[Doi 10.1007%2F978!94!010-1592-9_3] Merlan, Philip -- From Platonism to Neoplatonism Posidonius and Neoplatonism

II. POSIDONIUS AND NEOPLATONISM *

Both Iamblichus and Proclus are well aware that when theydiscuss the relation between soul and mathematicals they aretreating a traditional problem. Both know that their solutionconcerning the identification of the soul with all kinds of mathe-maticals (three in Iamblichus, four in Proclus) is not the onlyone offered by philosophers. In both the Iamblichus passageswe find representatives of three points of view: those who identifythe soul with the arithmetical, those who identify it with thegeometrical, those who identify it with the harmonical. Proclusenumerates representatives of only two points of view (arith-meticals and geometricals), and there are only two names(Severns and Moderatus) common to both lists. But both ob-viously feel that they are contributing to the solution of atraditional problem. The question is legitimate: How far backcan we trace the problem?The answer is contained in Plutarch, De animae procreatione

in Timaeo (Plutarchi Moralia, ed. C. Hubert, v. VI [1954]). Herewe read:"Some [scil. Xenocrates] think that the mixing of the indivisi-ble with the divisible substance means nothing else but theprocreation of number ... But this number [scil. the product ofthese two factors] is not yet soul, for it lacks active and passivemotion. However, soul was procreated by admixing 'the same'and 'the other', of which the latter is principle of movement andchange, the former principle of rest" (ch. II, 1012 D).Thus we have Xenocrates' definition of the soul as selfmovednumber. And this Plutarch takes to mean: The essence (sub-stance) of the soul is number (ch. III, 1013 D).Let us comment on this.First of all, we find here the report that Xenocrates interpreted

the psychogony as arithmogony. In terms of our problem, heidentified the world-soul in Plato's Timaeus with just onebranch of mathematics: numbers.In connection with this, he defined the soul as number. This chapter continues some of the ideas presented previously in: P. Merlan

"Beitraege zur Geschichte des antiken Platonismus", Philologus 89 (1934) 35-53;197-214 and idem, "Die Hermetische Pyramide und Sextus", Museum Helveticum8 (1951) 100-105.

P. Merlan, From Platonism to Neoplatonism Martinus Nijhoff 1975

POSIDONIUS AND NEOPLATONISM 35

Immediately he seems to have added: the soul undoubtedlyis principle of motion in Plato. Therefore, the number withwhich Plato's world-soul is to be identified must be defined asmotive.Hence the definition: the soul is self-moved number.But there remained one more question. Which of the in-

gredients of the mixture constituting the soul (soul having beendefined as number) is responsible for its motive power?Xenocrates singled out the two terms "sameness" and" other-

ness" *. They, he said, made the soul to be motive number.In the Plato passage in question there is, to be sure, not theslightest trace of the assertion that the soul is motive by beingcomposed of sameness and otherness.But this makes Xenocrates' interpretation all the more charac-teristic. He was the first (or among the first) to interpret Plato'sworld-soul as motive number (or, as we could also say, as numbercontaining the source of its change within itself). It is this identi-fication which serves as a background for lamblichus' query:how is it possible to identify the soul with mathematicals withoutadmitting the principle of motion to mathematicals? Xenocratesunhesitatingly did it at least to the extent of making some ofthe mathematicals move, these moving mathematicals beingidentified by him with the soul; others, among whom is the authorused by lamblichus in Isc ch. III and part of IV, objected.

It is interesting to notice that Aristotle also faces this problem.Generally, his mathematicals are nonmotive: the passagesDe caelo III 6,30Sa 25-26 and De motu animalium I 1,698a25-26 are particularly characteristic. But in a passage like Met.A 8,989b 32-33 he would add cautiously "except astronomicals";or he would introduce sciences intermediate between mathe-matics and physics (d. p. 62 n.), dealing with objects that aresemi-mathematicals and subject to motion.We now resume the discussion of Plutarch.[IJ Men like Posidonius "did not remove [the soulJ from matter

very far. [2] They took the phrase 'divided about the bodies'to mean 'substance [OUO'(IXJ of the limits'. They mixed them with

Cf. Arist., Met. K 9, I066a II: there are some who characterize motion asotherness (or inequality or non-being); see also Physics III 2, 20lb 19-21, with Ross'commentary a.I.

36 POSIDONIUS AND NEOPLATONISM

the intelligible, and [3] said of the soul, that it was idea [form]of the all-extended [d. Speusippus fro 40 Lang], existing accordingto number which comprises harmony.[4a] For on one hand, mathematicals are placed between thefirst intelligibles and the sensibles, [4b] while, on the other hand,the soul shares eternity with the intelligibles, passibility [change-ability] with the sensibles, [5] so that it is fitting that [its] sub-stance should be intermediate" (ch. XXII, 1023 B).What does this mean? Posidonius identified the world soulwith mathematicals. He did so, because on the one hand, thesoul is described by Plato as participating in the eternity of thefirst intelligibilia and of the changeableness of the sensibilia.This proves that the essence of the soul is intermediate. On theother hand, still according to Posidonius, the mathematicalshave their place between the first intelligibilia and the sensibilia.In other words, Posidonius said: In Plato's Timaeus the soul

is intermediate between intelligibilia and sensibilia. The mathe-maticals [and here we must add: in Plato, according to Posi-donius] are intermediate between intelligibilia and sensibilia.Therefore, Posidonius said, soul equals mathematicals.This resulted in the definition: the soul is idea (form) of theall-extended, being constituted according to number comprisingattunement. The similarity of this definition with the definitionsin Iamblichus and Proclus is obvious.What is most interesting in this definition is that it presentsthe first attempt to identify the soul not with one branch ofmathematicals, but with three. Once more: "idea (form) of theall-ex;tended" stands for geometricals; "number" representsarithmeticals; "number comprising harmony" represents theratios (proportions) or the musicals.The whole definition explains, and is explained in turn by,the two passages in Iamblichus' (Isc and On the Soul) and theProc1us passages quoted above (p.21-24). What is absent inPosidonius' definition is any explicit reference to the problemof motion and we do not know whether he treated it at all.All the other elements of Iamblichus' discussion can easily befound in Posidonius' definition. The main difference betweenPosidonius-Iamblichus and Proc1us is that the former assume


a tripartite mathematics, the latter assumes a quadripartiteone*.How did Posidonius arrive at his assertion that the world-soul

is intermediate between intelligibilia and sensibilia? He didit by interpreting Plato's phrases: "the undivided" and "whatis divided about the bodies" as standing for "intelligibilia" andfor "essence [substanceJ of the limits" respectively.

