Suggested prior reading: (Chaldean) Oracles of Zoroaster - an Introduction
We present first an exposition of Chaldaic beliefs according to 11th century author Psellus (as presented by Thomas Taylor) followed by our own understanding.
A Concise Exposition of Chaldaic Dogmas by Psellus
[As presented by Thomas Taylor in an article "Collection of the Chaldean Oracles" published in The Classical Journal, Volume 16, September and December 1817. All notations in square brackets  are editorial. Psellus was a Byzantine statesman and author (1018-1078 CE)]
"They assert that there are seven corporeal worlds, one empyrean [in highest heavens] and the first; after this, three ethereal [in the sky of the celestial sphere], and then three material worlds1, the last of which is said to be terrestrial, and the hater of life: and this is the sublunary place, containing likewise in itself matter, which they call a profundity [intense insight or depth]."
Note: 1 These three material worlds, are the inerratic [fixed. See inerratic circle below] sphere, the seven planetary spheres, and the sublunary regions.
"They are of opinion, that there is one principle of things; and this they celebrate as the one, and the good2."
Note: 2 So Plato.
"After this, they venerate a certain paternal profundity3, consisting of three triads; but each triad contains, father, power, and intellect."
Note: 3 This is called, by the Platonists, the intelligible triad; and is celebrated by Plato in the Philebus, under the names of bound, infinite, and the mixed; and likewise of symmetry, truth, and beauty, which triad, he says, is stated in the vestibule of the good.
"After this is the intelligible Iynx, then the Synoches, of which one is empyrean [in highest heavens], the other etherial, and the third material. The Teletarchae4 follow the Synoches."
Note: 4 The Iynx, Synoches, and Teletarchos of the Chaldeans, compose that divine order which is called, by the Platonists, the intelligible, and, at the same time, intellectual order; and is celebrated by Plato in the Phadrus, under the names of the super-celestial place, Heaven, and the super-celestial arch.
"After these succeed the fontal fathers5 [fontal meaning pertaining to or coming from a fountain or spring], who are also called Cosmagogi, or leaders of the world. Of these, the first is called once beyond, the second is Hecate, and the third is twice beyond."
Note: 5 These fontal fathers compose the intellectual triad of the Greeks, and are Saturn, Rhea, Jupiter.
"After these are the three Amilicti6; and, last of all, the Upezokus."
Note: 6 The three Amilicti are the same with the unpolluted triad, or Curetes, of the Greeks. Observe, that a fontal subsistence means a subsistence according to cause.
"They likewise venerate a fontal triad of faith, truth, and love. They assert that ihere is a ruling sun from a solar fountain, and an arch-angelic sun; that there is a fountain of sense, a fontal judgment, a thundering fountain, a dioptric fountain, and a fountain of characters, seated in unknown impressions. And, again, that there are fontal summits of Apollo, Osiris, and Hermes. They likewise assert that there are material fountains of centres and elements; that there is a zone of dreams, and a fontal soul.
"After the fountains, they say, the principles7 succeed: for fountains are superior to principles. But of the vivific8 [giving life] principles, the summit is called Hecate [otherwise Hecate is the goddess of darkness and witchcraft], the middle ruling soul, and the extremity ruling virtue."
7 These principles are the same with the Platonic supermundane order of gods.
8 The vivific triad consists, according to the Greek Theologists, of Diana, Proserpine, and Minerva.
"They have likewise azonic [not limited to a zone] Hecatae, such as the Chaldaic Triecdotis, Comas, and Ecklustike. But the azonic9 gods, according to them, are Serapis, Bacchus, the series of Osiris, and of Apollo. These gods are called azonic, because they rule without restraint over the zones, and are established above the apparent gods."
Note: 9 The azonic gods are the same with the liberated order of the Greek Theologists, or that order which is immediately situated above the mundane gods.
"But the zonic gods are those which revolve round the celestial zones, and rule over sublunary affairs, but not with the same unrestrained energy, as the azonic. For the Chaldeans consider the zonic order as divine; as distributing the parts of the sensible world; and as begirding [girding, binding] the allotments about the material region.
"The inerratic circle succeeds the zones, and comprehends the seven spheres in which the stars are placed. According to them, likewise, there are two solar worlds; one, which is subservient to the etherial profundity; the other zonaic, being one of the seven spheres.
