The fourth-century Arian controversy was a series of Christian disputes about the nature of Jesus Christ.
“The crisis of the fourth century was the most dramatic internal struggle the Christian Church had so far experienced” (Williams, p. 1).
It resulted in the Trinity doctrine, which some regard as "the centerpiece of orthodox theology." (GotQuestions)
“The trinitarian controversies of the fourth century constitute what is arguably the most crucially formative period in the development of the Christian doctrine of God.” (Anatolios, p. 21)
“The fundamental problem in understanding … these controversies stems from the nature of our sources. … The documentary evidence from this period is, in many cases, fragmentary.” (Ayres, p. 2)
Over the centuries, the church copied largely only 'orthodox' writings, Consequently, in previous centuries, scholars relied largely on Athanasius's explanation of the Controversy. However, in the 20th century, a store of additional resources have become available. Based on this and progress in research, scholarship since about 1960 explains the Controversy very differently than before.
"The study of the Arian problem over the last hundred years has been like a long-distance gun trying to hit a target. The first sighting shots are very wide of the mark, but gradually the shells fall nearer and nearer. The diatribes of Gwatkin and of Harnack, can to-day be completely ignored. Prestige hardly pays sufficient attention to Arianism to be able to understand it. Boularand consistently treats Arianism, from the title of his book, L' Heresie d' Arius et la {oi de Nicee, onwards as if it had been from the outset an easily recognised heresy in contrast to a known and universally recognised orthodoxy, which is far from being the case."
Traditionally, the most important of these controversies concerned the relationship between the substance of God the Father and the substance of his son. But Lienhard proposed that the dispute about substance was only a surface level symptom of a more fundamental disagreement, namely, the number of divine hypostases. A hypostasis is an "individual existence” (Hanson, p193):
The idea that God is both one and three (one Being but three Persons) did not exist for most of the fourth century. Only in the 360s did Athanasius reluctantly begin to accept the possibility of “three hypostases.” But Athanasius defended ‘one hypostasis’ to the end. The idea that God is one ousia (substance) but three hypostases (Persons) followed from the Cappadocians in the 360-370s. It was for that purpose that Basil of Caesarea made a distinction between the terms ousia (substance) and hypostasis (person).
In the traditional account, the Controversy began with the dispute in 318 between Arius and his bishop Alexander of Alexandria, two Christian theologians from Alexandria, Egypt. In this view, the Controversy was caused by Arius, who developed a novel heresy, claiming that the Son is a created being.
In reality, Arius did not develop a new theology. He was a conservative. Rather, Arius' dispute with his bishop was the continuation of the controversy that raged in the third century. The prominent theologians of the third century included Tertullian, who regarded the Son as part of the substance of the Father, Sabellius, who treated the Father and Son as a single hypostasis, and Origen, who believed that the Father, Son, and Spirit are three hypostases, meaning that the Son has distinct existence. In that century, Sabellian 'one hypostasis' theology was rejected in favour of Origen's three hypostases.
When the Controversy continued in the fourth century, while Arius defended three hypostases, Alexander taught one. 'Three hypostases' was accepted by most theologians in the East but in Latin-speaking North Africa, the traditional Monarchianism of the Western Church dominated. Consequently, Arius was excommunicated.
The Bible, according to R.P.C. Hanson, "does not give us a specifically Christian doctrine of God."
Christianity originated in Jerusalem in the Eastern Roman Empire. It expanded to Judea and also won Gentile converts, with Antioch as the early headquarters of the Gentile Church. In the first century, the church remained Jewish-dominated and continued to teach Jewish monotheism with Christ as an add-on.
In the second century, Christianity became Gentile dominated and, with that, several Gentile ideas crept into the church. With respect to Christology, the Apologists began to explain Jesus Christ as the Logos of Greek philosophy. In that philosophy, the Logos always existed inside God but became a second hypostasis (a distinct Being) when God decided to create. The Logos functioned as the divine Intermediary between God and creation. This theology evolved over time but remained the orthodox explanation of Christ into the fourth century.
In the late second century, Monarchianism (also called Modalism) opposed Logos theology. It accused Logos theology of teaching that God divided into two Gods, contrary to Jewish monotheism. Monarchians proposed that Father and Son are merely two names for the same Person.
