Opuscula psychologica, theologica, daemonologica

 After the judgment of the thoughts, an exact discernment of how the thoughts happen to be, whether they are good or otherwise but imagination is the

 to divide for us, by the established terms, the sesquitertian ratios into both the sesquioctave ratios and the leimmata, we would have stopped at thes

 having split it, he bent each one into a circle, bringing them together middle to middle with each other like a chi, having joined 7 them both to them

 left, or rather the one is an image of mind, the other of soul. And in the soul itself, the right is that which is turned toward the intelligible thin

 regarding the explanation of the Platonic psychogony, this we now discharge for you as a kind of debt. For Plato's statement that the division of thes

 and of exegesis. And there is a letter of mine placed among my books that has traced out and carefully examined the meaning in the sayings. But it is

 a ruler drives a team of two then of the 14 horses, one of them is noble and good and of such stock, but the other is from opposite stock and is oppo

 a body from one of the seeing things, such that it is able to be extended as far as the stars. But it was better, he says, than to say that the extern

 through which it is not swept into material disorder, but is joined to the divine light, holds it in its own place and makes it unmixed with matter, l

 of knowledge. For there is something intelligible, which you must understand with the flower of the intellect. And he says that the one in us is twofo

 agrees, but among them the salty is more than the drinkable. They say, for example, that every soul is either divine or changing from intellect to min

 to be deemed worthy of pardon in repenting. If the soul is a body according to some of the ancients, what is it that contains it? every body is three-

 distinction. Two kinds of air according to Aristotle, the vaporous from the exhalation of water and the smoky from the extinguishing of fire. The latt

 Plato. Pleasure is not a coming-to-be for coming-to-be is of things that are not, while pleasure is of things that are. And coming-to-be is swift and

 is natural, while habit is acquired and taught. Providence is the care for existing things that comes from God. Epicurus says: the blessed and incorr

 but such powers are simply and imperceptibly desired. What then? Do we have three souls? Solution: just as the soul, when united to the body, seems to

 When this is dimmed they also are dimmed the soul flourishes when this 34 withers. Further, everything desires to preserve its own substrate. If the

 actuality, as physicians, others in relation to something, others a double or one-and-a-half ratio. Potentiality is found in substance, as a man in th

 concerning form, matter and cause, for example the matter of the celestial bodies is not the four elements, but a certain fifth, spherical one, as be

 as knowledge (for knowledge is a transition from defined things to defined things for this reason it is also knowledge, as leading the mind to a stat

 this, for indeed the flesh also moves downwards and is none of the elements. Aporia: but matter, that is the element, is not soul, but the form that c

 definitions have as their beginning the most general things, as their end the most specific things. If, then, these are finite, so are the definitions

 and it acts according to one part and another. It seems to act in these ways as being one. For if it is divided, it is necessary for the parts to be e

 the rest, but this is about hot and soft, heavy and light, rare and dense, and many opposites. In humans, the cause of local motion is intellect, in i

 is nourished {which} is twofold: either as Matter or as an instrument. And the instrument is twofold: either moving and being moved, like the innate h

 is equal in distance to the zodiac signs. Light is not a body. for if it were a body, how would it be possible for it to have instantaneous movement,

 we see the introduction of the forms of things seen entering the sight, but how do we see the interval of the air in between? Solution: It is not that

 with a violent collision. In soft things no sound is produced, because the air is broken up in their pores and dispersed as in sponges. In things that

 a buzzing which is conveyed back to the sense of hearing. Others say that the sound occurring in the ears after the blockage is of the external air th

 For instance, fish, not having this, are cooled through their gills. Those that have a windpipe also have a lung. Fish have neither these nor a heart.

 the sense organs of touch, it is clear for every sense organ is both separated and known. Aristotle speaks of the senses both as one each and as many

 Aristotle in On the Soul : if sensation ceased, the sense-organ would also cease. But if the second is not, neither is the first. Sensation and sense-

 Some add also a sixth, the attentive [faculty], as when a man says, I perceived, I thought, I opined. To this part they also add the activities of t

