starting point of dialectics: the One
1. Dialectics is the logos of categorical eidos, and we should pay attention only to these categorical structures and be able to derive them one from another. Starting from the most primitive category we should be able to derive dialectically, i.e. so that every resulting eidos should follow with absolute eidetical necessity from its predecessor. What is this primaeval eidos? Abstracting from the all in any thing we see that most empty and most general categories are being and one.
2. Lets take the eidos of One, One but not Many, and nothing more. What will we get?
2.1. What is not Many has no manyness in itself, i.e., has no parts. What has no parts is not a whole because whole has its all parts. So, One has no parts and is not any whole(Plat. Parm. 137cd).2.2. Beginning and the end would be parts also, therefore One is unlimited (137de).
2.3. It has no figurality because the figure also would be its part (137e-138a).
2.4. Any figure is by taking its share of space and takes this share from an Other. Therefore One is nowhere because
a) it has no parts to border itself from an Other;
b) it could not border itself in itself because this border also would be some part (138ab).
2.5. It cannota) move nor in the meaning ofaa) qualitative change because then it would become Many, neither in the meaning ofb) but it cannot also be in rest because it is alone and cannot be in any state (139ab).
ab) spatial transition becauseaba) any rotation implies center or axis which would be some parts;
abb) transition into another place implies two kinds of it parts: some are still in itself whereas some other are already in Other (138c-139a).
2.6.1. It does not differs from itself because then it would be not the One (139b).2.6.2. It is not identical to Other because then it would be that Other (139c ab init.).
2.6.3. It does not differs from an Other because it in itself contains no difference whereas difference is some other than One (139c - medio).
2.6.4. It is not identical to itself because identity implies two: what is identified and with what it is identified whereas the One is the only One. So, the One is not identical neither to itself nor any Other, and does not differs from itself or some Other (139c-e).
2.7. If the One could be different from itself it would be more than One. Any quality makes it already Many, and all that has the quality of difference is not similar to itself or to some other. Because the One has no qualities it is neither similar nor unsimilar - to itself as to Other too (139e-140b).
2.8. It does not equals to itself or to some Other, and is not unequal to itself or to some Other because any equation implies value and metron which both are absent in this One as its parts: any identity of metron is identity of parts in the things we compare. So, the One is not more or less than itself or than some Other (140d).
2.9. Along with all these categories, the category of time is also inapplicable to the One, and it cannot, generally speaking, be in time at all. To be in time means to become continually older, and to become older than itself is possible only by difference from younger, i.e. younger continues to be younger in the process of aging. This means that aging is always not only older but also younger than itself. But all these traits are inapplicable to the One because inapplicable to it are all the categories of identity, difference and equality. Therefore, the One never occurred, never was, and never is, and also never will occur or be (141a-e).
2.10. Therefore, it does not is because has nothing to do with any being (141e).
2.11. Therefore, it cannot be itself also, i.e. it is not the One.
2.12. So, it has no name, no word to describe, no knowledge about - nor perception nor doxa. It could not be named, bethought, or known, and all its traits are incognoscible (142a).
3. Item, the One, conceived in its absoluteness as One without assertion about it as a fact or occuring some:a) denies any manyness, therefore any notion of whole or part;It, in its absolute assertion. denies:
b) loses any definiteness and turns into limitlessness;
c) is devoid of any figure or sight;
d) has no spatial presence and no place: neither within itself nor outside;
e) does not move or rest or change;
f) is not identical or different to itself or any Other;
g) is not similar or unsimilar to itself or any Other;
h) is not equal or unequal to itself or any Other;
i) is not in any or some time;
j) is not at all;
k) is not the One;
l) inaccessible to any thought, knowledge, or perception.1) quantity: a, b, c, d, e; 2) quality: f, g, h; 3) time: i; 4) being: j, l.
Any thinkable is some one. Nevertheless, dialectics has shown that this one, when it is thought as the One, has absolutely no categories, i.e., thought about it requires it be not thought. If we grasp the whole world, or the whole being, the set of all things,- we could not think about it as not the one, because the world is some definite. But, already, this unity of all the world necessarily should be outside any thought and any being. Thought absolutely requires unthinkable, and logical is absolutely identical to illogical1. "Any manyness is somewhat unity. <If no,> then any whole could not be some unity, nor any <element> of manyness".2. "Any unity is <simultaneously> one and not one. <...> One <aytoen> is not, and what <has the predicate of> one is not too. If it is one and simultaneously has the methexis to one and therefore is not the one kath'ayto, then it is not the one and one <simultaneously>, being, along with one, some Other. When it has some contents it is not the One. When it is affection of <one>, it is the One".