Sabellianism is named after the early third-century theologian Sabellius who wrote in Rome in the early 3rd century. Logos theologians criticized Monarchianism for not distinguishing between the Father and Son. Therefore, Sabellius explained the Father and Son as distinct parts or forms or portions of a single God. In a way, he explained God as a single Being but also distinguished between the Father and Son.
Tertullian also wrote in the early third century, around the year 215, in the West in Latin. He is highly regarded today for introducing certain terms that are orthodox today, but he was a Logos theologian. For example, he believed that the Son is subordinate to the Father, that the Father was not always Father, and that there was a time when the Son did not exist; views that became anathemas to later generations. For him, the Son was part of the Father's substance.
Origen wrote a decade or two later. He was the most influential theologian of the first three centuries. He was also a Logos theologian but rejected the two-stage theory and taught that the Son and the creation always existed. In opposition to the Monarchians, Sabellius, and Tertullian, he taught that the Father, Son, and Spirit are three distinct Beings (hypostases).
The rest of the third century saw a controversy between Origen's view of three hypostases and Sabellius' one. For example, around the year 360, the bishops of Rome and Alexandria, both named Dionysius, were in dispute over the term homoousios, which was associated with a ‘one hypostasis’ theology. A few years later, in 268, a council in Antioch, the main Christian center in the East at the time, rejected both Paul of Samosata’s ‘one hypostasis’ (one Person) theology and the term homoousios. This dispute spilled over to the fourth century.
The 4th century began with ten years of the bloodiest campaign against Christians that the empire had witnessed (303-313). This was only the 2nd empire-wide persecution and also the longest. It was Rome’s final attempt to limit the expansion of Christianity. Emperor Diocletian’s first edict commanded churches and holy sites razed to the ground, sacred articles burned, and believers jailed.
When the fourth century began, the Orthodox View was that the Son is subordinate to the Father. This was true during the first three centuries, at the beginning of the 4th century, and for most of the fourth. Even Athanasius, since he regarded the Son to be part of the Father, believed the Son to be subordinate. The Cappadocians were the first to insist on full equality.
In the fourth century the Controversy continued with the dispute between Arius and his bishop Alexander:
The Nicene Council consisted almost exclusively of delegates from the Eastern Church and they, generally, believed in three hypostases. Since Alexander's 'one hypostasis' view was consequently in the minority, Alexander joined forces with the Sabellians, who also proclaimed one hypostasis. The emperor took Alexander's part in the dispute. This gave the Sabellians much power and enabled them to insert the term homoousios in the Creed which, before Nicaea, was associated with Sabellianism. The anathema which seems to say that the Father and Son are a single hypostasis is another sign of 'one hypostasis' domination.
In the decade after Nicaea, Emperor Constantine allowed the Eusebians (traditionally but misleadingly called Arians) to dominate again. While the exiled Eusebians were allowed to return, the church exiled all leading pro-Nicenes. After that, the term homoousios also disappeared from the debate.
While Constantine was still alive, he maintained unity in the church. But when he died in 337, his sons divided the empire between them, creating the potential for division in the church also. The Western church, which was traditionally Monarchian, believing that the Father and Son are a single Person (hypostasis), did not take part in the Controversy while Constantine was still alive. However, after the Empire was divided, the Western Church entered the Controversy by accepting Athanasius and Marcellus as orthodox. Both Athanasius and Marcellus, consistent with Western theology, believed that the Father and Son are a single hypostasis.
During the 340s, while the Empire remained divided, the Latin (Western) and Greek (Eastern) churches also remained divided. While the West formulated a manifesto at Serdica that explicitly declared one hypostasis, the East issued the Dedication Creed that is mainly anti-Sabellians and confessed three hypostases.
In the early 350s, the Empire was united again under Constantius, Constantine’s remaining son, previously the Eastern Emperor. By manipulating church councils and exiling bishops, he forced both the Western and Eastern churches to accept a Homoian (Arian) Creed. Homoianism rejected the idea that the Son is homoousios (of the same substance) as the Father and viewed Him as subordinate to the Father. In the mid-350s, Athanasius re-introduced the term homoousios into the Controversy.
