by Robert Kraft, University of Pennsylvania
for the SBL Philo Group, November 1996 (New Orleans)
Main abbreviations and special uses:
Op = On Creation (De Opificio Mundi)
LA = Allegorical Interpretation (Legum Allegoria)
HM = Horst Moehring
article
KS = Karl Staehle dissertation
decad = the unit (one) and numbers up to and including ten
italics are used to identify sources and titles.
Translations are based on Loeb, but sometimes modified.
Karl Staehle,
Horst
Moehring, "Arithmology as an Exegetical Tool in the Writings of Philo of
Alexandria," a paper presented at the 1978 SBL sessions and published in volume
1 of the
KS was searching for the presumed common source of arithmological traditions
that surface in the first few centuries of the common era, especially in the
works of Theon of Smyrna (2nd century, writing on Plato's mathematical ideas)
and Anatolios of Alexandria and Caesarea (3rd century, on the first ten numbers
-- the "decad"), in addition to Philo. Previous research had focused on the
possibility that commentarial traditions on Plato's Timaeus provided the answer,
perhaps filtered through a lost work of that much-lost yet apparently highly
influential author, Posidonius of Apamea in Syria (about 100 bce), whose "neo-Pythagorean"
interests are also frequently highlighted. KS (following other studies\1/) thinks
it unlikely that the main carrier of the common materials was commentary on
the Timaeus, but that there was an early and influential arithmological treatise,
author and title unknown, from around the end of the 2nd century bce (perhaps
of "Alexandrian" provenance), that dealt with the decad and was used, directly
or indirectly, by Posidonius, Philo, and various other authors. His detailed
examination of arithmological passages in all of Philo is aimed at reconstructing
more of the common source.
---
\1/ KS relies heavily on the work of Frank Egleston Robbins in attempting to
unravel the question of Philo's source(s) for his arithmology -- "Posidonius
and the sources of Pythagorean Arithmology," Classical Philology 15 (1920)
309ff., and "The Tradition of Greek Arithmology," Classical Philology
16 (1921) 97-123. Robbins thinks that Posidonius wrote a work Peri\
Krithri/ou that was itself dependent on an earlier arithmetic source
that shows up also in Anatolios and in a slightly different form in Theon and
some allies (KS 15). Philo is also a witness to this lost arithmological source
(Decal 29 is a key text). Indeed, Robbins attempts to place Philo more
precisely into the flow by close analysis of Op, concluding that Philo
and Anatolios tend to agree against Theon et al. in certain test cases. KS is
not so sure about such a precise analysis, while agreeing with the general thrust
of the reconstruction. General questions about textcritical considerations both
with regard to the lost source and with Philo's works themselves are mentioned
but not pursued.
Other authors consulted by KS and listed in his notes include:
Chalcidius, on Plato's Timaeus;
Varro;
Capella;
Favonius Eulogius, commentary on Scipio;
Macrobius, commentary on Scipio;
Theologoumena Arithmetica.
===
HM is interested in Philo's exegetical techniques, and looks at the entire Philonic corpus with an eye to the function of arithmetric arguments associated with the number seven. HM agrees with KS on the probability of a neo-Pythagorean source used by Philo, especially in Op and LA, and explores the lengthy section on the number seven in Op in greater detail. An interesting issue raised by HM's analysis is the significance of attempting to distinguish "Greek" aspects or elements of Philo's material from "characteristically Jewish." If Philo, as a Greek Jewish interpreter, understood his universe in Platonic- Pythagorean terms, as seems to be clear in general, what is the value of such a distinction? For Philo, at least, if truth is unified, all these interepretations could be legitimately "Jewish" as well. On the other hand, it cannot be assumed that throughout his literary life Philo was entirely consistent and unwavering in his attitudes to and use of materials that he knew were controversial for some. On this subject, the comparison between the Philo of Op and the Philo seen elsewhere on the matters termed "Greek" by HM might well be useful. And perhaps some progress towards creating better labels might also be made.