3. "If what is not the One turns into One, concentrating therefore in itself and corresponding into itself, then it becomes one, contains the presence of the One, although is not the One itself <by itself>. It has methexis to one as long as it exerts the becoming the One. If it is already the One it does not becomes the One because the being does not becomes what it <already> is. If it becomes the One because of prior not-being the One, it will contain the One after originating in it of some <definite> unity".
4. "All what is united differs from what is the One kath' ayto. <...> What takes methexis in the the One is <simultaneously> one and not the one. <...> <Therefore it> should be different from the <proper> One. Because if the One is the same as united the amorphous manyness occurs, and the same with any <element> of the united".
5. "Any manyness is secondary when compared with the One. <...> <All the elements of any manyness> take methexis according to their nature in the One, and no element of this <set> cannot be thought as not being one, because if it is not the one, <...> it would be <amorphous Many of the> infinite number <of similar amorphous Manies>. <...> One with the Many as the Many with One are in communication. If some converging and communicating are converged from outside then this converging <factor> is earlier than these. <...> It could be not Many because it originates from One, and not nothing because it does converge. <...> Therefore is the One as itself, and any manyness originates from this One".
6. "Any manyness originates either from unitednesses (ex henomenon) or from unities (ex henadon). <...> If is the One as itself, then also is some what originally take methexis in it and is originally unitedness. Ant this is made of unities, because if it is from unitednesses, then these too from something and ad infinitum. It is necessary for original unitedness from unities to be. <...> <This is> principal (ex arches)".
notes for this chapter
Plat. Parm. is the most clear text in all Platonic and Neoplatonic literature about the One.
Some other texts: Plot. 2, 9, 1 (absolute simplicity); 5, 2, 1 (not a thing); 5, 3, 15 (absolute unity, its perilampsis, distinction between hen, hen polla and hen panta); 6, 8, 5 (higher than Noys and is called so simply because to designate the it is not something); 5, 3, 12-17; 5, 4, 2; 5, 7, 4-6; 12-13; 6, 1, 1-5 (higher than noys and being); 6, 2, 9-12 (is not the category). Porphyr. sent. intell. 43; Procl. Plat. theol. - whole second book; inst theol. -following chapters plus 113-115; 118-121. Damascius see (notes 30, 31).
Parmenides of PLATON maybe is book without which he would be not a philosopher at all.
Divisions of the dialogue (137c to 166c).
Two main themes: 137c-160b: dialectics of being of the One, and 160b-166c - dialectics of not-being of the One. Both these chapters are divided into two, and identically: each has inferences for the One itself, and for an Other. And further, each of four resulting subdivisions is divided into two once again, now according the main dialectic antithesis in Platonism : what would occur to the One if it would be thought as one and only, as opposed to as being in the quality of One, in some factual being, and when denied being, this denial only touches its presence in being and not its quality as One.
Parmenides is very unhappy dialogue of PLATON because the majority of historians of philosophy simply did not understood it and described it as a host of dark sophisms. In our turn, we think that
1) dialectics of Parmenides is the sensic skeleton of the deepest and most holistic world outlook, and therefore it is most easily detailed and expanded, what is accomplished in the commentaries of Neoplatonist, and2) PLATON himself had not tied these constructions with any particular mythology or metaphysics, therefore it is allowable to apply these to most diverse moments of philosophical system of Platonism in general.
cf. Plot 3, 8, 11 (noys as the unity of thinking and bethought requires higher unity which could not think or be bethought); 3, 9, 3 (first potentiality higher than movement or rest, about secondarity of thinking); 6, 1, 5 (all is due to numbers, ant these are because of influence of proto-hen to hyletic dyad); 6, 1, 6 (best explanation why the One must generate noys). CUS. de doct ign. 1, 1.
following JAMBLICH(DAMASC. pr. pr. 43), PROCLUS introduces triadic division into the One, and this triad is the template for all following triads: (65) peras - apeiron - number. These numbers is the result of monadic development (DAMASC pr. pr. 206), and, in the due course, monads are also paradeigme for eidoi (218) and things (297). Origins of numbers (193-!!!), types of numbers (227; 263).
Summary of the theory of the One (PLATON, PLOTINUS, JAMBLICHUS, PROCLUS, DAMASCIUS):
1. One is pure and absolute unthinkable, pure hyper.
2. One is relative unthinkable, as the beginnings of any dialectical construction, absolute unity.
3. One when mutually defined by Other gives potentiality for all being, or Number, pure "how" for any oysia. This is the sphere of hypernoetic numbers.