The following quote provides a succinct summary of the religious policies of the emperors in the 360s and 370s - between Constantius and Theodosius:
“Constantius, who had lent forceful support to the Homoian position, died in 361. He was succeeded briefly by his cousin Julian, who had renounced Christianity and sought to purge the empire of Christian influences, and by Jovian, who showed signs of favoring pro-Nicenes during his brief reign. In 364, imperial authority was again divided, now between Valens in the East (364–378) and Valentinian in the West (364–375). Valens was an active promoter of the homoian cause, while Valentinian followed a non-interventionist policy that was nevertheless sympathetic to the Nicene position. Upon his death in 375, Valentinian was succeeded by his son Gratian, who adopted a policy of general tolerance.” (Anatolios, p. 29-30)
Julian demanded the restoration of several pagan temples which Christians had seized or destroyed. In this period, the main Eastern emperor was Valens. He continued Constantius' religious policy and maintained the Homoian standard. He used the power of the state to promote his theology. He made sure that the right person was installed as archbishop, banished and imprisoned pro-Nicene clergy, put them to forced labor, and subjected them to taxes from which anti-Nicenes were exempt. But “his efforts at persecution were sporadic and unpredictable.” (Hanson, p791-792) The main Western emperors were Valentinian and his son Gratian. They tolerated different views, allowing the Western Church to return to its traditional Monarchianism roots.
Also during the 360-370s, the Cappadocian fathers accepted the Nicene Creed. However, like other Easterners, they believed in three hypostases, meaning that the Son is a distinct Person. Consequently, they interpreted homoousios as saying that the Father and Son are two distinct substances (Persons) who are equal in all respects. In what is known as the Meletian Schism, this brought Basil of Caesarea, the first Cappadocian, in severe conflict with Athanasius and the other Western pro-Nicenes, who believed that the Son is part of the Father.
In the traditional account, the church ended the Controversy by finally rejecting Arianism at the Second Ecumenical Council (the Council of Constantinople of 381). In reality, already in the preceding year, in February 380, Roman Emperor Theodosius, through Roman Law - the Edict of Thessalonica - made Nicene Christianity the State Religion of the Roman Empire and outlawed Arianism. Consequently, the subsequent council in 381 was a formality. Since Theodosius had already outlawed and criminalized Arianism, no Arian was allowed to attend.
Since the Western and Eastern pro-Nicenes were divided on the number of divine hypostases, the question arises whether Theodosius prescribed a 'one hypostasis' or a 'three hypostases' theology. The following supports the view that his was a Western 'one hypostasis' theology:
Both before and after the Council of 381, Theodosius implemented severe persecution of non-Nicene groups. Through further edicts, he forbade Arian worship meetings, confiscated Arian churches, and exiled and even killed their leaders. Theodosius required groups who claimed to be compliant with his edicts to submit to him their theologies and he personally decided which groups complied.
Lastly, the Controversy did not end at the 381-council. It continued in the fifth century.
The Roman Empire was not a democracy. It was a dictatorship. The emperors were also war generals. They decided which religions to allow and, in the Christian Roman Empire. the emperors were the ultimate judges in doctrinal disputes. For example, at Nicaea, Constantine insisted on the term homoousios. His son Constantius, in the 350s, when he became emperor of the entire Empire, manipulated church councils to force the church to accept a Homoian Creed. Theodosius, in the year after he had become the Eastern Emperor in 379, issued an edict which made Nicene Christianity the State Religion of the Roman Empire and outlawed and criminalized other forms of Christianity, followed by severe persecution.
Inside the Roman Empire, the pro-Nicene faction ultimately gained the upper hand through the Edict of Thessalonica, issued on 27 February AD 380 by the then reigning three co-Emperors. This edict made Nicene Christology the state religion of the Roman Empire. It criminalized all non-Nicene strands of Christianity, described them as “foolish madmen” and “heretics” and authorized their punishment. It said: “They will suffer … the punishment of our authority which … we shall decide to inflict.” This was enforced strictly. Two days after he had arrived in the capital of the Empire (Constantinople), Theodosius exiled the Homoian bishop of the city (Demophilus) and appointed as bishop one of the Cappadocians (Gregory of Nazianzus) from the small group of Nicene supporters. In January 381, he issued another edict, forbidding non-Nicene Christians from having church meetings and from settling in the cities. Later in 381, he called the 'ecumenical' Council of Constantinople but only pro-Nicenes and only were allowed to attend. The Western Church was not represented either. To ensure compliance, Theodosius appoint one of his unbaptized government officials as chairperson and as bishop of Constantinople. After the Council, Theodosius evicted non-Nicene Christians from their churches, causing great disturbances and riots which he put down by force.
