Holy Spirit.

Nestorianism is the error that Jesus is two distinct persons. The heresy is named after Nestorius, who was born in Syria and died in 451 AD, who advocated this doctrine. Nestorius was a monk who became the Patriarch of Constantinople and he repudiated the Marian title "Mother of God." He held that Mary was the mother of Christ only in respect to His humanity. The council of Ephesus was convened in 431 to address the issue and pronounced that Jesus was one person in two distinct and inseparable natures: divine and human.
Nestorius was deposed as Patriarch and sent to Antioch, then Arabia, and then Egypt. Nestorianism survived until around 1300.
The problem with Nestorianism is that it threatens the atonement. If Jesus is two persons, then which one died on the cross? If it was the "human person" then the atonement is not of divine quality and thereby insufficient to cleanse us of our sins.

Donatism was the error taught by Donatus, bishop of Casae Nigrae that the effectiveness of the sacraments depends on the moral character of the minister. In other words, if a minister who was involved in a serious enough sin were to baptize a person, that baptism would be considered invalid.
Donatism developed as a result of the persecution of Christians ordered by Diocletian in 303 in which all churches and sacred scriptures of the Christians were to be destroyed. In 304 another edict was issued ordering the burning of incense to the idol gods of the Roman empire. Of course, Christians refused, but it did not curtail the increased persecution. Many Christians gave up the sacred texts to the persecutors and even betrayed other Christians to the Romans. These people became known as "traditors," Christians who betrayed other Christians. (Note: traditor, not traitor)
At the consecration of bishop Caecilian of Carthage in 311, one of the three bishops, Felix, bishop of Aptunga, who consecrated Caecilian, had given copies of the Bible to the Roman persecutors. A group of about 70 bishops formed a synod and declared the consecration of the bishop to be invalid. Great debate arose concerning the validity of the sacraments (baptism, the Lord's Supper, etc.) by one who had sinned so greatly against other Christians.
Ater the death of Caecilian, Aelius Donatus the Great became bishop of Carthage and it is from his name that the movement is called. The Donatists were gaining "converts" to their cause and a division was arising in the Catholic church. They began to practice rebaptism which was particularly troublesome to the church at the time and was condemned at the Synod of Arles in 314 since it basically said the authority in the Catholic church was lost.
The Donatist issue was raised at several ecumenical councils and finally submitted to Emporer Constantine in 316. In each case the consecration of bishop Caecilian was upheld. However, persecution fuels emotions and by 350 the Donatists had gained many converts and outnumbered the Orthodox in Africa. But it was the apologetic by Augustine that turned the tide against the Donatist movement which eventually died out in the next century.

The problem with Donatism is that no person is morally pure. The effectiveness of the baptism or administration of the Lord's supper does not cease to be effective if the moral character of the minister is in question or even demonstrated to be faulty. Rather, the sacraments are powerful because of what they are, visible representations of spiritual realities. God is the one who works in and through them and He is not restricted by the moral state of the administrant.

Patripassionism is a theological error dealing with the Godhead which states that the Father became incarnate, was born, suffered, and died on the cross. Hence the Father's (patri) passion (suffer) on the cross.
This is an error because we know that Jesus spoke to the person of the Father and that it was Jesus who went to the cross. If the father and son are the same person that how is it possible for the father and son to speak to one another and have separate wills? It is not. Therefore, the doctrine of patripassionism is incorrect and heretical.

Apollinarianism was the heresy taught by Apollinaris the Younger, bishop of Laodicea in Syria about 361. He taught that the Logos of God, which became the divine nature of Christ, took the place of the rational human soul of Jesus and that the body of Christ was a glorified form of human nature. In other words, though Jesus was a man, He did not have a human mind but that the mind of Christ was solely divine. Apollinaris taught that the two natures of Christ could not coexist within one person. His solution was to lessen the human nature of Christ.
Apollinarianism was condemned by the Second General Council at Constantinople in 381. This heresy denies the true and complete humanity in the person of Jesus which in turn, can jeopardize the value of the atonement since Jesus is declared to be both God and man to atone. He needed to be God to offer a pure and holy sacrifice of sufficient value and He needed to be a man in order to die for men.
Jesus is completely both God and man. This is known as the Hypostatic Union.

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"In the beginning was the Word, and the Word was with God, and the Word was God...and the Word became flesh and dwelt among us..." (John 1:1,14).
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"for Him dwells all the fullness of deity in bodily form," (Col. 2:9).