"Of human souls, they establish a twofold foutal cause; viz. the paternal intellect10, and the foutal soul11: and they consider partial12 souls, as proceeding from the fontal, according to the will of the father. Souls of this kind, however, possess a self-begotten, and self-vital essence: for they are not like alter-motive natures. Indeed, since according to the Oracle, a partial soul is a portion of divine fire, a splendid fire, and a paternal conception, it inutt be an immaterial and self-subsisteirt essence; for every thing divine is of this kind; and of this the soul is a portion. They, assert too, that all things are contained in each soul; but that in each there is nn unknown characteristic of an effuble and ineffable impression. They are of opinion, that the soul often descends into the world, through many causes; either through the defiuxion of its wings,13 or through the paternal will. They believe the world to be eternal, as likewise the periods of the stars. They multifariously distribute Hades, at mie time calling it the leader of a terrene allotment, and at another the sublunary region. Sometimes they denominate it, the roost inward of the etherial and material worlds; at another time, irrational14 soul. In this, they place the rational soul, not essentially, but according to habitude, when it sympathises with it, and energises according to partial reason."
10 The Jupiter of the Greeks, the artificer of"the universe.
11 Called by the Greeks, Juno.
12 That is, such souls as ours.
13 So Plato: see my translation of the Phaedrus.
14 Hades is with great propriety thus called: for the rational, when giving itselt up to the dominion of the irrational soul, may be truly said to be situated in Hades, or obscurity.
"They consider ideas, at one time, as the conceptions of the father15; at another time, as universal reasons, viz. physical, psychical, and intelligible; and aguin, as the exempt hyparxes (or summits) of beings. They assert that magical operations are accomplished through the intervention of the highest powers, and terrene substances; and that superior natures sympathise with inferior, and especially with those in the sublunary region. They consider souls, as restored alter death to their pristine perfection, in the whales16 of the universe, according to the measures of their peculiar purifications; but some souls are raised by them to a supermundane condition of being. They likewise define souls to be media between impartible and partible natures. With respect to these dogmas, many of them arc adopted by Plato17 and Aristotle: but Plotinus, Porphyry, Janiblichus, Proclus, and their disciples, adopt the whole of them, and admit them without hesitation, as doctrines of a divine origin."
15 i.e. Jupiter, or the Demiurgos.
16 That is to say, the celestial and sublunary spheres.
17 Indeed, he who lias penetrated the profundity of Plato's doctrines, will find that they perfectly accord with these Chaldaic dogmas; as is every where copiously shown by Proclus.
"Thus far Psellus: I add, for the sake of those readers that are unacquainted with the scientific theology of the ancients, that as the highest principle of things is a nature truly ineffable and unknown, it is impossible that this visible world could have been produced by him without media; and this not through any impotency, but, on the contrary, through transcendency of power. For if he had produced all things without the agency of intermediate beings, all things must have been like himself, ineffable and unknown. It is necessary, therefore, that there should be certain mighty powers between the supreme principle of things and us: for we, in reality, are nothing more than the dregs of the universe. These mighty powers, from their surpassing similitude to the first God, were very properly called by the ancients gods; and were considered by them as perpetually subsisting in the most admirable and profound union with each other, and the first cause; yet so as amidst this union to preserve their own energy distinct from that, of the highest god. For it would be absurd in the extreme, to allow, that man has a peculiar energy of his own, and to deny that this is the case with the most exalted beings. Hence, as Proclus beautifully observes, the gods may be compared to trees rooted in the earth: for as these, by their roots, are united with the earth, and become earthly in an eminent degree, without being earth itself; so the gods, by their summits, are profoundly united to the first cause, and by this mean are transcendently similar to, without being, the first cause.
"Lines too, emanating from the centre of a circle, afford us a conspicuous image of the manner in which these mighty powers proceed from, and subsist in, the ineffable principle of things. For liere, the lines are evidently things different from the centre, to which, at the same time, by their summits, they are exquisitely allied. All these summits too, which are indescribably absorbed in centre, are yet no parts (i.e. powers) of it; for the centre has a subsistence prior to them, as being their cause."