Much of HM's article deals with more explicitly exegetical connections of the number seven in Philo's writings, apart from the long list in Op and its parallels. His conclusions regarding the Op materials will be critiqued in more detail below. In general, HM finds that "arithmology is a frequently used exegetical tool of Philo's, but it is only one among several and must be judged as an integral part of his entire exegetical approach. ... In his arithmology, Philo makes haevy use of Greek myths and symbols, which he applies to purely Jewish concepts. ... Arithmology allows Philo to stress two points: a. the cosmic and human order described by Moses is of universal validity ...; b. this order is represented most clearly and purely in Jewish law, liturgy, and tradition; the Jewish religion is, therefore, the most 'natural' religion. ... The superiority of the Jewish tradition is not esoteric in character: as can be shown through arithmology, it is reasonable and demonstrably so" (218). Thus HM has himself underlined the terminological dilemma to which I have already referred. If this is an accurate depiction of Philo's conceptual world, which requires that Philo's understanding of religious (and "philosophical") truth encompasses whatever is true in any available linguistic and cultural contexts, "Greek or barbarian," then we must find a way of speaking about that world in terms more appropriate to Philo's perceptions. He is, after all, a Greek Jew and a Jewish Greek, and his arithmological meanderings may demonstrate this as clearly as anything else in his extensive writings.
Philo encloses the body of his lengthy treatment of the number seven in Op 89-128 between the following glowing passages (based on Loeb ET, sometimes modified):
The intervening sections in Op (just over 13 Loeb Greek
pages of the 66 in the total treatise) comprise about 20% of the
treatise (HM estimated 23.26% by counting all the numbered
sections that deal with "seven") and include a large number of
the Greek or Latin arithmological associations for the number
seven known from antiquity,\2/ with much of the material also
being found in LA 1.8-16, packaged in only 2 pages of Loeb
Greek.
(1) Op 89 [see KS 33e]: Creation of the world is in
accordance with the properties of the number six, a perfect
number, after which the Father sanctified the seventh day as the
birthday of the cosmos;
(2) Op 116 [=KS 55]: Law enjoins the keeping of the
greatest and most public festivals at the time of the equinoxes,
each of which falls in a seventh month from the other (using
"inclusive" reckoning) -- it is not clear to me that even this
sort of calendar allusion deserves to be called "Jewish" by HM's
standards, since Philo could be understood to mean that cultures
in general have legislated spring and fall festivals (i.e., does
"law" here necessarily mean the law of Moses?).
(3) Op 128 [see above, the conclusion]: Moses exceeded the
scientists among the Greeks and barbarians in according honor to
the number seven by incorporating it into the Law and by
ordaining the observance of the seventh day as holy. HM observes
that "even in this perfunctory bow to Moses, Philo describes the
purpose of the sabbath observance in purely universalistic and
philosophical terms -- 'giving their time to the one sole object
of philosophy with a view to the improvement of character and
submission to the scrutiny of conscience.'"
In contrast, in this long section of Op Philo includes, in
addition to the relatively straightforward arithmological
statements, a number of interesting quotations from Greek authors
and allusions to Greek institutions. HM argues that unlike the
characteristically "Jewish" associations mentioned above, these
form an integral part of the section and cannot be deleted
without violating the structure of the whole, although in some
instances this seems questionable -- as a comparison with the
parallel material in LA, which has only one of these
explicitly identified references (#1) and that in a significantly
different form, illustrates (see further below). The passages
mentioned by HM as most sigfificant are the following:
(1) Op 100 [=KS 43-44]: Thus "other philosophers"
liken the number seven to the motherless Nike (that is, Athena =
Minerva), also a virgin [or, "and Parthenos," as a name] -- an
account has her appearing out of the head of Zeus; but the
Pythagoreans liken seven to the one who governs everything (i.e.
Zeus), the motionless one, concerning which Philo explicitly quotes
the 5th c bce Pythagorean Philolaus: "There is one God eternal,
governing and ruling everything, alone, motionless, himself like
(only) to himself, different from (all) others." The LA
1.15 parallel has significant differences but does refer more
vaguely to a tradition associated with "the Pythagoreans" (see
further below).
(2) Op 104-105a [=KS 62a]: Long quotation attributed to
Solon -- a poem on the ten stages of a human's lifetime, each
stage seven years long. Similar material appears in LA
1.10, introduced by the vague "they say" and limited to comments
on only three stages.
(3) Op 105 [=KS 62b]: Quotation from Hippocrates on the
seven stages of a human lifetime, also employing multiples of
seven years in the stages. For LA, see the previous
paragraph.\n/
(4) Op 119 [=KS 65]: Explicit and rather incidental reference to Plato
saying that through the mouth mortal things have their entrance, immortal things
their exit -- in Timaeus 75D, Plato actually establishes a contrast between
necessary things (a)nagkai=a) and best things (a)/rista).
The context in Philo is that the mouth is one of the seven openings in the head.
The parallel section in LA 1.12 does not mention the Plato connection.
