Heraclitae ab Heraclio auctore mole ardua, armorum genere terribilis de quibus mole rerum, quasi moletia. legio sex milium mole ossa dolerent. genitalia corporis partes, ut mole et similes sibi genuerit.
The Heraclites originate from the founder Heracleon. They accept only monks, reject marriage, and do not believe that children possess the kingdom of heaven.
The reason that the two names end up being associated with a sect of the same name is because the Heraclitae results in each case from attaching itae (= Gk -ίται) to the same consonant stem.
The form in Epiphanius for the sect associated with Heracleon is Ήρακλεωνίται but this might be just a deliberately chosen form to distinguish the two sects. It is worth noting that Epiphanius preserves separately a sect associated with a certain Hieracas (a variant of Heraclas) which sounds strikingly similar to what appears in Pseudo-Hieronymous. I will give the link here to Epiphanius's original discussion of the sect in Panarion 67 (what appears in the Life of Epiphanius is a later development of the report).
Hieracas (Hierax), an Egyptian teacher, from whom the sect of Hieracitae took their name. Our knowledge of him is almost entirely derived from Epiphanius (Haer. 67, p. 709), who states that he was contemporary with the Egyptian bp. Meletius and Peter of Alexandria, and lived under Diocletian's persecution. This agrees very well with the notice of him by Arius (vide infra), so that he may be placed at the very beginning of the 4th cent. Epiphanius treats him with more respect than other founders of heretical sects, and is willing to believe that he practised asceticism bond fide, which, in the case of his followers, he counts but as hypocrisy. According to Epiphanius, Hieracas lived at Leontopolis, in Egypt, abstaining from wine and animal food; and by his severity of life and the weight of his personal character did much to gain reception for his doctrines, especially among other Egyptian ascetics. He had great ability and learning, being well trained in Greek and Egyptian literature and science, and wrote several works in both languages. Epiphanius ascribes to him a good knowledge of medicine, and, with more hesitation, of astronomy and magic. He practised the art of calligraphy, and is said to have lived to 90 years of age, and to have retained such perfect eyesight as to be able to continue the practice of his art to the time of his death. Besides composing hymns, he wrote several expository works on Scripture, of which one on the Hexaemeron is particularly mentioned. It was, doubtless, in this work that he put forward a doctrine censured by Epiphanius, viz. the denial of a material Paradise. Mosheim connects this with his reprobation of marriage, imagining that it arose from the necessity of replying to the objection that marriage was a state ordained by God in Paradise. Neander, with more probability, conceives that the notion of the essential evil of matter was at the bottom of this as well as of other doctrines of Hieracas. This would lead him to allegorize the Paradise of Genesis, interpreting it of that higher spiritual world from which the heavenly spirit fell by an inclination to earthly matter. This notion would also account for a second doctrine, which, according to Epiphanius, he held in common with Origen, viz. that the future resurrection would be of the soul only, not of the material body; for all who counted it a gain to the soul to be liberated by death from the bonds of matter found it hard to believe that it could be again imprisoned in a body at the resurrection. The same notion would explain the prominence which the mortification of the body held in his practical teaching; so that, according to this view, Hieracas would be referred to the class of Gnostic ENCRATITES. The most salient point in his practical teaching was, that he absolutely condemned marriage, holding that, though permitted under the old dispensation, since the coming of Christ no married person could inherit the kingdom of heaven. If it was objected that the apostle had said, "marriage is honourable in all," he appealed to what the same apostle had said "a little further on" (I. Cor. vii.), when he wished all to be as himself and only tolerated marriage" because of fornication," i.e. as the lesser of two evils. Thus it appears that Hieracas believed in the Pauline origin of Hebrews, and his language seems to indicate that in his sacred volume that epistle preceded I. Corinthians. He received also the pastoral epistles of St. Paul, for he appeals to I. Tim. ii. 11 in support of another of his doctrines, viz. that children dying before the use of reason cannot inherit the kingdom of heaven; and asks if he who strives cannot be crowned unless he strive lawfully, how can he be crowned who has never striven at all? Arius, in his letter to Alexander in defence of his views concerning our Lord's Person (Epiph. Haer. 69, 7, p. 732; Athan. de Syn. i. 583; Hilar. de Trin. vi. 5, 12), contrasts his own doctrine with that of Valentinus, of Manichaeus, of Sabellius, of Hieracas; and presumably all these teachers, by rejection of whom he hopes to establish his own orthodoxy, were reputed as heretics. Hieracas, according to Arius, illustrated the relation between the first two Persons of the Godhead by the comparison of a light kindled from another, or of a torch divided into two, or, as Hilary understands it, of a lamp with two wicks burning in the same oil.
His doctrine concerning the Holy Spirit is more questionable. He was influenced by the book of the Ascension of Isaiah, which he received as authoritative. In it Isaiah is represented as seeing in the seventh Heaven, on the right and left hand of God respectively, two Beings like each other, one being the Son, the other the angel of the Holy Spirit Who spake by the prophets. Hieracas inferred that the latter Being, Who makes priestly intercession with groanings that cannot be uttered, must be the same as Melchisedek, who also was "made like unto the Son of God," and "who remaineth a priest for ever." These tenets are ascribed to Hieracas by Epiphanius, whose account is abridged by Augustine (Haer. 47), by Joannes Damascenus (66), and by "Praedestinatus" (47). The continued existence of the sect is assumed in a story told by Rufinus (Hist. Mon. 28, p. 196) of Macarius, who, when he had failed to confute the cunning arguments of a Hieracite heretic to the satisfaction of his hearers, vanquished him by successfully challenging him to a contest as to which could raise a dead body. Rufinus does not make the story turn on the fact that Hieracas denied the resurrection of the flesh.
The important thing for the reader to see is that Smith and Wace (p. ) cite Cotelier to explain the underlying relationship behind all these reports - viz. "that the name Hieracitae (followers of Hieracaa), became corrupted by copyists first into Hierachitae (see, for instance, Gennadius, Eccl. Dog. c. 67) and then into Heraclitae." Yet I am not so sure. I am very confident that all of these reports go back to the historical beliefs associated with the first Pope of Alexandria - viz. 'Heraclas.'