However, outside the Roman Empire, Arianism and other forms of Unitarianism continued to be preached for some time. The modern Roman Catholic Church and the Eastern Orthodox Church, as well as most other modern Christian denominations, have generally followed the Trinitarian formulation.
Arius described the Son as made out of nothing. In his view, perhaps, the Son was created. But Arius was an extremist. The mainstream ‘Arians’ believed that the Son was begotten from the being of the Father. For example, Eusebius of Caesarea, the theological leader of the ‘Arians’, said: “He alone was born of the Father himself” (LA, 58).
The Trinitarian historian Socrates of Constantinople reports that Arius first became controversial when he formulated his view as follows:
If the Father begat the Son, he that was begotten had a beginning of existence: hence it is that there was when the Son was not. It follows then of necessity that he had his existence from the non-existence.
Lienhard describes Eusebian Theology as follows:
“There is one God, who is the arche—the beginning, the first principle, the ultimate source, and the cause of everything else that exists. He is eternal and underived, and utterly transcendent, even unknowable, best described by the via negativa: as anarchos (without source), agen(n)êtos (unoriginate or unbegotten), akataléptos (incomprehensible). This God, the Father, and only He, is God in the truest and fullest sense of the word.” “Besides the Father, there also exists another hypostasis, which Scripture calls Son, Word, Image, Wisdom, Power, and ‘the firstborn of all creation’ (Col 1:15).”
In the third century, the term homoousios was preferred only by Sabellians. In was included in the Nicene Creed because the Sabellians preferred it, because the Sabellians allied with Alexander, and because the emperor took Alexander's part.
The Arian Controversy was not simply is dispute between 'Arians' and Nicenes. Both sides divided into factions and the disputes between these factions were as real as between the 'Arians' and Nicenes. The Meletian Schism was a dispute between two pro-Nicene factions, namely, between the Latin Western pro-Nicenes (Athanasius et. al.) and the Greek Eastern pro-Nicenes (the Cappadocians). While the Westerners believed in one hypostasis, the Cappacocians taught three. The term 'Meletian' is derived from the name of Meletius, the bishop of Antioch, who was opposed by Paulinus, who was supported by the Western pro-Nicenes.
"Arius's Christology was a mixture of adoptionism and logos theology. His basic notion was that the Son came into being through the will of the Father; the Son, therefore, had a beginning. Although the Son was before all eternity, he was not eternal, and Father and Son were not of the same essence. In Jesus, who suffered pain and wept, the logos became human. ... According to Athanasius, God had to become human so that humans could become divine. ... That led him to conclude that the divine nature in Jesus was identical to that of the Father and that Father and Son have the same substance. He insisted on the need for the Nicene homoousios to express the Son's unity with the Father.: 2
R.P.C. Hanson quotes with approval "a paper by R. D. Williams." "Alexander of Alexandria, Williams thinks, had maintained that the Son [...] is a property or quality of the Father, impersonal and belonging to his substance. Properties or qualities cannot be substances [...] they are not quantities. The statement then that the Son is idios to (a property or quality of) the Father is a Sabellian statement.": 92
The term ‘Arian Controversy' implies that Arius caused the Controversy by developing a novel heresy that became the main impetus of the Controversy. It also implies that the anti-Nicenes followed Arius. The reality is that Arius was not of any great significance. He had few real followers and did not leave behind a school of disciples. Nobody regarded his writings worth copying. His theology played no part in the Controversy after Nicaea. Therefore, the anti-Nicenes are mistakenly called 'Arians'. Neither should it be called the 'Arian Controversy. Since Arius was part of the 'trajectory' led by the two Eusebii, Ayres refers to the fourth century anti-Nicenes as 'Eusebians'.: 52 Arius taught an extreme version of the Eusebian teaching. In fact, the so-called Arians also opposed Arius.
The dispute between Alexander and Arius spread quickly because of "existing theological trajectories and tensions present in the early years of the fourth century.": 41 According to Eusebius's work, The Life of Constantine, the controversy had spread from Alexandria into almost all the African regions, and was considered a disturbance of the public order by the Roman Empire.
Constantine the Great (Constantine I) sent two letters to Arius and Bishop Alexander, asking the religious leaders to stop the controversy. The ongoing controversy led to Constantine's oversight of the First Council of Nicaea.
The traditional account of the Controversy assumed that Arius' theology was new but would not be contained within the Alexandrian diocese. It spread far beyond Alexander's see and had become a topic of discussion—and disturbance—for the entire Church. In reality, the dispute spread quickly because it was the continuation of an existing fire.