It seems clear, therefore, that Posidonius' essence (substance)of the limits stands for the sensible (divided), just as does Plato's"that which is divided about the bodies". Plato's phrase ishardly anything more than a circumlocution for the world ofchange, body extended, etc. Admittedly, it is an ambiguousphrase; in Enn. IV 2 Plotinus interpreted it as meaning thelimits which have become divided only by being embodied **.But Plotinus' interpretation is erroneous and simply the resultof his tendency to keep the soul as free from pollution by thebody as possible (d. H. R. Schwyzer, "Zu Plotins Interpretationvon Platons Timaeus 35 A", Rheinisches Museum 84 [1935J360-368, esp. 365-368). The result of his interpretation is aquadripartition (IV 2, 2, 52-54 Brehier) : the eternal (undivided,one), the indivisibly divided (soul, one-and-many), the divisiblyundivided (embedded forms, many-and-one), the divisiblydivided (body, many). Is this still Plato's Timaeus? Plato'scosmogony implies only three kinds of being: that of the eternalthat of the soul, and that of the temporal, changing, extended,i.e. divided bodily. And Posidonius remained true to thistripartition. If we do not assume this, the whole idea of inter-mediacy, so clearly the backbone of Posidonius' interpretation,would lose its basis.But can ~ TWV 7t&PcXTWV ouO'(oc ever stand for anything but

7tepocToc? Is it not to pervert the letter by interpreting it as

On the exclusion of astronomy from mathematics in Posidonius see E. Brehier,"Posidonius d'Apamee, tMoricien de la geometrie", Revue des Etudes grecques 27(1914) 44-58 (= Etudes de Philosophie antique [1955] 117-130). On the nonmotivecharacter of geometricals in Posidonius see A. Schmekel, Die positive Philosophie inihrer geschichtlichen Entwicklung 2 vv. (1938, 1914), v. I 105 f.

Cf. F. M. Cornford, Plato's Cosmology (1937) 63. See, however, also P. Shorey,"The Timaeus of Plato", American Journal 0/ Philology 10 (1889) 45-78, esp. 51 f.,and idem, "Recent Interpretations of the Timaeus", Classical Philology 23 (1928)343-362, esp. 352. But here as in so many cases the question of the correct interpre-tation of Plato is less important than the question how he was actually interpreted.


meaning that which is within the 1tepoc't'oc? the extended? thedivided?Not so, if we simply take it to be a subjective genitive.

Twv m:pIX't'


in the Academy: towards identification of Plato's world-soulwith mathematicals. Xenocrates was one of the first to do it -he identified the soul with number *. Speusippus did somethingsimilar: he identified the soul with the geometrical. The sourceof our knowledge of this fact is Iamblichus (see above p.20).GeometriGals, says Iamblichus, are one of the branches ofmathematicals; they are made up of form and extension, andSpeusippus, one of the men who define soul by mathematicals,defined the soul a"s idea (form) of the all-extended. Idea standsclearly for form. The Iamblichus reference seems absolutelyprecise, makes perfect sense, and seems entirely trustworthy(see below p. 43). As reported by him, Speusippus identified thesoul with a geometrical (d. fro 40 Lang).

It seems, then, that also Posidonius found Speusippus asidentifying the soul with another branch of mathematicals.Finally in Moderatus (if he preceded Posidonius) or some memberof the Academy, he found the soul identified with mathematicalharmony.2. In interpreting the Timaeus Posidonius made use of thePlatonic tripartition sensibilia, mathematicals, intelligibilia.He found it where Aristotle had found itQr in Aristotle (Met.A 6,987b14 and many other passages; d. Ross, Aristotle's Met.a.I. [v. I 166-168]). He combined it with the tripartition of theTimaeus: and as he already found a tendency to identify theworld soul with mathematicals (a tendency which originated,it seems, quite independently from the other tripartition), hecombined the two tripartitions, thus arriving at the equation:soul = intermediate = mathematicals.Therefore, to the extent to which we find the identification:

soul = intermediate = mathematicals in Iamblichus or Proclus,they follow Posidonius. Iamblichus, with his identification of thesoul with three branches of mathematicals, follows him moreclosely than does Proclus. From Posidonius a straight line leadsto Iamblichus and Proclus.Did Posidonius interpret the mathematicals realistically?We can answer this question with only a modicum of certainty.We know that Posidonius insisted on defining "figure" in terms

Cf. K. Praechter, art. Severus 47 in RE II A 2 (1923), esp. p. 2008 with n. .


of circumference rather than included area or volume (d. ProclusIn Eucl. p. 143, 6-17 Fr.; Hero Delinitiones 23, p.30,8-11Heiberg). But, contrary to what Schmekel (op. cit., above p. 37n., v. I 100-106) says, this does not speak either for or againstPosidonius' realism. More decisive is the passage in DiogenesLaertius VII 135 where Posidonius is credited with the assertionthat the geometric surface exists in our thoughts and in reality atthe same time. He was quite obviously at variance with otherStoics quoted by Proclus In Eucl. Def. I, p. 89 Fr (SVF II 488)who asserted that the limits of bodies existed only in our thoughts.In other words, there was at least a strain of mathematicalrealism in Posidonius *.Into which of the different pictures of Posidonius of more recentyears does our description of Posidonius fit best? Undoubtedlyinto that of W. Jaeger (Nemesius von Emesa [1915]). He presentedhim as the protagonist of the bond-and-intermediacy idea. Sucha man must be sympathetic to the idea of an intermediate. Earlierthan anybody else, he is likely to discover the intermediateplace of Plato's world-soul (described in mathematical terms)on one side, the intermediate place of mathematicals in Platoas reported by Aristotle on the other side, and to identify thesetwo intermediates.This, then, seems to be established beyond doubt: Posidoniusdid influence Neoplatonism. The sector in which he did it(interpretation of the Timaeus; identification of Plato's world-soul with mathematicals) may seem small; we shall see later howimportant it was **.