(5) Op 124 [=KS 59]: Reference to Hippocrates for the time
needed for the solidification of the seed and the formation of the
embryo in childbirth. Not in LA.
(6) Op 126 [=KS 73]: Reference to the seven vowels of Greek
language [aehiouw] (HM adds "appropriate for Ionian" -- and why
this passage is thought by HM to be specifically "Greek" as
opposed to "Jewish" -- including Greek speaking Jews -- escapes
me). A shorter parallel appears in LA 1.14b.
(7) Op 127 [=KS 74]: Etymologies for both the Greek and
Latin words for seven, which prove that seven is a holy number.
(Again, why HM sees this as "Greek" as opposed to "Jewish" is not
clear.) Despite the Loeb formatting, which joins Op 127 to
what precedes, it is possible to read it rather as the start of a
summary statement that continues into Op 128 [see above and
below]; in any event, it serves well as a transition to that
concluding section. No parallel appears in LA.
(8) Op 128 (concluding section summary) [=KS 75]: The most
approved investigators of mathematical science (presumably
including astronomers) among the Greeks and barbarians (non-
Greeks) pay honor to the number seven. Not paralleled in
LA.
As has been noted, a similar, detailed summary of the properties
of the number seven is also to be found in LA 1.5-18. In
the paragraph preceding the LA section, Philo states the
purpose of his arithmological speculations, which of course, he
ascribes to Moses himself: "Moses' wish is to exhibit alike the
things created of mortal kind and those that are incorruptible as
having been formed in a way corresponding to their proper
numbers" (LA 1.4b -- HM underscores the importance of this
passage for understanding the entire system of arithmology in
Philo).
This introduction to the discussion of seven in LA closes with an unattributed,
perhaps "proverbial," saying (traceable to Euripides, frg 839) -- "Naught that
is born does ever die,/ Its severed parts together fly,/ And yield another shape/"
-- in which the author stresses the integral link between birth and death, an
idea Philo will put to use in his discussion of the relationship between the
numbers one and seven. Otherwise, with the following exception, the LA
section does not include the explicit references to Greek authors listed above.
(See below for a comparative overview of the relative contents of the lists
in Op and LA.)
The section closes in LA 1.15 with a reference to "the
Pythagoreans, mythologizing," who liken the number seven to the
ever-virgin and motherless one (Athena), who neither was born nor
will bear (see above on Op 100, which gives a somewhat
different view of the "Pythagorean" position); this is followed
by a resumptive reference to Gen. 2.2, in accord with the
commentary format of LA, so that the predominantly "Greek"
main part of the section is, as it were, framed by two specific
references to things unmistakably Jewish -- namely, the
consecutive text of Genesis (why MH thinks this is worth
mentioning escapes me since the format of LA expects such
framing; as has been noticed elsewhere, MH's attempt to
distinguish the "Greek" from the "Jewish" is to some extent
forced).
A quick summary of the purely arithmological statements on the
number seven, without specific application to biblical texts,
would have to include the following items, following the sequence
in Op 90-127. They constitute the basic material which
Philo uses in his exegetical application of arithmology. In what
follows, the exact order in Op will be followed, using its
section numbers as identification marks. KS and HM both list
these items, but with different organization and sequence suiting
their respective purposes, but thus possibly blurring any
subtleties in Philo's chosen order. KS also conviently excerpts
the relevant Greek texts and provides brief references to similar
passages in other ancient authors.
e.g.,
In Op 92a, the latter type (outside the decad) is described
as superior (although in Op 95a, the former type is called
"not at all inferior" to the other!); the seventh term of any
regular procession, starting from unity and with a ratio of 2, 3,
or any number, is both a cube and a square [it is a mathematical
given that the third item in the sequence will always be a
square, the fourth a cube, and the seventh both a square of the
cubed number and a cube of the squared number], combining both
the corporeal and the incorporeal. (In other places such as
QG 1.77 Philo will argue that the ones are prior to the
tens both in order and in power, so that seven is more archetypal
and elder than seventy.)
This mathematical phenomenon is obviously of great interest to
Philo, for he returns to it in another context in Op 106
[=KS 41b], where he emphasizes the elements 3 and 4 that combine
to make up seven (within the decad!) as they relate to the
aforementioned progression based on doubling, where the third
item is a square, the 4th a cube (still within the decad -- 4
and 8), and the 7th (64, outside the decad) is both a square (of
8) and a cube (of 4). Thus the same mathematical phenomenon does
double service.
