Semi-modalistic trinitarianism is built upon a twisting of the Nicene concept of co-essentiality. The pro-nicene church fathers of the mid-fourth century defined co-essentiality as meaning nothing more than that the persons of the trinity, as truly distinct rational individual beings (that is, persons) shared a common nature or species. A common analogy used by the Nicene fathers to capture their meaning, for example, is of three men being co-essential, in that they, while remaining three distinct individuals, share a common and identical human nature. Although there are three men, there is only one nature between them, human nature. Such was the original meaning of co-essentiality.
For example, Athanasius said:
“Even this is sufficient to dissuade you from blaming those who have said that the Son was coessential with the Father, and yet let us examine the very term ‘Coessential,’ in itself, by way of seeing whether we ought to use it at all, and whether it be a proper term, and is suitable to apply to the Son. For you know yourselves, and no one can dispute it, that Like is not predicated of essence, but of habits, and qualities; for in the case of essences we speak, not of likeness, but of identity. Man, for instance, is said to be like man, not in essence, but according to habit and character; for in essence men are of one nature. And again, man is not said to be unlike dog, but to be of different nature. Accordingly while the former [men] are of one nature and coessential, the latter are different in both.”
Hilary of Poitiers likewise clarified:
“Since, however, we have frequently to mention the words essence and substance, we must determine the meaning of essence, lest in discussing facts we prove ignorant of the signification of our words. Essence is a reality which is, or the reality of those things from which it is, and which subsists inasmuch as it is permanent. Now we can speak of the essence, or nature, or genus, or substance of anything. And the strict reason why the word essence is employed is because it is always. But this is identical with substance, because a thing which is, necessarily subsists in itself, and whatever thus subsists possesses unquestionably a permanent genus, nature or substance. When, therefore, we say that essence signifies nature, or genus, or substance, we mean the essence of that thing which permanently exists in the nature, genus, or substance.”
And Basil of Caesarea wrote:
“The distinction between οὐσία [essence] and ὑπόστασις [person] is the same as that between the general and the particular ; as, for instance, between the animal and the particular man.” (Letter 236)”
This understanding of co-essentiality is likewise required by the council of Chalcedon:
“our Lord Jesus Christ, the same perfect in Godhead and also perfect in manhood; truly God and truly man, of a reasonable [rational] soul and body; consubstantial [co-essential] with the Father according to the Godhead, and consubstantial with us according to the Manhood”
Its clear, then, that the original intent of declaring that the Father, Son, and Spirit share one essence was not to make Them out to all be one person, one individual being, but simply to declare that They shared a common nature or species. This meaning changed, however, and was not kept clear as time went on; the Western churches going to far as to eventually formally change the meaning of co-essentiality in the 4th Lateran council in 1215. Rather than indicating a generic unity of sharing one nature, now co-essentiality was defined as teaching that the unity the persons shared was of being one single numerically individual reality, one rational individual being- that is, in reality, one person. The ‘essence’ was no longer viewed as a nature, but a single subsistent ‘supreme reality’.
“We, however, with the approval of this sacred and universal council, believe and confess with Peter Lombard that there exists a certain supreme reality, incomprehensible and ineffable, which truly is the Father and the Son and the holy Spirit, the three persons together and each one of them separately. Therefore in God there is only a Trinity, not a quaternity, since each of the three persons is that reality — that is to say substance, essence or divine nature-which alone is the principle of all things, besides which no other principle can be found. This reality neither begets nor is begotten nor proceeds; the Father begets, the Son is begotten and the holy Spirit proceeds.” (From Canon 2)
This teaching is a drastic departure from the faith of the early pro-nicene bishops, and represents the culmination of what many in the Nicene era had feared might result from the introduction of ‘essence’ speculation into the church’s dogma. A council of fathers gathered in Antioch in 345 had specified their belief that the Father, Son, and Spirit were not “one supreme reality”, that is, one person, one individual rational being, but rather, three:
“Nor again, in confessing three realities and three persons, of the Father and the Son and the Holy Ghost according to the Scriptures, do we therefore make Gods three; since we acknowledge the self-complete and unbegotten and unbegun and invisible God to be one only, the God and Father (John 20:17) of the Only-begotten, who alone has being from Himself, and alone vouchsafes this to all others bountifully.” (Macrostich)
Later in the same creed they went on to condemn the very view the 4th Lateran would later make dogma for the Roman churches:
“And those who say that the Father and Son and Holy Ghost are the same, and irreligiously take the three names of one and the same reality and person, we justly proscribe from the Church, because they suppose the illimitable and impassible Father to be also limitable and passable through His becoming man. For such are they whom Romans call Patripassians, and we Sabellians. For we acknowledge that the Father who sent, remained in the peculiar state of His unchangeable Godhead, and that Christ who was sent fulfilled the economy of the Incarnation.”
But one need not wait until the fourth century to find fathers who clearly taught that the Father, Son, and Spirit were not one numerically individual thing, one person. Second century father Justin Martyr, one of the earliest and best of the fathers, clearly understood the Father and Son to be numerically distinct persons, two distinct rational individual beings, not merely two names of or modes of one and the same reality:
“When Scripture says, ‘The Lord rained fire from the Lord out of heaven,’ the prophetic word indicates that there were two in number: One upon the earth, who, it says, descended to behold the cry of Sodom; Another in heaven, who also is Lord of the Lord on earth, as He is Father and God; the cause of His power and of His being Lord and God.” (Dialogue With Trypho, Chapter 29)
“And that this power which the prophetic word calls God, as has been also amply demonstrated, and Angel, is not numbered [as different] in name only like the light of the sun but is indeed something numerically distinct, I have discussed briefly in what has gone before; when I asserted that this power was begotten from the Father, by His power and will, but not by abscission, as if the essence of the Father were divided; as all other things partitioned and divided are not the same after as before they were divided: and, for the sake of example, I took the case of fires kindled from a fire, which we see to be distinct from it, and yet that from which many can be kindled is by no means made less, but remains the same.” (Dialogue With Trypho, Chapter 128)
“You perceive, my hearers, if you bestow attention, that the Scripture has declared that this Offspring was begotten by the Father before all things created; and that which is begotten is numerically distinct from that which begets, any one will admit.” (Dialogue With Trypho, Chapter 129)
Semi-modalistic trinitarianism, then, in proclaiming the the persons of the Trinity are numerically one substance, one individual, is clearly at odds with both the original dogmatic conception of co-essentiality held by the Nicene fathers, which proclaimed co-essentiality to mean nothing more than a mere generic unity of nature between really distinct individuals, as well as being at odds with the faith of the ante-nicene fathers, going back as close to the apostles as we can find.
For a look at how this semi-modalistic conception of the Trinity is opposed to scripture itself, and the very fundamental tenets of the Christian faith it teaches, see here.