And now a few words on Speusippus' and Xenocrates' identifi-cation of the soul with one particular branch of mathematics.The report of Iamblichus according to which Speusippus definedthe soul as the idea of the all-extended has recently been scruti-nized by H. Chemiss (Aristotle's Criticism 01 Plato and the

Cf. L. Edelstein, "The Philosophical System of Posidonius", American Journal0/ Philology" 57 (1936) 286-325, esp. 303; also P. Tannery, La Giometrie grecque(1887) 33 n. 2; H. Doerrie, "rTt6f1T(Xa~",Nachrichtentier Ak. d. Wiss. GiJttingen, I.Philol.-hist. Kl., 1955, p. 35-92, esp. p. 57. On Posidonius in the Middle Ages ct. also R. Klibansky, The Continuity 0/ the

Platonic Tradition During the Middle Ages2 (1950) 27.


Academy v. I [1944J 509-512}. He is inclined to consider ituntrustworthy, or at least unintelligible. According to him, itimplies that Speusippus considered the soul to be a mathematicalentity, while Aristotle said (Met. Z 2,1028b21-24) explicitlythat Speusippus distinguished sharply between magnitude andthe soul.Why Cherniss should trust unconditionally Aristotle's report

is not quite clear. This report is obviously highly critical ofSpeusippus and interested in presenting him as a "disjointer"of being. Even so, as the difference between soul and geometricalsis, according to Aristotle himself, not much greater than thedifference between numbers and geometricals (the soul followingimmediately the geometricals), we must allow the possibilitythat Aristotle stressed the difference and left the similarityunmentioned. It is true that "idea of the all-extended" soundsalmost like the definition of a geometrical solid; and we can onlyguess, how, then, the soul differs from any other geometricalsolid. Does "idea of the all-extended" imply motion? Is thisthe reason why the soul is a branch of mathematics rather thana mathematical tout court? We do not know; but still the contra-diction between Aristotle's report and the mathematical inter-pretation of Speusippus' definition does not seem to be particu-larly serious. It may amount to the difference between "mathe-matical entity" and "what is closest to a mathematical entity".How close is closest?But let us suppose that the definition as reported and inter-preted by Iamblichus is incompatible with Aristotle. What wouldfollow? Do we have to reject it or wind up with an "ignoramus"as to its true meaning? This is hardly necessary. Perhaps Speu-sippus expressed himself ambiguously; perhaps he changed hisopinion; perhaps he was flatly contradicting himself. After all,he survived Plato only by some eight to nine years (DiogenesLaertius IV I; ct. F. Jacoby, Apollodors Chronik [1902J 313) *;It is difficult to assume that he "gave up" the theory of ideas

It seems that insufficient attention is being paid to this fact. The majorityof the philosophic works of Speusippus must have been written during Plato's lifetime,and it is very difficult not to see in his appointment as Plato's successor the latter'sapproval. Even if some non-philosophic considerations determined Plato's decision,he still could not have thought of Speusippus as professing a doctrine of which he,Plato, disapproved. Cf. E. Frank, Plato una die sogenannten Pythagoree, (1923) 239.


from the very beginning of his philosophic career, of which hespent the greatest part in the Academy. Speusippus must havechanged or contradicted himself in this respect, too.Having rejected the mathematical interpretation, Chemiss

suggests that it meant perhaps a defense of the Timaeus againstAristotle: the soul is not a magnitude, as Aristotle has asserted,but idea of the body just like Aristotle's et8oc;; *. And Chemissquotes some passages proving that Aristotle identified 7tepOCC;;and et8oc;; of the extended body.Now, Chemiss' whole discussion culminates in the assertionthat Aristotle never suggests that the Platonists called the soula form; and he obviously considers this silence to be anotherproof that they actually did not do so. But if Speusippus, accord-ing to Chemiss, said: the soul in the Timaeus is an et8oc;; - justas you, Aristotle, make her an et8oc;; - does not this mean thathe called the soul a form? Or would Chemiss deny that et8oc;;as used by Aristotle to designate the soul should be translated"form"? In the paper by P. Merlan, "Beitraege zur Geschichtedes antiken Platonismus", Philologus 89 (1934) 35-53; 197-214to which Chemiss refers, it is said (206) that the interpretationof Speusippus (and Xenocrates) ** therein suggested seems toblur the difference between the Peripatetic and the Academicdefinitions of the soul and the attempt is there made to showthat the difference between the Aristotelian soul as et8oc;; and theAcademic soul as t8eoc = form was perhaps indeed not so greatas is usually assumed. Does not Chemiss confirm this fully byhis interpretation of Speusippus' definition? And if so, does henot contradict himself? After reading his keen discussion one isalmost tempted to sum it up by saying: perhaps one of the maindifferences between the Academic and the Peripatetic inter-pretations of the soul was that the former tended towards theidentification of forms of all bodies with the soul (mathematicalforms being the most outstanding representatives of form),

Cf. H. Chemiss, The Riddle 0/ the Early Academy (1945) 74... With regard to Xenocrates, Chemiss (511) says that Merlan's attempt to identify

the soul with intermediate mathematicals results in the impossible identification ofthe aO~otO",,6vwith the fLotll1JfLotTLK6v; and he kindly explained (orally) that such anidentification is impossible because, mathematicals being the highest sphere of beingin Xenocrates, the coordination of 36~ot with mathematicals would leave imO"'rijfL1Jwithout any subject matter. But why should not imO"'rijfL1J concern itself with theprinciples of mathematicals? Cf. also below, p. 44.


while Aristotle limited the equation soul = form by describingthe soul as the form of living bodies alone *. In any case, if,according to Cherniss, Speusippus said: Plato meant the soul inthe Timaeus to be an t3EiX = e:l30~, how can Cherniss say thatthe Platonists never called the soul an idea or form.?But perhaps it would be appropriate to explain how t3EiX =

e:l3o~ could mean both form and essence. The form (figure, shape,contour, outline) of a thing is (I) what keeps it apart from allother things - the boundary between it and its surroundings;(2) the framework which remains stable though the matterconstantly changes - this framework being either rigid, or"elastic" as in the case of living organisms. In other words, itis the form by which everything remains identical with itselfand different from every other thing. Thus, the form representsthe element of being (stability) as opposed to the element ofbecoming. The form, then, is the equivalent of the presence ofthe idea in the thing. To the extent to which a thing has form,it participates in the idea. It is easy to see that this interpretationcan equally well be applied to any quality, e.g., the just, thebeautiful, etc., though in such cases form loses its visibility andbecomes an abstract boundary.One further word of warning must be added. A reader ofCherniss may be misled into believing that it was only somemodern interpreter who said that Speusippus' definition meantto make the soul a mathematical entity (in fact, it is not quiteclear whether Cherniss doubts just this or only whether Speu-sippus could have made it an intermediate mathematical).We must not forget, however, that it is only in Iamblichus thatwe find the definition of Speusippus; and Iamblichus saysexplicitly that this definition was meant to give geometricalstatus to the soul. It seems risky to accept from Iamblichusthe words of Speusippus and reject his interpretation on theground that it seems to contradict Aristotle. After all, thepresumption is that Iamblichus read the words of Speusippusin their context; and he quite obviously had no interest in mis-interpreting them (as Aristotle had). The whole Iamblichus