Op 95-96 [=KS 42]:
Op 95b-96 (see also 107-110) [KS 46]:
Op 97 [=KS 48]:
Op 98 [=KS 49]:
Op 99-100 [=KS 43-44] (see also LA 1.15, VMos
2.210, QG 2.12, SpecLeg 2.56, Heres 170 and 216,
VCont 65, Praem 153, Decal 102):
Op 101 (see also 111) [=KS 50]:
(1) In the world of the intellect, it is a symbol for "that which
is exempt from movement and passion," as has been shown above;
(2) in the world of the senses, the hebdomad is a most essential
force [in the movement of the planets], from which all earthly
things derive advantage.
Op 101b [=KS 56] (see also LA 1.8, SpecLeg
1.178):
Op 102 (compare 98 and 106) [=KS 49]:
Op 103-105a [=KS 62a] (compare LA 1.10):
Op 105 [=KS 62b] (compare LA 1.10):
Op 106 (see above Op 98, 102) [=KS 41]:
Op 107-110 [=KS 47] (see alsoVMos 2.210):
Op 111 [=KS 50] (see also LA 1.8a):
Op 112 [=KS 51]:
Op 113 [=KS 52] (see also LA 1.8b, SpecLeg 2.57,
Decal 102, QE 2.78):
Op 114 [=KS 53] (see LA 1.8c):
Op 115 [=KS 54]:
Op 116 [=KS 55]:
Op 117a [=KS 58]
Op 117 [=KS 63] (see also LA 1.11, QG 2.12):
Op 118 [=KS 64] (see also LA 1.12):
Op 119 [=KS 65] (see also LA 1.12d):
Op 120 [=KS 66]:
Op 121 [=KS 67] (see also LA 1.14d):
Op 122 [=KS 68] (see also LA 1.12a):
Op 123 [=KS 69] (see also LA 1.13a):
Op 124a [=KS 59]:
Op 124b [=KS 60] (see also LA 1.13c):
Op 124c [=KS 61] (see also LA 1.9b):
Op 125 [=KS 70] (see also LA 1.13b):
Op 126a [=KS 71] (see also LA 1.14a):
Op 126b [=KS 72] (see also LA 1.14c):
Op 126c [=KS 73] (see also LA 1.14b):
Op 127 [=KS 74]:
Op 128 [=KS 75]:
HM makes the following concluding observations about this
material:
1. Philo almost certainly took it over from some Neo-pythagorean
work either on arithmology in general, or on the number seven.
The Greek origin of the list is obvious from the references to
Greek mythology and the quotations from authors.
2. Although Philo has collected in the list a veritable armory of data, a glance
at the list of the passages in which any of the items re-occurs outside the
lists themselves in Op and LA, indicates that he actually made
very little use of this material in his own exegetical work. Only items from
Op 99-100, 101b, 113, and 117 occur in any of the other treatises of
the Philonic corpus. Among these, the most frequently used statement is one
of Greek provenance: the number seven can be likened to the goddess Athena.
The rest of the repeated items all refer to the seven planets in general or
to the moon in particular.
3. These observations seem to justify the conclusion that Philo
occasionally introduced arithmological statements for their own
sake, without putting them to work as exegetical tools in
connection with specific biblical passages. It should be noted,
however, that this is more obvious in the case of the hebdomad
than with any other number, if for no other reason than that for
no other number does he introduce so long and detailed a list of
statements.
4. The shorter list of statements on the hebdomad in LA is
based upon the longer one in Op. Not only do many of the
items occur in the same sequence [RAK: but see the lists below!],
but even the transitional clauses are strictly parallel:
Op 101 // LA 1.8 transition to sensible world [RAK:
actually this is less a "transition" in LA than it is the
proper start of the arithmological section.]
Op 117 // LA 1.9 transition to man [RAK: the
transition actually comes in Op 102, to the perfecting
power of 7, and is quite different from LA 1.9, which moves
fairly smoothly from heavenly bodies to their influence on
humans.]
Op 126a // LA 1.14a transition to sciences [RAK: yes, this is
a good parallel, on grammar and music.]
The only exception to this pattern is the transitional clause
introducing the hebdomad within the decade, which is found only
at Op 95. The introductory statement on the hebdomad quoted
above also has no parallel anywhere in Philo.
Thus far HM. By way of modification and addition I offer the
following observations:
It seems to me that the relationship between these two lists is much more complex
than HM suggests and may hold some valuable clues to Philo's literary activities.