 We can say ten, but not indeed opine it, so that opinion is not up to us. But neither do we imagine what we wish for we see at night what we do not w

 in the case of children, the one according to state, and the one in act, as the one governing all things or the one entering from without. Plato says

 theoretical versus the practical. The theoretical corresponds to a vision discerning of forms, while the practical corresponds to a vision not only kn

 organs. Moreover, at night the nutritive faculty is more active, but the locomotive faculty is not at all. A difficulty: the vegetative faculty produc

 simpler, or rather the things inherent in the matter, into which the matter is also divided, which are also prop[erly] called its elements. I say then

 he hints that it is not completed from both of the things mixed, but is produced in the union of the soul and the body, not by the soul itself giving

 closing the senses, so as to know unknowingly the transcendent substance of that which is. For according to their own opinions, the philosopher who ha

 he himself will also pardon his own student for the apparent 78 opposition to him and others will come here again to bear witness for us, the philoso

 it grows and is naturally constituted to decay, must in every way grow along with and decay along with the other in a connate manner for that by whic

 a demonstration, so also the soul in an infant's body and a more imperfect one, if it were in another, perfect body, would immediately have shown its

 I shall use the argument. In what do you say virtue is inherent? or again, is it superimposed on the formless and incorporeal and uncompounded nature,

 Porphyry has philosophized in harmony with this. For in discussing the soul, he says: “Just as insomniacs, by the very act of wanting to sleep and wat

 have they cast off? Perhaps those who hold the contrary opinion will vex us with these things. But their objection is like a spider's web, which will

 to have received watchwords from the first father, nor that they possess the fullness of many bosoms, nor would I accept that they stand before the bo

 both the Sibylline and the Orphic ones, and those according to which the Berytian Bulls came to be and Amous the Egyptian, and Socrates and Plato (for

 of the bonds by which they were bound, and after this, turning their minds upward, they will approach God. And if the account told about the Sibyl wer

 has the front part? What then do you think? a mind scattered in so great a size is from this cause for him both slack and weak, and the soul is simply

 would remember any of the things here. But as many of the souls as were allotted to more humble portions and their whole mind has not been snatched aw

 Let us not altogether reject the analogy of the eye in the case of the soul, let it be and be called a more precise substance of the soul but if some

 The manner of the entry of souls, and likewise of their release or separation from hence, both are most difficult or hard to explain for of the first

 but by such powers the soul is led like some kind of thing moved by another, being drawn towards whatever the leaders happen to lead it, but then rath

 For that which is according to reason, knowledge is readily at hand, but that which is contrary to reason, is so because it has received such a nature

 of beasts, but perhaps the matter which reason has shown not to exist. Therefore our bodies will be resurrected, and there will be nothing to prevent

 fitting and gluing it to that by means of a suitable analogy, not placing the rational and intellectual substance into any of the animals for this is

 are generated from these powers alone, for this reason, having abandoned the others, they divided the substance of the soul into these alone. But if y

 it is in fourths, when one might contemplate these both in the third order of the intellectual virtues and in the fourth of the paradigmatic virtues,

 and so interpreting the Platonic opinion, but they do not seem to me to have grasped the precise meaning of his doctrine. But if I shall clarify for y

 and with nothing separating them, it is necessary for the one to be ordered, and the other to order and the one which is ordered has its form divided

 what is hard and resistant in them has been smoothed out by me. But what follows from this must be attributed to them alone for, proposing to speak a

 proceeds from it and returns to it.” Then indeed he works out the point by division. For if it only remained, it would in no way differ from its cause

 in our sacred writings, neither a whole soul nor any whole nature, apart from the partial ones, has been dogmatically established1. I for my part reje

 by the energy, then also the substance is perfected according to it, and these things stand in each other according to one energy. For he who does not

 having a life activated according to intellect and reason the psychic is defined according to reason 124 and takes care of divisible souls the physi

 tormenting them. But there are, they say, both on earth divine daimons and in the air, guardians of the animals there, and <in> the water, extending t

 make it superior to the confusion of life, but, if possible, may you not even leave behind in the terrestrial world the very body which you have put o

 cast under your mind: for there is no plant of truth on earth» that is: do not busy your mind with the great measures of the earth, as the geographer