Cf. e.g. N. Hartmann, "Zur Lehre vom Eidos bei Platon und Aristoteles",Abh. der Berl. Ak., Phil.-hist. Kl., 1941 p. 19= Kleinere Schriften, v. II (1957) 129-164,p. 145, on the role of mathematics and biology respectively in Plato and in Aristotle.


excerpt in Stobaeus (I 49, 32, p. 362, 24-367, 9 Wachsmuth)makes the impression of a solid piece of work *; several times,he makes it clear that he knows the difference between a reportand an interpretation very well (see e.g. I 49, 32, p. 366, 9Wachsmuth).Perhaps another word of criticism may here be added.According to Cherniss, Xenocrates could not have made thesoul a mathematical entity because of its "intermediate" position,since he identified numbers and ideas. True, the latter is preciselywhat Theophrastus said (Met. 13, p. 2 Ross and Fobes), if thereference is to Xenocrates; but the same Theophrastus says alittle later (III 12, p. 12 Ross and Fobes) that Xenocrates"derives" everything - sensibles, intelligibles, mathematicals,and also divine things - from the first principles (fr. 26 Heinze).Intelligibles and mathematicals are kept apart (the Ross-Fobesrendering: "Objects of sense, objects of reason or mathematicalobjects, and divine things" is an interpretation not a translation;d. their discussion of this passage on p. 56 f; for the simpletranslation see Ross, Aristotle's Met. p. LXVI or LXXV) **.If "the divine things" are astronomicals, we here simply haveAristotle's pattern (sensible-perishable, sensible-imperishable,eternal - however with the latter subdivided into mathematicalsand intelligibles) ***. It seems therefore unwarranted to deny alto-gether the possibility of intermediate mathematicals in Xeno-crates. It is characteristic that Theophrastus mentions Xeno-crates' name only in the second of the two passages quotedabove; in the first he perhaps relies on Aristotle alone. But evenAristotle never quoted Xenocrates by name as the one whoidentified ideas with numbers. It may well be that Aristotlewas not absolutely sure of his interpretation of Xenocrates. And an ambitious one at that. Iamblichus obviously tries to replace what he

considers an inadequate outline underlying Aristotle's presentation of the opinionsof his predecessors in De anima.

The interpretation of Ross and Fobes aims at the reconciliation of fro 5 and fro 26Heinze. In the former, Sextus Empiricus, Adv. math. VII 147 reports that Xenocratesassumed three spheres of being (things outside the heavens, accessible to vouc; and7ttG't"I)!L'l); the heavens, accessible to both ala&rjGtc; and vouC;, the mixture of whichis equivalent to 86~a; and things within the heavens, accessible to ala&rjGtc;; thesethree spheres corresponding to the three !Lo!pat). In fro 26 Heinze Theophrastusmentions four entities (a!a&rjTcX, VO'l)T!X. !La6'l)!LaTtx!X, 6e:!a). But is this reconciliationnecessary? Is it not more likely that Xenocrates suggested different divisions ofbeing in different contexts?

Cf. P. Merlan, "Aristotle's Unmoved Movers", T,aditio 4 (1946) 1-30, esp. 4 f.


We should not overlook either that Xenocrates might haveidentified ideas and numbers, but kept geometrica1s apart.This, indeed, seems to be the gist of Arist. Met. e2, 1028b24(fr. 34 Heinze with Asclepius a.l.). Of the five remaining Aristo-telian passages gathered by Heinze only one says that the manwhom we suppose to have been Xenocrates identified ideaswith mathematica1s tout court; the rest speak of numbers. Theonly passage which seems to say that Xenocrates denied thedifference between ideas and magnitudes (Met. M6, 1080b28 ;fro 37 Heinze) admits of a different interpretation. When Aristotlesays that Xenocrates believes in mathematical magnitudesbut speaks of them unmathematically, we should perhapsaccept the first part of this assertion at its full value and discountthe second as implying a criticism. All this should make uscautious. It is risky to assert positively that Xenocrates wasalways or ever a dualist (or a trialist only in the sense in whichAristotle was a trialist, by subdividing the sphere of the sensib1esinto perishables and imperishab1es).

It is not easy to see why Cherniss finds it so strange that somescholars tried to "reconcile" (the quotation marks are his) Platoand Xenocrates, ascribing to the former the doctrine thatsoul is number (572). All he says against this reconciliation isthat Aristotle never ascribes this doctrine to Plato and considersit as peculiar to Xenocrates. Just how convincing is this argu-ment? Is it not clear, on the contrary, that Xenocrates interpretedPlato as having said precisely that? And was his interpretationso thoroughly mistaken?Cherniss interprets Plato's system as teaching the intermediacy

of the soul between ideas and phenomena (606; d. 407-411) *.

Cf. 442,453. Cherniss faces the following dilemma. Aristotle asserts (Met. Z2,1028bI8-24) that Plato knew only three spheres of being, ideas, mathematicals,and sensibles, whereas Speusippus knew more than three, viz. sensibles, soul, geo-metricals, arithmeticals. Either Cherniss accepts the part referring to Plato as trust-worthy (in spite of Tim. 30 B). Then there was no place for a soul in Plato's systemas mediating between ideas and sensibles and Cherniss' interpretation of Plato wouldbe erroneous. Or he considers Aristotle's presentation of Plato's system to be erroneousor perhaps an illegitimate translation of the epistemological intermediacy of mathe-maticals as suggested by Plato's Republic VII, into ontic intermediacy (see, howeverW. D. Ross, Plato's Theory of Ideas [1951] 25 f.; 59-66; 177) - then he should notrely on his presentation of Speusippus. The way out seems to be to assume that (I)Aristole's presentation of Plato is correct because in Plato's system the soul can beidentified with the mathematical; (2) in presenting Speusippus Aristotle interpretsdifferences within the realm of the mathematical (arithmeticals, geometricals, soul)


According to him there is no fWlction left for God in Plato'ssystem; as to the vou~, it is part of the soul (and the ideas areoutside of it). Thus there remain only three spheres of being(or whatever Cherniss would call them). He would not denythat Aristotle time and again repeated that Plato assumed threespheres of being: ideas, mathematicals, sensibles. How far isCherniss from Aristotle?Cherniss accepts Cornford's interpretation of the Timaeus

(d. above p. 13 note). He would not deny that Aristotle describedthe mathematicals as having a "mixed" character: they shareeternity with the ideas, multiplicity with the sensibles. Areeternity and multiplicity anything else but aspects of indivisi-bility and divisibility, respectively? How far is Cherniss fromAristotle?Still it cannot be maintained that there is no difference at allbetween his and Aristotle's interpretation. But this differencecan be reduced to just one statement: the soul is motive accordingto Cherniss, the mathematicals are not (579 f.).

