-
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
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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.
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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
-
POSIDONIUS AND NEOPLATONISM 37
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.
-
38 POSIDONIUS AND NEOPLATONISM
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'
-
POSIDONIUS AND NEOPLATONISM 39
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. .
-
40 POSIDONIUS AND NEOPLATONISM
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.
-
POSIDONIUS AND NEOPLATONISM 41
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.
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42 POSIDONIUS AND NEOPLATONISM
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.
-
POSIDONIUS AND NEOPLATONISM 43
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.
-
44 POSIDONIUS AND NEOPLATONISM
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.
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POSIDONIUS AND NEOPLATONISM 45
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)
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46 POSIDONIUS AND NEOPLATONISM
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.
-
POSIDONIUS AND NEOPLATONISM 47
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
-
48 POSIDONIUS AND NEOPLATONISM
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
-
POSIDONIUS AND NEOPLATONISM 49
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
-
50 POSIDONIUS AND NEOPLATONISM
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.
-
POSIDONIUS AND NEOPLATONISM 51
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
-
52 POSIDONIUS AND NEOPLATONISM
\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
-
POSIDONIUS AND NEOPLATONISM 53
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.
-
54 POSIDONIUS AND NEOPLATONISM
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.
-
POSIDONIUS AND NEOPLATONISM 55
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.
-
56 POSIDONIUS AND NEOPLATONISM
(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.
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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
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58 POSIDONIUS AND NEOPLATONISM
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.