 Gregory by reason and contemplation leads the soul up to the more divine things by reason that is according to us, the more intellectual and better,

 such a lion-bearing fount of heaven and the stars, but the ruling part of its own existence conceals the vision of them. Chaldaean Oracle. From all si

 often appearing, they feign the semblance of some goodness towards the one being initiated. Chaldean Oracle. The soul of mortals will draw God into it

 they can. Whence everything they say and show is false and insubstantial for they know existing things through forms but that which knows future thi

 and fear is the holding back of his goodness towards us for the sake of the economy. Chaldean Oracle. The Father snatched himself away, not even enclo

 they are possessed by passions. Therefore, it is necessary for these also to receive their part of the whole judgment and, having been filled up with

 for it is higher than being venerated, than being uttered, and than being conceived. A Chaldean Oracle. The Iynges, being conceived by the Father, the

 an unknown password, spoken and unspoken. And they often bring the soul down 148 into the world for many reasons, either through the shedding of its w

 of truth and of love. After which are the demiurgic fountains, such as that of the ideas, according to which the cosmos and the things in it have shap

 enclosing the triad towards itself and they call these also intelligible. After these, another order of the intelligible and at the same time intelle

 to the setting [sun], and the pit to the one just at mid-heaven. And thus, gently separating the membrane of the liver, [which is placed] upon the org

 parts of philosophy is necessary. For according to moral philosophy it is necessary to assume that not all things are and come to be by necessity, but

 knowledge and sees not only the essences themselves, but also their powers and their activities, both those according to nature and those contrary to

 he acquired. For even before the birth of both, God knew that the one would be good, and the other would turn out bad and this knowledge is an unchan

 from the one who knows, and it revolves around the thing known and is made like the one who knows. I mean something like this: the knowledge of the so

 they fabricate. For I too had a certain little man, ignoble in soul, but by no means the least of storytellers to him, at any rate, such phantoms pre