In other words, Cherniss can object to the identification ofthe soul with mathematicals only for the same reason for whichthe author used as source in I sc ch. III objected. But there is noreason for him, either, to deny that the soul is some kind ofmathematical entity and, together with other mathematical entities,intermediate.Thus, as we said, the wording in the Timaeus was an invitationto identify soul and mathematicals *. Speusippus and Xenocratesavailed themselves of this invitation - at least partly.Posidonius accepted Aristotle's tripartition and Speusippus'definition of the soul as being Platonic. We know the results.One step remained to be taken: to make the mathematicalsmotive. This is precisely the step which Cherniss refuses to take.But how wrong is this step? Who could say that it is not in thespirit of Plato (d. Zeller 11/1 5 781 nJ)? Only if we acceptunconditionally Aristotle's assertion (d. p. 35) that all mathe-maticals are nonmotive (an assertion in the name of whichGalilei's application of mathematics to physics was opposed)

as if they were absolute differences, because he is interested in presenting the viewsof Plato and Speusippus as entirely different, which they, however, are not. Cf. E. Zeller, I1f15 (1922) 780-784, esp. 784 n. I.


can we do it. But should we not expect Aristotle to stress andoverstress the nonmotive character of mathematicals - thesame Aristotle who so emphatically denied the presence of anymotive entity in Plato's system? Chemiss criticizes him severelyfor having failed to see that in Plato's system the soul is motive;is it so impossible to assume that, with regard to mathematicalstoo, Aristotle took for granted what neither Plato nor orthodoxPlatonists would have conceded as obvious? To be sure, theidentification of soul with mathematicals is not pure and un-alloyed Platonic doctrine; but it could be goodAcademic doctrine.Especially, this equation cannot be called un-Platonic becauseof the motive character of the former, the nonmotive characterof the latter.This leads to still another question. How great is the differencebetween the definition of the soul by Xenocrates (self-movedor self-changing number) and that of Speusippus (idea of theall-extended) ? Both definitions stress the mathematical characterof the soul, though one stresses more the arithmetical, the othermore its geometrical aspect (d. Zeller, ibid., p. 784 n.1). Con-sidering the fact that Plato describes his world-soul in termsof numbers first, in terms of circles afterwards, there is nothingsurprising in the difference, nor in the similarity, of the twodefinitions. lamblichus compares them from this point of view;and on reading the whole passage (149,32, p. 364, 2-10 Wachs-muth) instead of dissecting it into single M~iXL one can hardlydoubt the correctness of his interpretation. Just as Xenocratesasserted that Plato's psychogony is actually arithmogony,Speusippus might have asserted that it was schemagony. Now,to prove that Xenocrates' self-moving number has nothing to dowith figure, Chemiss (p. 399 n. 325) quotes Cicero, DisputationesTusculanae (I 10,20, fr.67 Heinze): Xenocrates animi figuramet quasi corpus negavit esse, verum numerum dixit esse. Chemissdoes not translate "verum"; but it seems obvious that it means"still", not "on the contrary", so that Xenocrates is made tosay by Cicero: though the soul should not be described as ageometrical figure or solid (quasi corpus = geometrical body orvolume, as differing from corpus = tangible body), still it isa number - i.e. we here have the difference between two branches


of mathematics, with Xenocrates giving preference to arithmetic,whereas someone preferred geometry.And it may very well be that with regard to the problem ofmaking mathematicals (arithmeticals or geometricals) motive,the difference between Xenocrates andSpeusippus can be broughtdown to this: according to the former the soul, Le. a self-changingnumber, is part of the realm of mathematicals, according to thelatter we should not make any of the mathematicals motive,but rather posit moved mathematicals = soul as a separatesphere of being, following the unmoved mathematicals ratherthan being part of them.

In short, the report of Iamblichus, according to which bothSpeusippus and Xenocrates identified the soul with a mathe-matical (whether they did it interpreting the Timaeus or pro-fessing their own doctrine is immaterial in the present context),is unobjectionable. And there is nothing in the Timaeus to ruleout this identification as completely un-Platonic *.

We can now return to the problem of how the mathematicalcharacter of the soul (in other words, the soul being an ideaas mathematical form) is related to the Aristotelian soul asd8oc; of a living body. Perhaps the following interpretation maybe suggested. For Aristotle the soul becomes a form of thebody (Le. no longer a subsistent entity) within the same trainof thought which led him to give up excessive realism inmathematics **. Mathematicals for Aristotle no longer subsist; There is no more reason to expect that the doctrines of the Timae14s concerning

the soul should be compatible with the ones in the Phaed,14s, than to do so withregard to the structure of the universe and its history as presented in the Timae14son one hand and the Politic14s on the other... On relics of Plato's treatment of mathematics ("ezisten:ableitende Mathematik")

in Aristotle ct. F. Solmsen, "Platos Einflusz auf die Bildung der mathematischenMethode", Quellen 14nd St14dien :14' Geschichte de, g,iechischen Mathematik ... Abt. B:Studien I (1931) 93-107; see on this problem also idem, Die Entwickl14ng de' a,isto-telischen Logik 14nd RhetMik (1929), esp. 79-84; 101-103; 109-130; 144 f:, 223; 235-237; 250f. Solmsen's interpretation, particularly his analysis of the Analytica P,iMaand Poste,io,a has recently been criticized by W. D. Ross (A,istotle's P,io, andPoste,io, Analytics [1949] 14-16). To the extent to which Ross' criticism refers tothe problem of the chronological order within Aristotle's Analytics it does not concernus here. But what is of interest in the present context is Ross' assertion that "thedoctrine of the Poste,io, Analytics is not the stupid doctrine which treats numbers,points, planes, solids as a chain of genera and species ... " (p. 16). Now, whetherthe relation of point to line, etc. can be stated precisely in terms of genus and species