Constantine I legalized Christianity in 313 through the Edict of Milan. "Constantine desired that the church should contribute to the social and moral strength of the empire, religious dissension was a menace to the public welfare." Consequently, the emperor had taken a personal interest in several church issues, including the Donatist controversy in 316. He also wanted to bring an end to the Arian dispute. Through the Council of Nicaea in 325, he attempted to unite Christianity and establish a single, imperially approved version of the faith.
To this end, the emperor sent bishop Hosius of Corduba to investigate and, if possible, resolve the controversy. Hosius was armed with an open letter from the Emperor: "Wherefore let each one of you, showing consideration for the other, listen to the impartial exhortation of your fellow-servant."
Earlier in 325, a pro-Alexander council met in Antioch which formulated a creed (that does not contain the term homoousios) and provisionally excommunicated Eusebius of Caesarea; the leader of the 'Arians'.
As the debate continued to rage despite Hosius' efforts, Constantine in AD 325 took an unprecedented step: he called an ecumenical council at Nicaea composed of church prelates from all parts of the empire to resolve this issue, possibly at Hosius' recommendation. Around 250-300 bishops attended, almost exclusively from the East. Italy, Spain, Gaul, North Africa, Persia, and Scythia each sent one bishop.
The Bishop of Rome, Sylvester I, himself too old to attend, sent two priests as his delegates. Arius himself attended the council as well as the young deacon Athanasius, who attended as an assistant to Alexander of Alexandria and who would become the champion of the Nicene Creed and spend most of his life battling Arianism. Also there were Eusebius of Caesarea and Eusebius of Nicomedia, supporters of Arius and the leaders of the Eusebians (traditionally called 'Arians'). Eusebius of Caesarea, the historian and theologian, was universally acknowledged to be the most scholarly bishop of his day. Ossius presided as the emperor's agent. The emperor participated in and even led some of its discussions. "Constantine took part in the Council of Nicaea and ensured that it reached the kind of conclusion which he thought best." (Hanson, p. 850)
It is traditionally erroneously claimed that Athanasius played a significant role at Nicaea. He was not yet a bishop and not yet 30 years old. It is also sometimes erroneously claimed that Athanasius' opponents were led by Arius the presbyter. Arius was of little importance. Alexander's opponents were led by the two Eusebii and may be called the Eusebians.
For about two months, the two sides argued and debated, with each appealing to Scripture to justify their respective positions. Arius maintained that the son of God was a creature, made from nothing; and that he was God's first production, before all ages. He also argued that everything else was created through the son. Thus, said Arius, only the son was directly created and begotten of God; furthermore, there was a time that he had no existence. He was capable of his own free will, said Arius, and thus "were He in the truest sense a son, He must have come after the Father, therefore the time obviously was when He was not, and hence He was a finite being."
According to some accounts in the hagiography of Saint Nicholas, debate at the council became so heated that at one point, he slapped Arius in the face. The majority of the bishops at the council ultimately agreed upon a creed, known thereafter as the Nicene Creed formulated at the first council of Nicaea. It included the word homoousios, meaning 'consubstantial", or 'same in essence', which was incompatible with Arius' beliefs. On June 19, 325, council and emperor issued a circular to the churches in and around Alexandria: Arius and two of his unyielding partisans (Theonas and Secundus) were deposed and exiled to Illyricum, while three other supporters—Theognis of Nicaea, Eusebius of Nicomedia and Maris of Chalcedon—affixed their signatures solely out of deference to the emperor. However, Constantine soon found reason to suspect the sincerity of these three, for he later included them in the sentence pronounced on Arius.
Ironically, Constantine's efforts, particularly the inclusion of the term homoousios which, before Nicaea, was associated with Sabellianism, caused deep divisions after Nicaea.
In 358, the emperor Constantius II requested two councils, one of the western bishops at Ariminum (now Rimini in Northern Italy) and one of the eastern bishops at Nicomedia.
In 359, the western council met at Ariminum. Ursacius of Singidunum and Valens of Mursa, following the new creed drafted at Sirmium (359), proposed that, "according to the scriptures," the Son was "like the Father." This is known as the Homoian view which held that the Bible does not reveal whether the son is of the same substance as the Father and we, therefore, should not speculate about such things. This view is in opposition to the "of the same substance" (homoousios) view of the Nicene Creed. The council, including some supporters of the older creed, accepted this proposal. After the council, Pope Liberius condemned the creed of Ariminum, while his rival, Pope Felix II, supported it.