This writer's understanding of the belief system of the Oracles is as follows:
Framework of the Oracle's Belief System
a) A derogation of the material existence as compared with the ideal of the divine existence;
b) A concept of human nature as a divine spark trapped in a material existence;
c) A method or process of freeing the soul from the vicissitudes of the material existence i.e. salvation or enlightenment that involves a ritual or spiritual ascent of the soul, a process called henosis; and
d) The placing of philosophical and spiritual concepts in a mythology that includes the gradual anthropomorphizing of concepts into deities and the assignment of gender to the deities.
Theology of the Oracles
The supreme transcendent God of the Oracles is often described in Pythagorean terms as the Monad.
The Monad, however, is described in triadic terms - a triadic-monad or three-in-one deity (cf. Christian Trinity): "the Father removed (snatched) himself (from his emanations/creations?) away, and did not enclose his own Fire in his Intellectual Power." (Psellus). "For everywhere power has been assigned the middle place; and within the intelligibles, it connects the Father and Intellect." notes Proclus in commentary of his quote from the Oracles, "For Power is with him while Intellect if from him." [To us this sounds like Intellect is an emanation while Power is a possession of the Father, the Monad.]
Proclus goes on to quote the Oracle as saying, "For the First Transcendent Fire does nor transfer (enclose) its own Power in matter by means of works, but by Intellect. For Intellect derived from Intellect is the first Craftsman of the fiery cosmos." There is a lot we can glean from the Oracle quotation by Proclus. First, a description of the supreme divinity as the First Transcendent Fire. The next is the function of the divine Intellect or Wisdom. Here, the Supreme divinity's intellect begets another Intellect which conceives the material existence, the "fiery cosmos". Psellus quotes the Oracle: "All things have been generated from one fire."
Psellus quotes the Oracles as saying, "For the Father perfected all things and handed them over to the Second Intellect, which you - the entire human race - call the First Intellect." Then we read from Simplicius a quote from the Oracles stating, "the First Fire and the other (Second) Fire are eager to mingle."
Damascius' quote from the Oracles states, "...for the Monad is extensible which generates duality (the Dyad)." We return to the writings of Proclus "...besides this one sits a Dyad." "For it has a double function; it both possesses the intelligibles in its mind and brings sense perception to the worlds."
The function of the First Intellect is to think Ideas. The Second Demiurgic Intellect's function is to fashion the intelligible, empyrean world on the model of the Ideas. The Second Demiurgic Intellect does this by projecting the Ideas like Zeus' lightening bolts into the womb of the feminine World Soul Hecate, the mediating power between the First & Second Intellects or a girdling membrane between the two levels. The First & Second Intellects together with the World Soul make up a Primordial Triad.
A complex chains of lesser beings, Iynges, Connectors, Teletarchs, angels and demons fill the void between the Primordial Triad and the material world. These lesser beings are issues of the Father and serve as messengers, mediators and separators between the empyrean and material worlds. The Teletarchs are associated with - and preside over - faith, truth and love, the three virtues through which the theurgist can seek unity with the Supreme.
Reference: The Chaldean Oracles: Text, Translation, and Commentary by Julianus (the Theurgist). Translation and Commentary by Ruth Dorothy Majercik
A Summary of Gnostic Beliefs
At the bottom end of the All lies Matter, made by the Demiurge. The world is a foul tomb and a form which the higher human soul must escape, shedding the lower soul's vehicle or garment, acquired during its descent through the stars and planets. Meditation, contemplation, ascetic conduct and correct ritual will free the soul from the astrological confines of Fate, and defend it against the demonic powers who fill the realm between the divine and mortals. Plotinus promoted contemplation and mediation as the means to reunion with the Divine while Iamblichus of Calcis (Syria) (a student of Porphyry himself a student of Plotinus) promoted invocation and ritual. According to Proclus, "The vehicle of every particular soul descends by the addition of vestures increasingly material; and ascends in company with the soul through divestment of all that is material and recovery of its proper form, after the analogy of the soul which makes use of it: for the soul descends by the acquisition of irrational principles of life; and ascends by putting off all those faculties tending to temporal process ith which it was invested in its descent, and becoming clean and bare of all such faculties as serve the uses of the process. (Elements of Theology, Proposition 209, quoted from Culianu, Psychanodia, p. 12.)"
Suggested prior reading: (Chaldean) Oracles of Zoroaster - an Introduction