and therefore the soul cannot subsist either, because soul andmathematicals coincide. Whether he was ready to accept thecomplete denial of the subsistence of the soul (i.e. the completedenial of its immortality and pre-existence) is a well-knownmatter for controversy. If the above suggestion is accepted, ifthe giving up of mathematical realism is another aspect of thesame development which led him to give up what could becalled psychical realism, we should expect a strong tendencyto assume for the soul only the same kind of subsistence, pre-existence, and post-existence which Aristotle was ready to grantto mathematicals - whatever their subsistence might havemeant to him. Jaeger boiled down the change in Aristotle's

in our customary sense of the word is certainly doubtful. But what matters is justthis: number is prior to the point, point to the line, etc. - and in this, only in thissense of the word is what is prior at the same time more general (or universal). Theline implies the point etc., not the other way round. It is perhaps a strange but hardlya stupid doctrine to say that you "derive" the line from the point by "adding"something - this process of addition resembling somewhat, but being completelydifferent from the determination of a genus by a specific difference. And it is preciselythis doctrine of "derivation" by "addition" that can be found in the Analytics. InAn. Post. 127, 87a31-37 Aristotle says: Among the reasons why one science is moreexact than another is also this that one is 1; Aotn6vwv, the other, less exact, X7t'POa6tCl&W


psychology to the formula: from the soul as e:i~oc; 'n to the soulas e:i~oc; 'moc; (A ristoteles2 [1955] 44). The same formula can beused to describe the change in the status of mathematicals -from realism to moderate realism. Objecting to Jaeger, Cherniss(op. cit. 508) turned attention to the fact that even in Met. M2,1077a32-33 the soul still is considered to be Et~oc; and !J.0pcp~'nc;o However, first of all Cherniss overlooks that this assertionmay be hypothetical (otov EE iXpoc ~ ~UX:1j 't'oLo\hov) *; but let itbe supposed that Cherniss is right. This would only prove thatAristotle was somewhat dubious as to the relation between hisformer and his more recent conception of the soul - just as inMet. E 1, 1026a15 he is still somewhat dubious as to the entirestatus of mathematicals. All this, including the passage justquoted by Cherniss, once more proves how orthodox-Academicthe equation soul = mathematicals is. Aristotle says in Met.M2: Lines cannot subsist (or: be ouaLocL) as forms, the way souldoes (or, according to the above interpretation: the way thesoul is supposed to do). The very fact of comparing lines withforms and souls shows how easily Aristotle switches in histhoughts from mathematicals to the soul. What we see happeningin the Metaphysics, we see even better in De anima: in II 3,414b28we find a detailed (and puzzling) comparison of the problemsinvolved in the definition of the soul and in that of a geometricalfigure. We could perhaps say: without this equation soul =mathematicals as a background, it would be hardly comprehensi-ble why Aristotle elaborates the comparison hetween soul andgeometrical figure in such detail.A comparison of two Simplicius passages is also instructive.He says on Xenocrates (In And he says on Aristotle's

Arist. De an. 404b27, p. 30, 4 Eudemus (In Arist. De an.Hayduck and 408b32, p. 62, 2 429alO, p. 221, 25 Hayduck,Hayduck, fr. 64 Heinze): fro 46 Rose, fro 8 Walzer):By his definition of the soul as [Stressing] the intermediacy ofself-moved number Xenocrates the soul between the undivided

Continued on page 5I

In F. Nuyens, L'Evolution de la Psychologie d'Aristote (1948) we find a curiouslyself-contradictory interpretation of this phrase. On p. 173 n. 76 he approves (quitecorrectly) of the translations of Tricot (comme I'ame, si bien I'ame est bien telIe eneffet) and Ross (as the soul perhaps is). But his own translation is (173): commec'est sans doute bien Ie cas pour I'ame.


intended to point out its inter-mediacy between ideas and therealm shaped by ideas (and itst~LOV).

and the divided and the factthat the soul shows charactersof both the shape and theshaped [opo


\m6a't'iXaLV . ci).)..oc yocp 't'ou't'wvou't'wc; q6VTwv, XiXl. XiX't'OC 't'1jvcipxli6ev tl1t66eaLV 't'eaaiXpwv OVTWVcipL6{Lwv ev ote; &AYO{LeY XiXl.'t'1jv TIje; lJiuxlic; tOiXV 7tepLxea6iXLXiX't'OC 't'ov EviXP{L6vLOV A6yov '"

the fifth, and the octave] ...OVTWV ~e: cipL6{LWV 't'ecraiXpwv 't'WV

7tpW't'WV . ev 't'olhOLe; XiXl. ~ TIje;lJiuxlie; t~iX 7tepLxe't'iXL XiX't'OC 't'OV&ViXp{L6vLOV A6yov .. et Oe: &V 't'ij)

0' cipL6{Lij) 't'O 7tiiV XeL't'iXL &x lJiuxlic;XiXl. aW{LiX't'OC;, ciA:1]6e:e; &piX XiXL, /)'t'LiXt GU{L


mologici di Nicomaco ed Anatolio", Rivista Indo-Greca-Italica 6[1922] 51-60 and 49-61) suggested that this source might havebeen among others Posidonius who in his commentary onPlato's Timaeus commented on the number four. Now, whetherit was in a formal commentary or simply in some commentson Plato's Timaeus, de Falco seems to have well establishedhis thesis that Posidonius commented on the four in such a wayas to make it correspond to a pyramid and the soul at the sametime; this would jibe perfectly with his definition of the soulas quoted by Plutarch (above p. 36). But perhaps it is againpossible to go one more step back *. In the well known quotationfrom Speusippus (Theologoumena arithmeticae 61-63, p.82,10-85,23 Falco) Iamblichus reports that in his little book onPythagorean numbers Speusippus in the first half of it devotedsome space to a consideration of the five regular solids. It isalmost impossible to imagine that in this consideration theequation four = pyramid did not occur, just as it occurs in thesecond half of his book (p.84, II Falco). Perhaps it is not toorisky to assume that it also contained the equation pyramid =soul or at least some words making it easy for an imitator toproceed to this equation. Perhaps it contained the definition(fr.40 Lang) soul = "idea" of the all-extended, quoted byIamblichus. It could very well have been among the sourcesof Posidonius or at least have inspired him and others to identifythe soul with some mathematical. The equation soul = pyramidsounds very crude, but so does the whole discussion concerningthe number ten, preserved for us by Iamblichus in the formof a literal quotation from Speusippus (fr. 4 Lang).In any case and whatever the ultimate source, the equation

sOul = the three fundamental harmonies = pyramid = numberfour, as found in Sextus Empiricus and Anatolius-Iamblichus, isanother characteristic example of the attempts to identify thesoul with three branches of mathematics.