to divide for us, by the established terms, the sesquitertian ratios into both the sesquioctave ratios and the leimmata, we would have stopped at these. But now (for it is not possible) one must proceed by another method. Let it be proposed then from the beginning to fill up the double ratio with the aforementioned means and with the sesquioctave ratios. It will be necessary, then, to take the sub-ratio of the double as such that there may be in it both two sesquioctave ratios and another sesquitertian. Let there be taken then first the third from the monad according to the octuple ratio, which is ˉξˉδ. From this it is possible to set off two sesquioctave ratios; for every multiple leads as many superparticular ratios named after it, as its position is from the monad; but there is no sesquitertian. Therefore, having tripled it, I make it ˉρˉϟˉβ, of which the sesquitertian is ˉσˉνˉϛ, and the sesquioctave is ˉσˉιˉϛ, and the sesquioctave of this is ˉσˉμˉγ. The ratio of the leimma, therefore, is what is left after the subtraction of the two sesquioctave ratios, ˉσˉμˉγ to ˉσˉνˉϛ; for from every sesquitertian, when two sesquioctave ratios have been subtracted, the ratio of the leimma is left over. But the sesquioctave of ˉσˉνˉϛ is ˉσˉπˉη, which preserves the harmonic mean, being placed between ˉρˉϟˉβ and ˉτˉπˉδ, which makes a double ratio with ˉρˉϟˉβ, and a sesquitertian with ˉσˉπˉη. If, then, it were possible to set off two sesquioctave ratios from ˉσˉπˉη, we would have filled up this sesquitertian as well with the sesquioctave ratios and the leimma. But now it is not possible; for its sesquioctave, ˉτˉκˉδ, does not have an eighth; wherefore it is not possible for there to be a sesquioctave ratio with it for those wishing always to keep the monad uncut; for its eighth is 40. Therefore, having doubled it, in order that we might make the half a whole, we will be able to take a sesquioctave of it as well. And through this we shall be compelled to double all those before it and those after it. There will be then instead of ˉρˉϟˉβ, ˉτˉπˉδ; instead of ˉσˉιˉϛ, ˉυˉλˉβ; and instead of ˉσˉμˉγ, ˉυˉπˉϛ; and instead of ˉσˉνˉϛ, ˉφˉιˉβ; and instead of ˉσˉπˉη, ˉφˉοˉϛ; and the sesquioctave of this is ˉχˉμˉη, and the sesquioctave of this is ˉψˉκˉθ, then ˉψˉξˉη, being the double of ˉτˉπˉδ, and having to ˉψˉκˉθ the ratio of the leimma. And so indeed the double interval has been filled up with the sesquialter, sesquitertian, and sesquioctave ratios in these numbers: ˉτˉπˉδ, ˉυˉλˉβ, ˉυˉπˉϛ, ˉφˉιˉβ, ˉφˉοˉϛ, ˉχˉμˉη, ˉψˉκˉθ, ˉψˉξˉη. If then we should wish to fill up the whole diagram, we shall set out6 in order instead of the first part, ˉτˉπˉδ; and instead of the double of this, ˉψˉξˉη; and instead of the triple of the first and sesquialter of the second, ˉ#ˉ2ˉ2ˉαˉρˉνˉβ; and instead of the quadruple of the first, ˉ#ˉ2ˉ2ˉαˉφˉλˉϛ; and instead of the fifth, which is the triple of the third, ˉ#ˉ2ˉ2ˉγˉυˉνˉϛ; and instead of the sixth, which is the octuple of the first, ˉ#ˉ2ˉ2ˉγˉοˉβ; and instead of the seventh, which is twenty-seven times the first, ˉ#ˉ2ˉ2ˉαˉτˉξˉη. If then we should wish to fill these up with both the harmonic and the arithmetic means, which, when inserted, will make the sesquialter and sesquitertian intervals, there will be, so that I may speak of one mean, between the double ˉτˉπˉδ and ˉψˉξˉη both ˉφˉιˉβ making the harmonic mean and ˉφˉοˉϛ the arithmetic. Know this also, that no superparticular ratio can be cut into equal parts; at any rate the semitone cannot be obtained in numbers, but is found in the middle of the seventeenth and the sixteenth ratio; and the seventeenth is greater than the so-called leimma, which was less than the precise semitone. The secret explanation of the Platonic psychogony, then, is another matter; but the mathematical one is this. Explanation of another Platonic thought from the Timaeus You love the Platonic spring insatiably. For still being full of the stream and overflowing with his wisdom, you desire to drink again from his spring. For you ask, what in the world these things also are: «This composition, therefore, (Plato says, speaking of the demiurge) he split in two lengthwise

