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These notes on how Proclus' tradition interprets the Parmenides might be useful for students.
First, on the interpretation of the narrative transmission and the characters of the dialogue, from Florin George Călian "'Clarifications' of Obscurity: Conditions for Proclus’s Allegorical Reading of Plato’s Parmenides":
Allegorization of the narrative transmission. Proclus interprets the various stages in the transmission of the original conversation as the progression of the forms into matter, as a chain of ontological Ievels: Cephalus's audience represents the primordial material (hypodoche) in which the Demiurge, according to the Timaeus, impresses the forms; Antiphon's speech to Cephalus represents the progression of the forms into physikai ousiai; Pythodorus's description of the conversation to Antiphon stands for the progression of the forms into souls (Antiphon's interest in horses is related to the image of the soul in Plato's Phaedrus); the conversation itself stands for the Nous and the intelligible world of the forms.
Allegorization of the characters. According to Proclus, Parmenides is an analogon for the unparticipated and divine lntellect; Zeno is an analogon for the participated lntellect; and Socrates represents the particular intellect. Proclus discovers other kinds of analogia as well: Parmenides is the symbol of Being, Zeno that of Life, Secrates that of lntellect, Pythodorus stands for the angels, Aristoteles for individual souls (the fact that he becomes one of the thirty tyrants signifies the keenness of the souls to descend into the tyranny of the passions), Pythodorus for the "divine Soul" (he uncovers the intelligible world and receives Iogoi from it), Antiphon for the "demonic soul" (his association with horsemanship hints that he desires to rule the physical world), Cephalus for the "individual soul."
First, on the interpretation of the narrative transmission and the characters of the dialogue, from Florin George Călian "'Clarifications' of Obscurity: Conditions for Proclus’s Allegorical Reading of Plato’s Parmenides":
Allegorization of the narrative transmission. Proclus interprets the various stages in the transmission of the original conversation as the progression of the forms into matter, as a chain of ontological Ievels: Cephalus's audience represents the primordial material (hypodoche) in which the Demiurge, according to the Timaeus, impresses the forms; Antiphon's speech to Cephalus represents the progression of the forms into physikai ousiai; Pythodorus's description of the conversation to Antiphon stands for the progression of the forms into souls (Antiphon's interest in horses is related to the image of the soul in Plato's Phaedrus); the conversation itself stands for the Nous and the intelligible world of the forms.
Allegorization of the characters. According to Proclus, Parmenides is an analogon for the unparticipated and divine lntellect; Zeno is an analogon for the participated lntellect; and Socrates represents the particular intellect. Proclus discovers other kinds of analogia as well: Parmenides is the symbol of Being, Zeno that of Life, Secrates that of lntellect, Pythodorus stands for the angels, Aristoteles for individual souls (the fact that he becomes one of the thirty tyrants signifies the keenness of the souls to descend into the tyranny of the passions), Pythodorus for the "divine Soul" (he uncovers the intelligible world and receives Iogoi from it), Antiphon for the "demonic soul" (his association with horsemanship hints that he desires to rule the physical world), Cephalus for the "individual soul."
On the discussion between Socrates and Parmenides.
For Proclus, the problems reveal properties of form as such, and of the levels of forms: "Let us now deduce from all these problems [130e-134c] the nature of the primal Idea. From the first [130e–131e] we may gather that it is incorporeal; for if it were a body, it would not be possible to participate in it either as a whole or in a part of it. From the second [132a–b], that it is not coordinate with its participants; for if it were coordinate, it would have some property in common with them, because we would have to postulate another Idea prior to it. From the third problem [132b–c] we gather that it is not a thought [noēma] of Being [ousia], but itself Being [ousia] and existent [on], in order that that which participates in it may not be necessarily participant in knowledge. From the fourth [132d–133a] we gather that it is exclusively a model and not also an image, as is the case with the reason-principle [logos] at the level of Soul, lest its having some similarity to that which derives from it may involve the introduction of another Idea prior to it. For the reason-principle in Soul is a Being also, but it is not a model only, but also an image--for the Soul is not Being only, but also Becoming. From the fifth [133a–134c], we gather that it is not intelligible to us immediately, but only through its images, for the faculty of knowledge in us is not on the right level to grasp it. From the sixth [134c-134e], that it intelligizes what proceeds from it not coordinately but causally; for in intelligizing itself it knows itself as a paradigm, and what proceeds from it in a secondary way, and by knowing itself as their cause." (In Parm. 934)
For Proclus, the problems reveal properties of form as such, and of the levels of forms: "Let us now deduce from all these problems [130e-134c] the nature of the primal Idea. From the first [130e–131e] we may gather that it is incorporeal; for if it were a body, it would not be possible to participate in it either as a whole or in a part of it. From the second [132a–b], that it is not coordinate with its participants; for if it were coordinate, it would have some property in common with them, because we would have to postulate another Idea prior to it. From the third problem [132b–c] we gather that it is not a thought [noēma] of Being [ousia], but itself Being [ousia] and existent [on], in order that that which participates in it may not be necessarily participant in knowledge. From the fourth [132d–133a] we gather that it is exclusively a model and not also an image, as is the case with the reason-principle [logos] at the level of Soul, lest its having some similarity to that which derives from it may involve the introduction of another Idea prior to it. For the reason-principle in Soul is a Being also, but it is not a model only, but also an image--for the Soul is not Being only, but also Becoming. From the fifth [133a–134c], we gather that it is not intelligible to us immediately, but only through its images, for the faculty of knowledge in us is not on the right level to grasp it. From the sixth [134c-134e], that it intelligizes what proceeds from it not coordinately but causally; for in intelligizing itself it knows itself as a paradigm, and what proceeds from it in a secondary way, and by knowing itself as their cause." (In Parm. 934)