Or two steps, if we accept the theory of F. E. Robbins, "Posidonius and theSources of Pythagorean Arithmology", Classical Philology 15 (1920) 309-322 andidem, "The Tradition of Greek Arithmology", ibid., 16 (1921) 97-123, esp. 123 (ct.K. Staehle, Die Zahlenmystik bei Philon von Alexandreia [1931] 15) according to whichthere is behind Posidonius some arithmological treatise composed in the 2nd century.


For modem thinking, the identification of soul and mathe-maticals probably sounds somewhat fantastic *. But perhapsit can be explained in rather simple terms. When we speak ofsoul (or intelligence, vouc;, etc.), semiconsciously we take theword to designate something subjective - consciousness, etc. -as opposed to the objects of consciousness. But this is not theonly possible point of view **. Reasonableness and reason mayvery well be interpreted as two aspects of one and the samereality (whether or not we are going to use the term Absolute,Absolute Identity, etc. for it) - reasonableness as reason inits self-alienation and reason as reason having become consciousof itself. Indeed, can it be denied that in some sense of the word,reason is what it thinks, or that the objects are what they arethought to be? If we assume that the universe has a reasonablestructure, we can express this conviction by saying that it hasa soul, intelligence, etc. Now, the best proof that the universehas a reasonable structure is that it is amenable to mathematicalcalculation ***.In other words, it seems to be helpful to approach Greek

philosophy by way of Schelling, or even, to a certain extent,Kant. The latter turned our attention to the problem of appli-cability of mathematics to reality ****. To be sure, he explainedit in terms of his theory of the a priori and formal element of ourknowledge and of his Copernican tum, certainly a most un-Greekexplanation. But this is precisely the point where Schelling(and, in his Schellingian phase, Hegel) stepped in: reason isapplicable to the universe because the universe is (objectively)reasonable. When Plato says that the world-soul causes by herthinking the reasonable motions of the universe, this is tanta-

Cf. also A. Delatte, Etudes sur la litterature pythagoricienne (1915), esp. 206-208 andidem, "Les doctrines pythagoriciennes des livres de Numa", Bull. de l'AcatUmie R. deBelgique (Lettres) 22 (1936) 19-40, tracing back the revival of Pythagorism to thebeginning of the 2nd century B.C. See e.g. W. D. Ross, Plato's Theory of Ideas (1951) 213... Cf. H. Heimsoeth, Die seeks groszen Themen der abendlaendischen Metaphysik3

(1954) 90-130, esp.92f.; 118; E. Bickel, "Inlocalitas", p.9 ,in: Immanuel Kant.Festschrift zur zweiten ]ahrhunderlfeier seines Geburlstages. Hg. von der Alberlus-Universitaet in Koenigsberg i. Pro (1924) .... Cf. C. F. von Weizsaecker, The History of Nature (1949) 20. The extent to which this problem still is with us can be seen e.g. in V. Kraft,

Mathematik, Logik und Erfahrung (1947). Cf. also O. Becker, "MathematischeExistenz", ]ahrbuch fuer Philosophie und phaenomenologische Forschung 8 (1927)439-809, esp. 764-768; M. Steck, Grundgebiete der Mathematik (1946) 78-95.


mount to the assertion that there 'are reasonable motions in theuniverse, which can be known *.Thus, it may be appropriate to conclude this chapter by aquotation from Schelling's Ueber das Verhaeltnis der bildendenK uenste zur N atur (1807):

For intelligence (Verstand) could not make its objectwhat contains no intelligence. What is bare of knowledgecould not be known either. To be sure, the system ofknowledge (Wissenschaft) by virtue of which nature works, isunlike that of man, which is conscious of itself (mit derRellexion ihrer selbst verknueplt). In the former thought(Begrill) does not differ from action, nor intent from exe-cution (Saemtliche Werke, 1. Abt., v. VII [1860] 299).

Appendix

1. The most recent presentation of Posidonius is that of K.Reinhardt in RE XXIIll (1953). Here on the passage in question(Posidonius in Plutarch) see p. 791 (d. M. Pohlenz, Die Stoa, vol.II [2nd ed., 1955], p. 215). To reconcile this passage with theirinterpretation of Posidonius both Pohlenz and Reinhardt mustassume that the passage is strictly interpretative and does notimply that Posidonius shared the views which he credited Platowith.2. For accepting the testimony of Iamblichus in preference

Cf. e.g. E. Hoffmann, "Platonismus und Mittelalter", VQrtraege der BibliothekWarburg I9Z3-I9Z4 (1926) 17-82, esp. 54 f. (but see also 72-74). Also J. Moreau,L'A me du monde de Platon aux 5toiciens (1939) should be compared. However, Moreauinsists on the non-realistic interpretation of both the soul and mathematicals (50-53)and, in his La Construction de l'Uealisme platonicien (1939), on not separatingmathematicals from ideas as a separate sphere of being (343-355). J. Stenzel, Me-taphysik des Altertums (in: Handbuch der Philosophie I [1931]) 145 and 157 uses theformula "metaphysical equivalence" to describe Plato's system. This is hardly any-thing else but Schelling's principle of identity - the Absolute precedes both beingand consciousness. Cf. also N. Hartmann, "Das Problem des Apriorismus in derPlatonischen Philosophie", 5B der Berl. Ak. 1935,223-260, esp. 250-258 = Kleinere5chrijten, v. II (1957) 48-85, esp. 74-83. In R. G. Bury, The Philebus 01 Plato (1897)we find Platonism interpreted as Schellingian pantheism (LXXVI f.); and a similarinterpretation is that in R. D. Archer-Hind, The Timaeus 01 Plato (1888) 28 -however his interpretation of the particutar as "the symbolical presentation of theidea to the limited intelligence under the conditions of space and time," (ibid., p. 35)is unduly subjectivistic.