ἐκκειμένοις ἡμῖν ὅροις τοὺς ἐπιτρίτους λόγους εἴς τε τοὺς ἐπογδόους καὶ τὰ λείμματα διελεῖν, μέχρι τούτων ἂν ἔστημεν. νῦν δέ (οὐ γὰρ οἷόν τε) δι' ἄλλης ἰτέον μεθόδου. Προκείσθω οὖν ἐξ ἀρχῆς καταπυκνῶσαι τὸν διπλάσιον λόγον ταῖς εἰρημέναις μεσότησι καὶ τοῖς ἐπογδόοις. δεήσει ἄρα τὸν ὑπόλογον τοῦ διπλασίου τοιοῦτον λαβεῖν, ὥστε εἶναι αὐτοῦ καὶ δύο ἐπογδόους καὶ ἐπίτριτον ἄλλον. εἰλήφθω οὖν πρῶτον ὁ τρίτος ἀπὸ μονάδος κατὰ τὸν ὀκταπλάσιον λόγον, ὁ ˉξˉδ. ἀπὸ τούτου δύο μὲν ἐπογδόους ἀποστῆσαι δυνατόν· ἅπας γὰρ πολλαπλάσιος τοσούτων ἐπιμορίων ἡγεῖται λόγων ἀντιπαρωνυμούντων αὐτῷ, ὁπόστος ἐστὶν ἀπὸ μονάδος· ἐπίτριτον δὲ οὐκ ἔστι. τριπλασιάσας οὖν αὐτὸν ποιῶ τὸν ˉρˉϟˉβ, οὗ ἐπίτριτος μὲν ὁ ˉσˉνˉϛ, ἐπόγδοος δὲ ὁ ˉσˉιˉϛ, καὶ τούτου ἐπόγδοος ὁ ˉσˉμˉγ. ὁ ἄρα τοῦ λείμματός ἐστι λόγος ὁ μετὰ τὴν ἀφαίρεσιν τοῖν δυοῖν ἐπογδόοιν λειπόμενος ˉσˉμˉγ πρὸς τὰ ˉσˉνˉϛ· ἀπὸ παντὸς γὰρ ἐπιτρίτου δύο ἐπογδόων ἀφαιρεθέντων καταλείπεται ὁ τοῦ λείμματος λόγος. ἀλλὰ τοῦ ˉσˉνˉϛ ἐπόγδοος ὁ ˉσˉπˉη, ὃς τὴν ἁρμονικὴν σῴζει μεσότητα τεταγμένος μεταξὺ τοῦ ˉρˉϟˉβ καὶ τοῦ ˉτˉπˉδ διπλάσιον πρὸς τὸν ˉρˉϟˉβ λόγον ποιοῦντος, πρὸς δὲ τὸν ˉσˉπˉη ἐπίτριτον. εἰ μὲν οὖν ἦν δυνατὸν ἀποστῆσαι δύο ἐπογδόους ἀπὸ τοῦ ˉσˉπˉη, κατεπυκνώσαμεν ἂν καὶ τοῦτο τὸ ἐπίτριτον τοῖς τε ἐπογδόοις καὶ τῷ λείμματι. νῦν δὲ οὐχ οἷόν τε· ὁ γὰρ ἐπόγδοος αὐτοῦ ὁ ˉτˉκˉδ ὄγδοον οὐκ ἔχει· διὸ πρὸς αὐτὸν ἐπόγδοον γενέσθαι λόγον οὐ δυνατὸν τοῖς ἄτμητον τὴν μονάδα φυλάττειν ἀεὶ βουλομένοις· τὸ γὰρ ὄγδοόν ἐστιν αὐτοῦ μ διπλασιάσαντες οὖν αὐτόν, ἵνα τὸ ἥμισυ ὅλον ποιήσωμεν, ἕξομεν καὶ αὐτοῦ λαβεῖν ἐπόγδοον. ἀναγκασθησόμεθα δὲ διὰ τούτου καὶ τοὺς πρὸ αὐτοῦ διπλασιάσαι πάντας καὶ τοὺς μετ' αὐτόν. ἔσται οὖν ἀντὶ μὲν σοῦ ˉρˉϟˉβ ὁ ˉτˉπˉδ ἀντὶ τοῦ ˉσˉιˉϛ ὁ ˉυˉλˉβ, αἀντὶ δὲ του ˉσˉμˉγ ὁ ˉυˉπˉϛ, ἀντὶ δὲ τοῦ ˉσˉνˉϛ ὁ ˉφˉιˉβ, ἀντὶ δὲ τοῦ ˉσˉπˉη ὁ ˉφˉοˉϛ· καὶ τούτου ἐπόγδοος ὁ ˉχˉμˉη, καὶ τούτου ἐπόγδοος ὁ ˉψˉκˉθ, ἔπειτα ὁ ˉψˉξˉη διπλάσιος μὲν ὢν τοῦ ˉτˉπˉδ, πρὸς δὲ τὸν ˉψˉκˉθ ὁ λόγον ἔχων τὸν τοῦ λείμματος. καὶ οὕτω δὴ συμπεπλήρωται τὸ διπλάσιον διάστημα τοῖς τε ἡμιολίοις καὶ ἐπιτρίτοις καὶ ἐπογδόοις λόγοις ἐν τοῖσδε τοῖς ἀριθμοῖς· ˉτˉπˉδ, ˉυˉλˉβ, ˉυˉπˉϛ, ˉφˉιˉβ, ˉφˉοˉϛ, ˉχˉμˉη, ˉψˉκˉθ, ˉψˉξˉη. εἰ οὖν ἐθελήσαιμεν ὅλον συμπληρῶσαι τὸ διάγραμμα, ἐκθήσο6 μεν κατὰ τὸ ἑξῆς ἀντὶ μὲν τῆς πρώτης μοίρας τὸν ˉτˉπˉδ, ἀντὶ δὲ τῆς διπλασίας ταύτης τὸν ˉψˉξˉη, ἀντὶ δὲ τῆς τριπλασίας μὲν τῆς πρώτης, ἡμιολίας δὲ τῆς δευτέρας τὸν ˉ#ˉ2ˉ2ˉαˉρˉνˉβ, ἀντὶ δὲ τῆς τετραπλασίας τῆς πρώτης τὸν ˉ#ˉ2ˉ2ˉαˉφˉλˉϛ, ἀντὶ δὲ τῆς πέμπτης, ἥ ἐστι τριπλασία τῆς τρίτης, τὸν ˉ#ˉ2ˉ2ˉγˉυˉνˉϛ, ἀντὶ δὲ τῆς ἕκτης, ἥ ἐστιν ὀκταπλασία τῆς πρώτης, τὸν ˉ#ˉ2ˉ2ˉγˉοˉβ, ἀντὶ δὲ τῆς ἑβδόμης, ἥ ἐστιν ἑπτακαιεικοσαπλασίων τῆς πρώτης, τὸν ˉ#ˉ2ˉ2ˉαˉτˉξˉη. εἰ δ' οὖν ἐθελήσαιμεν τούσδε καταπυκνῶσαι ταῖς τε ἁρμονικαῖς καὶ ταῖς ἀριθμητικαῖς μεσότησιν, αἳ παρεντεθεῖσαι τά τε ἡμιόλια καὶ ἐπίτριτα διαστήματα ποιήσουσιν, ἔσονται, ἵνα μίαν ἐρῶ μεσότητα, μεταξὺ τοῦ ˉτˉπˉδ καὶ τοῦ ˉψˉξˉη διπλασίου ὅ τε ˉφˉιˉβ ποιῶν τὴν ἁρμονικὴν μεσότητα καὶ ὁ ˉφˉοˉϛ τὴν ἀριθμητικήν. ἴσθι καὶ τοῦτο, ὅτι οὐδεὶς ἐπιμόριος λόγος εἰς ἴσους τέμνεσθαι δύναται· τὸ γοῦν ἡμιτόνιον ἐν ἀριθμοῖς οὐκ ἔστι λαβεῖν, ἀλλ' ἐν μέσῳ εὑρίσκεται τοῦ ἑπτακαιδεκάτου καὶ τοῦ ἑκκαιδεκάτου λόγου· καί ἐστιν ὁ ἑπτακαιδέκατος μείζων τοῦ καλουμένου λείμματος, ὃς ἦν ἐλάττων τοῦ ἀκριβῶς ἡμιτονίου. Ἡ μὲν οὖν κρύφιος τῆς Πλατωνικῆς ψυχογονίας ἐξήγησις ἄλλη· ἡ δὲ μαθηματικὴ αὕτη. Ἑτέρας Πλατωνικῆς διανοίας ἐξήγησις ἀπὸ τοῦ Τιμαίου Ἐρᾷς τῆς Πλατωνικῆς ἀκορέστως πηγῆς. ἔτι γὰρ πλήρης ὢν τοῦ νάματος καὶ ἐπιχειλὴς τῆς ἐκείνου σοφίας, αὖθις ἀπὸ τῆς αὐτοῦ ὀρέγῃ πιεῖν. ζητεῖς γάρ, τί ποτε καὶ ταῦτά ἐστι· «ταύτην οὖν τὴν σύστασιν (περὶ τοῦ δημιουργοῦ λέγων ὁ Πλάτων) διπλῆν κατὰ μῆκος