Here is an overview of the roughly 20 items that are paralleled, first following
the order found in Op, then the order in LA:
Organizationally, each list has a certain coherence. The Op material
follows a fairly obvious, often explicitly described, flow and provides much
more procedural commentary by the author. Occasionally it appears to be repetitious,
but even the repetitions fit the flow. The list in LA, on the other hand,
provides few clues to its organization beyond the statement in 8a that it deals
with evidence from "nature." Still, sequences of three can be seen in the ordering,
whether Philo was aware of or intended this or not -- e.g. heavenly bodies (planets,
great bear, moon), human development stages (only the first 3 are mentioned!),
body parts (inner, outer, face), bodily functions (discharges, illness, menstruation),
grammar/music (vowels, lyre, accents). Not covered by such an analysis are the
sections on development of fetuses, which can be seen as an appropriate lead-in
to the three stages of human growth, on parts of the soul and on bodily motions,
which are themselves in sequence between the stages of human development and
the parts of the body.
A look at the detailed differences between the treatment of seven
in these treatises, could suggest that the LA material is
sometimes less developed than that in Op, or is developed
in a different manner, or is a rather careless or awkward
summary.
Seldom does LA show signs of more sophistication than
Op! A possible exception is in LA 1.15 (see also
DeusImm 11, 13 [=KS 45]), on how seven, following the
perfection of six, is in some senses the same as the monad --
something that seems to be implied in Op 89, but not
explicitly stated. (HM points out that the affinity between one
and seven plays an important role in Philo, who also demonstrates
it on the basis of the biblical text.)
LA 1.4 on the six "mechanical" motions [=KS 38], followed
by 1.12 on the seven (adding "rotation" to the list) is difficult
to assess. KS mentions parallels to both approaches, so it is
unlikely that the addition of "rotation" was a specifically
Philonic contribution. But if LA is based on the material
in Op, it also does other things with that material.
LA 1.10a on the development of speech in the first seven years of human
development is quite different from the outline of stages attributed to Solon
and/or Hippocrates in Op 103-105, where the shedding of teeth is at issue;
and while Op goes on to list 10 stages of human existence (the Solon
tradition) or seven (Hippocrates), LA only mentions the first three seven
year periods, without attribution to any specific authority. Furthermore, LA
has humans reaching full maturity (defined in terms of growth) in stage 3, at
21 years of age, while Op has this accomplishment (defined in terms of
strength [103] or growth [105]) in stage 4, at 28 years. It could be argued
that in writing LA, Philo recognized the artificiality of the "Solon"
and "Hippocrates" cycles and abandoned those schemes, or that in Op,
Philo had learned more about the cycle theories and had added to the arsenal.
Or that different influences operated on Philo in different ways when he wrote
the two treatises in question, incompatible with the simple model of direct
development.
LA 1.15 has Pythagoreans comparing the number seven to
"the ever-virginal motherless one," but in Op 100, the
Pythagoreans are credited with likening it to the motionless
soverign while unidentified "other philosophers" make the
Nike/Athena identification. Has Philo learned something between
the writing of LA and Op, or is something else
happening here? It is doubtful that he had Op clearly in
mind when he wrote the LA summary, unless he had changed
his mind about who claimed what (or no longer cared).
Finally, LA tends to neglect the more theoretical evidences
found in Op, e.g. on musical harmonies or mathematical
relationships or geometrical forms, focusing much more summarily
on bodies in nature (see LA 1.7b/8a), although LA
1.15 does end on a more abstract mathematical note. Of course,
Philo's expected distinction between the world of ideas and the
world of the senses comes into play here, with LA focusing
on the latter.
Also absent from LA are the following "sense world" items:
Such evidence is rather frustrating to interpret, insofar as
there are other reasons to believe that Op is a relatively
"early" production relative to the larger Philonic corpus and
relative to the "allegorical" treatises. Possibly Op went
through two or more editions before reaching the form we have. Or
LA on these arithmological materials reflects a waning of
interest and of recollection which produces a rather pale
reflection of the more impassioned and wide-ranging treatment in
Op, which also probably found its way into Philo's lost
treatise On Numbers (possibly written about the same time
as Op -- see Op 15, perhaps suggesting that a
treatment of the One was available, and Op 52, on the
intention to write on number four, or perhaps on numbers in
general).
NOTE that KS first seems to agree with Cohn in placing Op
after QG (apropos 4.151, a possible ref to On
Numbers; see also 3.49, 4.110 and VMos 2.115), and thus
thinks that On Numbers was already available or at least on
Philo's agenda before Op appeared (8 n.1), but presumably
did not include a treatment of the number seven! But then KS
recognizes the difficulty of squaring such a chronology with the
statement in Op 52 that seems to look to the production in
the future of a treatise On Numbers, and admits without
conviction that perhaps Op actually preceded the
Questiones commentaries (9)! I would incline to the latter
possibility, at least for a "first edition" of Op. It is
also possible that the conjectured single treatise On
Numbers was in reality a series of treatises or an evolving
work that defies exact pinpointing in the existing Philonic cross
referencing. The pieces of evidence are unharmonious if not
conflicting, precluding any simple solution at this time.
On what seems, viewing the two lists comparatively, to be an
obvious tendency in LA to play down the association of the
traditions with known literary and scientific authorities (Solon,
Hippocrates, philosophers and grammarians, etc. -- and even when
"Pythagoreans" are mentioned, what is the flavor of the term
"mythologizing" applied to them?!), we might ask whether this is
better understood as a phenomenon of "youth" flowing from lack of
precise knowledge, or perhaps of mature "conservativism," which
has abandoned some aspects of early rebelliousness or idealism,
or some other factor (failure of memory, reliance on a different
source, adjustment to different audiences) -- including the
possibility of revisional stages fathered by Philo himself, or
occuring during the transmission of his writings.
If I am forced to draw some tentative conclusions from all this,
my feeling is that Op is a product of confident informed
and enthusiastic youth, from an author who has not yet felt the
sting of criticisms from his associates and others from whom he
expected support. His discourse on seven is a draft of what he
also included in On Numbers around the same time, but never
introduced in such a full sampling in subsequent writings. If
LA is based directly on that material, it is a faint and
extensively reworked echo. It is easier for me to believe that
Op is an improved version of what appears in LA, or
perhaps simply an alternate version. I can also understand
LA as a faint and toned down echo of the more inclusive and
sophisticated tradition by an author who had lost or laid aside
some of the boldness or brashness he once exhibited.
Alternatively, but with less enthusiasm, I might resort to a
theory of early and later editions of Op to explain how
LA might reflect such a weak form of the "seven" tradition,
being based on the early edition that was considerably
strengthened later, after On Numbers had been completed.
There are many paths; but they are all conjecture.
I doubt whether anyone could adequately celebrate the
properties of the number seven, for they are beyond all words.
Yet the fact that it is more wondrous than all that is said about
it is no reason for maintaining silence regarding it. Nay, we
must make a brave attempt to bring out all that is within the
compass of our understanding, even if it be impossible to bring
out all or even the most essential points. [Op 90 (=KS 39)]
These and yet more than these are the statements and
philosophical insights of men on the number seven, showing the
reasons for the very high honor which that number has attained in
nature, the honor in which it is held by the most approved
investigators of the mathematical science among Greeks and
barbarians, and the special honor accorded to it by that lover of
virtue, Moses.... [Op 128a]
---
\2/HM notes that W. H. Roscher has listed over a hundred different functions
of the number seven (or its multiples) reaching all the way from the cult of
Apollo to the use of seven black beans for magic purposes and in connection
with the cult of the dead [196; see Roscher, "Die enneadischen und hebdomadischen
Fristen und Wochen," Abhandlungen der philologisch-historischen Klasse der
Kgl. Sächsischen Gesellschaft der Wissenschaften 21.4 (1903); "Die
Sieben- und Neunzahl im Kultus und Mythus der Griechen," ibid. 24.1 (1904);
"die Hebdomadenlehre der griechischen Philosophen und Arzte," ibid 24.2/6 (1906)].
===
According to HM, the Op section "contains only three short
passages of unmistakably Jewish content," and they are not
considered integral to the section. [KS is not particularly
interested in them, since he is looking for Philo's general
hellenistic Greek source(s)]:
---
\n/For later developments of this theme, see Elizabeth Sears,
===
Op 91 [=KS 40]:
Definitional -- there are two categories of "seven" or "seventh"
in terms of the properties and relationships of numbers:
(1) within the decade consisting of seven units and determined by
the sevenfold repetition of the unit -- Philo returns to this
aspect in Op 95, as an introduction to the discussion of
harmonies, etc.; and
(2) outside the decade.
Op 92-94 [=KS 41a]:
Outside the decade: starting from one, the desired number is
obtained by doubling, tripling, etc., to the seventh place in the
sequence:
(x2) = 1, 2, 4, 8, 16, 32, 64
(x3) = 1, 3, 9, 27, 81, 243, 729
(x4) = 1, 4, 16, 64, 256, 1024, 4096
(x5) = 1, 5, 25, 125, 625, 3125, 15625
(x6) etc.