(or, as I should chose to say, fn addition) to that of Aristotle andthus assuming that Speusippus (sometimes at least) identified thesoul with a mathematical (geometrical) I was more than oncecriticized *. Unfortunately my critics limit themselves simply tothe statement that Aristotle is more trustworthy than Iamblichus.One wonders how they arrived at this conclusion. One wondersspecifically whether they ever read the whole passage in which itappears or limited themselves to reflecting on just this onefragment. As the whole passage has now been translated andprovided with an extensive commentary ** it is, I think, easy tosee that as a historian of philosophy Iamblichus is not given toreading his own ideas into authors whose doctrines he simply setout to present. On the contrary, Iamblichus here makes theimpression of a reporter, completely neutral with regard to theauthors whom he quotes. Why, precisely, should we distrust himwhen he contradicts (or seems to contradict) Aristotle?Besides, I did not evade the problem of reconciling the report

of Aristotle (certainly never a neutral reporter he) with that ofIamblichus. Shouldn't my critics, instead of flatly rejecting thetestimony of Iamblichus, try to explain why he should havecommitted the error they charge him with?3. Perhaps some semi-systematic reflections will be consideredpertinent.To most modern readers the assertion that the soul is (orresembles) a geometrical will sound unintelligible. But if a modernphilosopher should say that the geometrical structure of thecrystal is its soul, we may dissent, we may find his assertionfantastic, but would we say that we don't 'understand' what hemeans? I don't think so. .And our attitude (if we so like, understanding in the same wayin which a psychiatrist understands his patient) would hardlychange if the philosopher now continued and said that theuniverse should be interpreted as a giant crystal.

If we now instead of the crystal as a product, think of theprocess of crystallization, it is easy to understand that the geo-

* Esp. by G. de Santillana, Isis 40 (1957) 360-362 and G. B. Kerferd, The ClassicalReview 69 (1955) 58-60.

** [A.-J.] Festugiere, La Rtvllation d'He,mes T,ismegiste. III. Les Doct,ines del'ame (1953) 177-264, esp. 179-182.

POSIDONIUS AN D NEOPLATONISM 57

metrical structure of the crystal could be thought of as motiverather than as a result brought about by the process.Now, it is well known that in the 20th century attempts were

made to explain biological processes in terms of what could becalled a motive form and which the author of such an expla-nation, Driesch, called an entelechy.Considering all this, the definition of the soul as form of the all-extended (the three-dimensional, space) should loose much of itsstrangeness. Moreover, its close relation to Aristotle's classicdefinition of the soul as entelechy of a living body should becomeobvious.

BIBLIOGRAPHICAL NOTE

The two passages in Plutarch (on Xenocrates and Posidonius) andSpeusippus' definition of the soul have very frequently been discussed.Here are some items:A. Boeckh, Ueber die Bildung der Weltseele im Timaeos des Platon(1807) repro in: Gesammelte kleine Schriften, V. III (1866) 109-180, esp.131 f; Th. Henri Martin, Etudes sur Ie Timee de Piaton, 2 vV. (1841).V. I 375-378; A. Schmekel, Die Philosophie der mittleren Stoa (1892)426 f.; 430-432; R. M. Jones, The Platonism of Plutarch (1916) 68-80,esp. 73 n. 12; 90-94 - his own paraphrase of 7j TWV m:p&Twv OUcrtlX is"the basis of the material world", with a refutation (93 f.) of G. Alt-mann, De Posidonio Platonis commentatore (1906), who interpretedit as geometricae formae; L. Robin, Etudes sur la Signification et la Placede la physique dans la Philosophie de Piaton (1919), repro in La PenseehelUnique (1942) 231-366, 52-54; R. M. Jones, "The Ideas as theThoughts of God", Classical Philology 21 (1926) 317-326, esp. 319;A. E. Taylor, A Commentary on Plato's Timaeus (1928) 106-136,equating 7j TWV m:p&TWV ouallX with extension; P. Merlan, "Beitraege zurGeschichte des antiken Platonismus. II. Poseidonios ueber die Weltsee1ein PIatons Timaios", Philologus 89 (1934) 197-214; H. R. Schwyzer "ZuPlotins Interpretation von Platons Tim. 35A", Rheinisches Museum 84(1935) 360-368, equating after Posidonius 7j TWV m:p&TWV ouatlX with/LE:ptcrTIj ouallX (363); J. Helmer, Zu Plutarchs "De animae procreationein Timaeo" (1937) 15-18; L. Edelstein, "The Philosophical System ofPosidonius", American Journal of Philology 57 (1936) 286-325, esp. 302-304; P. Thevenaz, L'Ame du monde, Ie Devenir et la Matiere chez Plu-tarque (1938) 63-67, with a polemic against my equation l)A'I) = /LE:ptcrT6v= 1tEPIXTIX = TO 1t&YnJ 8tIXaTIXT6v on p. 65; K. Praechter, art. Severns 47in RE II A 2 (1923).Of the more recent literature on Posidonius only W. Jaeger, Nemesios

von Emesa (1915) need to be mentioned in the present context. Foreverything else see K. Reinhardt, art. Poseidonios in RE XXIIll (1953).For discussions concerning the status of mathematicals in Plato's

philosophy see particularly L. Robin, La Theorie platonicienne desIdees et des Nombres d'apres Aristote (1908) 479-498; J. Moreau, La


Constt'uction de l'Idealisme Platonicien (1939), esp. 343-366 (according tohim they differ by their mode, not by their essence and they are in-conceivable unless thought) ; idem, L'A me du M onde de Platon aux Stoiciens(1939), esp. 43-53; F. Solmsen, Die Entwicklung det' at'istotelischen Logikund Rhetot'ik (1929) 79-84; 101-103; 237; 250; E. Frank, "The Funda-mental Opposition of Plato and Aristotle", Amet'ican joumal 01 Philology61 (1940) 34-53; 166-185, esp. 48-51.In many respects my identification of Plato's world-soul with themathematicals is a return to F. Ueberweg, "Ueber die PlatonischeWeltseele", Rheinisches Museum 9 (1854) 37-84, esp. 56; 74; 77 f. Cf. alsoJ. Moreau, Realisme et idealisme chez Platon (1951) with the criticisms byH. D. Saffrey in Revue des Sciences TMologiques et Philosophiques 35 (1951)666 f.

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[Doi 10.1007%2F978!94!010-1592-9_3] Merlan, Philip -- From Platonism to Neoplatonism Posidonius and Neoplatonism