Further, from In Parm. 969-70: [F]or the primal Forms are the intelligible ones, and secondary are those which are intelligible on the one hand, but in the intellectual, and the third are those which are cohesive of all things, and fourth are those which bring to completion all intellectual and supracosmic realities, and after these again are the intellectual forms, such as have this characteristic in its proper form; the sixth rank is taken up by the assimilative forms, through which all the secondaries are made like to the intellectual forms, while the seventh rank is taken up by the transcendent and supracelestial forms which have a unifying force in respect of those forms which are divided about the cosmos, and the last rank is held by the forms in the cosmos; and of these some are at the level of intellect, some at the level of soul, others at the level of nature, others at the level of sense-perception, and of these latter some are immaterial and others are material. It is down as far as these that the procession of the forms descends from the intelligible Forms on high, making their first appearance at the limit of intelligible beings, and having their final manifestation at the limit of the sense-world. Indeed, from all the levels of forms there necessarily descends some particular characteristic to all the lower forms which proceed from them, down to the lowest of the forms in the sense-world—as, for instance, from the intelligible forms the characteristic of unchangeability, for they are primally eternal; from the primal level of intelligible-intellectual forms each bears a token, not susceptible to knowledge, of its own paradigms, according as each has been allotted one or other divine characteristic; from the middle rank the characteristic of each being a whole and holding together with its wholeness the multiplicity of its parts; from the third rank the characteristic that each form is perfective of that which previously existed only potentially; from those which are in the realm of the intellectual the characteristic of being distinguished according to all the variety of numbers, and of separating the things that participate in them; from those among the supra-cosmic the characteristic of each being assimilated to their own paradigms; from those which are simultaneously above the cosmos and in the cosmos the characteristic of each being such as to collect all those things which are in a pluralised state into the aggregates proper to each; and from those in the cosmos the characteristic of being unseparated from the nature dependent upon them and the characteristic of, with this nature, bringing to completion the generation of composite entities, From each level of forms, then, there should come some characteristic to the forms in the sense-realm, these being the ultimate limits of the chain of forms.
Next, on the Hypotheses discussed by Parmenides and Aristoteles. The first quotes are how the hypothesis is introduced in the text, the following quotes some useful remarks from Proclus' commentary.
First Hypothesis, 137c–142a, “If it is one.” “Signifies an autonomous divine henad” (Proclus, IP 1062). “The One God, how he generates and gives order to all the orders of Gods,” (1064).
Second Hypothesis, 142b–155e, “So there would also be the being of the one, and that is not the same as the one.” The ontic hypostases (i.e. Intellect, from which the hypostases are constituted in reflection). “Each of these divine orders … have been expressed by philosophic names, not by such names as are customarily celebrated by those who compose theogonies, but which do not reveal their essences, such as are the epithets of the divine classes given out by the Gods,” (1062). “A multiplicity of autonomous henads, on which are dependent the entities about which the Second Hypothesis teaches us,” (ibid.). “The whole of divinized being … be it intelligible, intellectual or psychic,” (1063). “All the divine orders, how they have proceeded from the One and the substance which is joined to each,” (1064).
Third Hypothesis, 155e-157b, “Let’s speak of it yet a third time. If the one is as we have described it – being both one and many and neither one nor many, and partaking of time – must it not, because it is one, sometimes partake of being, and in turn because it is not, sometimes not partake of being?” Includes discussion of the instant or moment (exaiphnēs, 156d). Ontic soul. “Not about all Soul pure and simple, but such as has proceeded forth from the divine Soul; for the whole divine Soul is comprised in the Second Hypothesis,” (1063). “The souls which are assimilated to the Gods, but yet have not been apportioned divinized being,” (1064).
Fourth Hypothesis, 157b–159b, “What would be proper for the others to undergo, if one is… what properties things other than the one must have, if one is.” Form in matter, pathēmata. “The Forms-in-Matter have existence of a sort (for these in some way participate in the One Being),” (1060). “Forms-in-Matter, how they are produced according to what rankings from the Gods,” (1064).
Fifth Hypothesis, 159b–160b, “what properties things other than the one must have, if one is… Must not the one be separate from the others, and the others separate from the one?” Matter, which “although not participating in the One Being in so far as it is Being, yet it does so in so far as it is One,” (1060). “Matter, how it has no participation in the formative henads, but receives its share of existence from above, from the supra-essential and single monad,” (1064).
“It is reasonable that the first three, which ask what relation the One has to itself and to others, should concern the three transcendent ruling principles, while the last two [of the positive hypotheses], which ask what relation the Others have to each other and to the One, introduce immanent Form and Matter; for these are truly ‘other’ and belong to others rather than to themselves, and are contributory causes rather than true causes [Phaedo 98bff.],” (1059).
The final four negative hypotheses are counterfactual.
Sixth Hypothesis, 160b–163b, “if the one is not”. Sensation alone. Matches the Second.
Seventh Hypothesis, 163b–164b, “if one is not, what the consequences must be for it.” “Every mode of knowledge and object of knowledge is abolished,” (1059). Matches the Third.
Eighth Hypothesis, 164b–165e, “what properties the others must have, if one is not.” “The others are in the state of dreams and shadows,” (1059). Matches the Fourth.
Ninth Hypothesis, 165e–166c, “if one is not, but things other than the one are.” "The Others will not even attain to a dreamlike substantiality,” (1060). Matches the Fifth.