Transitional -- returning to the general mention of this category
in Op 91, Philo presents mathematical observations about
"seven" or "seventh" within the decad:
All partitions of the hebdomad produce musical harmony
(Philo's enthusiasm for musical harmonies appears elsewhere in
his writings -- e.g. Post 103-111, VCont 80 and 84,
QG 3.3 -- but is not usually expressed in arithmetic
terms):
7 = 1 + 6 (6:1 greatest distance from highest to lowest note)
7 = 2 + 5 (5:2 fullest power in harmonies, almost like diapason)
7 = 3 + 4 (4:3 first-harmony, the sesquitertian or diates saron).
Similarly, with geometric relations, in the right-angled
triangle, 3 and 4 (components of 7) produce the right angle.
The hebdomad is also the starting point of all plane and solid
geometry, or: the hebdomad is the starting point of all things
corporeal and incorporeal.
The hebdomad within the decad is uniquely neither product nor
factor. For this reason some "other philosophers" have likened it
to the motherless Athena, also a virgin. "The Pythagoreans" liken
it to the governor of all (Zeus). (HM notes that seven is likened
to Athena or Zeus no fewer than eleven times in Philo -- "the use
of motifs from Greek religion is obviously not a problem for
Philo.")
Transitional section, noting that the hebdomad serves as a symbol
in both the intelligible and the sensible world:
On the circuits of the moon -- the phases of the moon last seven
days.
Spacial relations in the material universe illustrate aspects of
seven.
There are ten stages of seven years each in a person's life
(attributed to Solon). KS (p.17) refers to F.E.Robbins'
discussion of such details as the arrival of teeth in 7 months
(Theon et al.), which is not found in Philo, Anatolios, or
Clement of Alexandria. It is not difficult to imagine how
"growing of teeth" (number of months) and "shedding of teeth"
(number of years) could become confused or amalgamated in the
traditions -- see the Solon quotation which mentions both growing
and shedding together, and Op 103b, where only "growing" is
mentioned in Philo's introductory summary for the first seven
years!
There are seven ages in a human's life, in multiples of 7 years,
although not entirely continuous (attributed to Hippocrates) --
i.e. stage 5 = 21 years and stage 7 is perhaps open ended. KS
(p.17) refers to Robbins' discussion of what happens at 21 years,
where Theon et al. focus on beard and size, and at 28 girth,
while Chalcidius et al. say beard at 21 and size at 28. KS notes
that Philo has similar deviation between the details in Op
105 (beard at 21, full growth at 28) and in LA 1.10 (full
growth at 21; see KS 62c)!
On how "in the order of nature" 3 represents a plane, 4 a solid,
and both are part of the mathematical sequence leading to
correspondence of cube and square.
The hebdomad is absolutely harmonious, the source of the most
beautiful scale, which contains all the harmonies (see also
above on Op 95b-96):
that yielded by the interval of 4
that yielded by the interval of 5
that yielded by the octave.
Transitional, having explored the significance of seven in the
incorporeal world, now a closer look at seven in the visible
universe.
Heaven is girded by seven zones. Note that Dionysius of Halicarnassos (1st bce)
in Antiq.Rom. 2.5.3.6ff speaks of five.
There are seven planets and they cause a variety of earthly phenomena. (HM notes
that in SpecLeg 1.16, Philo comes close to the basic principle of astrology,
when he speaks of the sun, the moon, and the other stars "in accordance with
their sympathetic affinity to things on earth acting and working in a thousand
ways for the preservation of the All." At the same time he warns against "supposing
that they alone are gods." Later, in SpecLeg 2.56f [=KS 57], Philo states
that because of its influence upon the stars the hebdomad is called kairo/v).
Ursa maior consists of seven stars, which sea pilots use to
advantage. Note that Aristotle and others speak of 12 stars in
the "Bear"; Alexander of Aphrodisias (ca 200 ce) says there are
12, but that the "Chaldeans" number them differently.
The Pleiades consist of seven stars.
The two equinoxes are seven months apart. (As noted above, HM
considers this to be one of the three passages in Op 89-128
in which Philo introduces a clearly Jewish element. Philo says
that "each of the equinoxes occurs in a seventh month," and
refers to "law" that calls for major public festivals at each
time; HM assumes that Philo is adducing the sacred character of
the hebdomad as a reason for the dates of the highest Jewish
festivals.)