4. One as realized potentiality, i.e. eidos, i.e. number as eidos.
5. One, as eidetical number fills itself with contents and becomes one of something (transition of one to many, and finally, to being). See (n65)
Resume of chapter about types of unity in LOSEV, IAE, 7, 2, 2, 5, 2:
SIX TYPES OF UNITY IN THE FIRST NEOPLATONIC HYPOSTASIS.
PROCLUS discerns specific unities in all three first hypothesis of Parmenides. E. g., first type is such an unity which involves absolutely all and incomparable because nothing remained, and therefore, could not have any trait.
PLOTINUS did it too: not only Noys is unity, but also Psyche (5, 1, 2). But he details: along with uncognoscible the One Noys is designated as hen polla, and Psyche - hen kai polla.
In "Classic kosmos and modern science" five types of unity are indicated prior to the derivation of second hypostasis. Between these two is the sphere of noetic numbers, and it also is unity, but not the primaeval One. This One too has no quality but already is divided. First three types are formulated by PROCLUS (Plat. theol. 3, 8: One as the synthesis of peras and apeiron with reference to Phileb. 23c). In 3, 10-12 he clearly states that one kind of this synthesis belongs to noymenal sphere, whereas other is prior to it and sits in the realm of the One. But in such a way we could derive not a number itself, but only henads, which are the unities resulting from the thesis of number, i.e., potentialities of number: any concrete number is not the sum of separate henads bu is some indivisible whole and new unity, i.e., eidos. This is the fifth kind of unity. Until we have number as eidos, we cannot speak about any number of somethings. In order to get a complete number we should prior to this have all structures of unity necessary for this. Then, because these complete numeric substances does not remain as such but are the energy of their noymenal realization, here we obtain sixth type of unity: the strength of number to number somethings. And all this still in noymenal sphere. So, we have:
1. Unity as absolute all-embracing, more than any separate, and pure unthinkable hyper. (Principle of all principles).
2. Unity as peras incorporating first thesis of something (Principle of unity).
3. Unity as unlimited, because limits can be only when limitless is present (Principle of manyness).
4. Unity as synthesis of peras and apeiron, or henad - the one as potentiality of numeric sequence (Principle of one-manyness).
5. Unity as formed whole of ones, or as number as eidos of number (holistic manyness).
6. Unity as energetically charged number, or as a number of something, although this something is still absent, it is the principle of transcendence of hypernoetic sphere of proto-hen to noymenal sphere of logical categories (Principle of becoming one-many whole, or number as as energy).
Then is the realm of qualitatively filled categories, realm of noys, which is the One taken as being, and therefore Manyness still is retained by the One in the categorical entities and not allowed to expand into Any.Damasc. pr. pr. 13 (one as principle of all principles); 27 (cause of unity); 28 (telos); 134 (makes peras and apeiron); 136 (is in any hypostasis); 273 (more than whole); 305 (principle of construction of kosmos); 349 (genesioyrgon), etc.
cf. Plot. 6, 2, 19 - about antinomy of genera and species:
1) no single genus separate from others cannot make individual eidos, because all individual is outside the general;
2) individual eidos is the incorporation of all relevant genera: they do not vanish in eidos and do not turn into simple predicates;
3) general noys is common, and eidetic noi are specific ones originating from it. Also, eidetic noi contain within themselves as their part, and they are general for it, because it is always the same.Doctrine of ARISTOTELES about unity.
Aristotelian concept of unity and distinctions within this concept is the excellent commentary to entire Platonic science of unity.1. Unity as accidens (Metaph. 1015b16-36).In comparison with Platonism, ARISTOTELES:
2. Unity kath' ayto:2.1. as continuum (1015b36-1016a).3. Alternative formulation (1016b31-1017a2):
2.2. as eidetic indiscernibility in the substrate: continuum as the changing traits of things (1016a17-24).
2.3. Unity as formal logic unity of genus : generic continuity (1016a24-32).
2.4. Unity as to ti en einai (1016a32-b17).3.1. Numerical unity (=2.2).
3.2. Eidetical unity (not the matter, but sense is the same).
3.3. Formal-generic unity (=2.3).
3.4. Proportional unity (unity of structural relations of the whole).a) does not recognizes the One as absolute and relative unthinkables;
b) the One as potentiality is not before eidos, between proto-hen and oysia, but after eidos, i.e. as energy of be-sensing of some earthly thing;
c) making stress upon the concepts of potention and energy, he draws into the first place one as to ti en einai, i.e., this unity is unity of eidos and meon, and not of eidos proper;
d) this is explained by descriptive phenomenologism which fixes sensic givennesses of earthly things without their dialectical construction; therefore the rejection of two first types;
e) ARISTOTELES gives such a description of unity which perfectly fits into the system of Platonism after its dialectical fixation.