An earthquake struck Nicomedia, and in 359 the eastern council met at Seleucia Isauria instead. The council was bitterly divided and procedurally irregular, and the two parties met separately and reached opposing decisions. Following the Homoian view, Acacius of Caesarea declared that the son was "like the Father". However, Basil of Ancyra and his party, following a (Homoiousian) Creed of Antioch from 341, declared that the son was of "similar substance" to the Father. The majority at Seleucia accepted the "similar substance" view and deposed the opposing party.
Constantius did not accept this outcome and requested a third council, at Constantinople (359), of both the eastern and western bishops, to resolve the split at Seleucia. Acacius and Basil of Ancyra, respectively, again proposed the "like the Father" and "similar substance" views, as were explained at Seleucia. However, Maris of Chalcedon, Eudoxius of Antioch, and the deacons Aëtius of Antioch and Eunomius of Cyzicus proposed a third view which was similar to Arius' teachings, namely that the son was of "a dissimilar substance" from the Father. The Heteroousians ("dissimilar substance") won the victory over the other two views in an initial debate. However, Constantius was not willing to accept this outcome either. He intervened and banished Aëtius; one of the leading proponents of the "dissimilar substance" view. After this, the council, including Maris and Eudoxius, agreed to a fourth view, namely the homoian ("like the Father") view that was already agreed to at Ariminum. They made only minor modifications to the Ariminum creed.
After the Council of Constantinople, the homoian bishop Acacius deposed and banished several homoiousian bishops, including Macedonius I of Constantinople, Basil, Eustathius, Eleusius of Cyzicus, Dracontius of Pergamum, Neonas of Seleucia, Sophronius of Pompeiopolis, Elpidius of Satala and Cyril of Jerusalem. At the same time, Acacius also deposed and banished the Anomoean deacon Aëtius.
In 360, Acacius appointed Eudoxius of Antioch to replace Macedonius and Athanasius of Ancyra to replace Basil, as well as Onesimus of Nicomedia to replace Cecropius, who had died in the earthquake at Nicomedia.
These disagreements divided the Church into various factions. There was no formal schism.
As indicated by the names of the "sides" listed below, the Arian controversy was not about the entire Nicene Creed but focused on the term Homoousion (same substance). The Homoousians supported theview that the Son's substance is the same as the Father's. The Heteroousians claimed that, since the Father alone exists without cause, the Son's substance must be different from the Father's uncaused substance. The Homoiousians were somewhere midway between the Homoousians and Heteroousians. They also rejected the word homoousion and but maintained that, since the Son was figuratively born from the Father and inherited some of the Father's characteristics, He must be of a "similar substance." But perhaps the Homoians rebelled most against the word homoousion because they claimed that it is utter arrogance to speculate about the substance of God because this is not revealed in the Bible.
It was mainly under the influence of the Cappadocian Fathers that the terminology was clarified and standardized so that the formula "three hypostases in one ousia" came to be accepted as an epitome of the orthodox doctrine of the Trinity.
The Homoousians taught that the son is of the same substance as the Father, i.e. both exist without cause. In the 3rd century, the Sabellians used the term but it was condemned as heresy by Pope Calixtus. However, the term was included in the Nicene Creed of 325 and confirmed by the Council of Constantinople in 381. Since then, it has become the basis of most of modern Trinitarianism.
According to the historian Socrates of Constantinople, Marcellus of Ancyra and Photinus taught "that Christ was a mere man." Their opponents associated the teachings of Marcellus of Ancyra and Photinus of Sirmium with those of Sabellius and Paul of Samosata, which had been widely rejected before the controversy.
The Homoiousian school taught that the Son is of a similar substance to the Father but not the same.
The Homoians taught that the son is similar to the Father, either "in all things" or "according to the scriptures," without speaking of substance. Several members of the other schools, such as Hosius of Cordoba and Aëtius, also accepted certain Homoian formulae.
The Heteroousians taught that the son is of a different substance from the Father, i.e. created. Arius had taught this early in the controversy, and Aëtius would teach the later Anomoean form.
Many critics of the "Nicene" Creed cannot be clearly associated with one school, often due to lack of sources, or due to contradictions between sources.
General info from Wikipedia.org