Transitional -- just as earthly things depend on the heavenly
bodies in their hebdomadic relationships, so the number seven is
important in human matters.
The irrational part of the soul has seven components (5 senses,
speech and generation).
The body consists of seven outer parts (head, chest, stomach, 2 hands, 2 feet)
and seven inner parts (spla/gxna = stomach, heart,
lung, spleen, liver, 2 kidneys) -- the order is reversed in LA, with
other minor deviations of detail. KS (p. 17) notes that Robbins finds sto/maxov
only in Philo and Anatolios, while Theon et al. have glw=ssa.
The head has seven essential parts (2 eyes, 2 ears, 2 nostrils,
mouth). Instead of "head," LA has "face," in agreement with
most of the other sources noted by KS.
There are seven things that can be seen -- corporality,
extension, shape, size, color, motion, rest.
There are seven different intonations of the voice -- acute,
grave, circumflex, rough, smooth, long, short.
There are seven types of motion -- up/down, right/left,
forward/back, rotary: but note that in LA 1.4, Philo uses
the same list (minus rotation) in support of the number six [=KS
38].
There are seven bodily excretions -- tears, nose mucus, mouth
phlegm, urine, feces, perspiration, sperm. KS notes no parallels
to this tradition.
Semen solidifies for embryo formation in seven days, according to
Hippocrates. Note the connection with the mention of sperm at the
end of the immediately preceding series.
Menstruation lasts at most seven days (apparently also attributed
to Hippocrates).
Fetuses that come to birth in the seventh month survive (possibly
also attributed to Hippocrates), while those born in the 8th
month tend to expire. KS (p.17) reports the observations of
Robbins that only Philo and Anatolios give such a brief notice
here, while Theon, Chalcidius, Varro, Capella, Favonius,
Macrobius and the Theologoumena make additional observations.
Illnesses reach their critical stage (kri/siv) on the
seventh day.
Transitional -- the number seven also is influential in grammar
and music.
The lyre has seven strings.
There are seven vowels (not named as such).
Etymologies are given for both the Greek and Latin words for
seven, which prove that seven is a holy number. As noted above,
this section serves well as a transition to the concluding
statements.
The most respected investigators of mathematical science
(presumably including astronomers) among the Greeks and
barbarians (non-Greeks) pay honor to the number seven, as does
Moses with the sabbath day law.
4. Towards Some Conclusions
Op
Topic
LA 1
99a
unbegotten, unbegetting
15b
100
motherless and virgin
15c
101a
realm of sense/nature
8a
101b
stages of the moon
8d-e
103
ability to procreate
10b
105
attainment of maturity
10c
113
seven planets
8b
114
great bear constellation
8c
117a
heavens affect earth
9a
117b
parts of the soul
11
118a
parts of outer body
12c
118b
parts of inner body
12b
119a
parts of the head/face
12d
121
voiced accents
14d
122
types of motion
12a (see also 4 !)
123
bodily discharges
13a
124b
menstrual period
13c
124c
fetuses in womb
9b
125
illnesses
13b
126a
on grammar (and music)
14a
126b
the lyre
14c
126c
vowels
14b
Op
Topic
LA 1
101a
realm of sense/nature
8a
113
seven planets
8b
114
great bear constellation
8c
101b
stages of the moon
8d-e
117a
heavens affect earth
9a
124c
fetuses in womb
9b
--
human speech develops
10a
103
ability to procreate
10b
105
attainment of maturity
10c
117b
parts of the soul
11
122
types of motion
12a (see also 4 !)
118b
parts of inner body
12b
118a
parts of outer body
12c
119a
parts of the head/face
12d
123
bodily discharges
13a
125
illnesses
13b
124b
menstrual period
13c
126a
on grammar (and music)
14a
126c
vowels
14b
126b
the lyre
14c
121
voiced accents
14d
99a
unbegotten, unbegetting
15b
100
motherless and virgin
15c
Op 102b, on the seven dimensions of bodies -- length,
breadth, depth, point, line, surface, solid;
Op 112a, on the seven zones that gird the heaven --
artic, antartic, summer and winter solstices, equinox (apparently
counting as one; but see Op 116!), zodiac, and the milky
way (!), but Philo refuses to count the horizon;
Op 115, on the seven stars of the Pleiades;
Op 116, on the two equinoxes, each in a 7th month from
the other (with attendant festivals);
Op 120, on the seven dimensions of what is seen --
presence, extension, shape, size, color, movement, rest;
Op 124a, on semen solidifying to form the embryo in seven
days (Hippocrates);
//end//