Alexander Polyhistor's existing writings are fragmentary and are often
cited from secondary or paraphrased sources. In addition to having
recorded the geographies of ancient Greek and Roman empires and
transcribing the writings of Hellenistic Jewish scholars that would
otherwise be lost, Alexander Polyhistor is recognized for his
interpretation of Pythagorean doctrines, all the while not being
officially recognized as a Pythagorean in written histories.
Alexander's writings on Pythagorean ideas address central doctrines:
the harmony of numbers as Unity and the ideal that the mathematical
world has primacy over, or can account for the existence of, the
physical world. Yet the often conflicting accounts of Pythagorean
concepts of numbers and Unity, the order giving rise to each, and
their relation to the concept of matter and the origin of the universe
make it difficult to determine with certainty how Alexander's
interpretation complements or embodies the varied lineages of the
Pythagorean thinkers. Nonetheless, Alexander Polyhistor's attempt at
reconciling these ideas is considered a concise and valuable remnant
of ancient Pythagorean thought, the importance of which still occupies
scholars.
1. Life
Lucius Cornelius Alexander Polyhistor was a Greek scholar, imprisoned
by the Romans in the war of Sulla against Mithridates of Pontus and
brought as a slave to Rome for employment as a tutor. After
Alexander's release he lived in Italy as a Roman citizen. He had
written so many books on philosophy, geography, and history, that he
received the name Polyhistor. The writings of Alexander are now lost;
only fragments exist, providing valuable information on antiquarian
and eastern Mediterranean subjects. Alexander's most important
treatise consisted of 42 books of historical and geographical accounts
of nearly all the countries of the ancient world. His other notable
work is about the Jews; it reproduces in paraphrase relevant excerpts
from Jewish writers, of whom otherwise nothing would be known. One of
Alexander's students was Gaius Julius Hyginus, Latin author, scholar
and friend of Ovid, who was appointed by Augustus to be superintendent
of the Palatine library.
2. Work
As a philosopher, Alexander Polyhistor had written Philosophers'
Successions, mentioned several times by Diogenes Laertius in his Lives
and Opinions of Eminent Philosophers [hereafter 'DL']. Usually
Diogenes used bio-bibliographical information from Alexander — on
Socrates, Plato, Carneades of Cyrene, Chrysippus of Soli, Pyrrho of
Elea, and others. There is also one passage about the Pythagoreans
[DL, VIII, 25-36], containing several thoughts (on contradictions,
fate, life, soul and its parts, perfect figures), and different
curiosities (do not eat beans, do not touch a white cock, and
similar). All these are of less importance.
3. Thought
Diogenes has preserved one extraordinarily interesting paraphrase of
Alexander Polyhistor, concerning the Pythagorean idea of numbers as
the elements of the universe:
The beginning of all is unity (monas); unity is a cause of
indefinite duality as a matter; both unity and indefinite duality are
sources of the numbers; the points are proceeding from numbers; the
lines – from the points; from the lines are plane figures; from plane
are volumetric figures; from them – sensibly acceptable solids, in
which four elements are – fire, water, earth, and air; moving and
changing totally, they give rise to the universe – inspired,
intelligent, spherical, in the middle of which is the earth; and the
earth is also spherical and inhabited from all sides. [DL, VIII, 25]
Here and elsewhere Alexander expounds Pythagorean doctrines. (It is
interesting to mention that Alexander states that he found all his
information in some Pythagorean notes, and an addition to these notes
made by Aristotle [DL, VIII, 36]). However, straight evaluation of
Alexander himself as a Pythagorean does not follow from the quote.
Also, the "catalogue of the Pythagoreans" by the Neo-Platonist
Iamblichus [On Pythagorean Life 267] includes 218 persons, but
Alexander's name is absent. Most likely, he was an erudite scholar,
well-informed of different philosophical schools. It is proved by his
nickname and his use of the genre of "successions of philosophers," as
well as references in other of Diogenes' books, unrelated to
Pythagoreanism.
The passage quoted above explains in its own way a harmonious
conception of some mathematical idealism. The physical world is
secondary with regard to the mathematical one. F.M. Cornford
considered this information to be related to the Old Pythagoreans. He
approved that the "original Pythagoreanism was monistic." He thought
that the Pythagoreans, from the very beginning, had taken unity as the
first principle of all. [Classical Quarterly, XXVII, 1933, p.104] This
seems to be in correspondence with the beginning of the fifth chapter
of the first book (A) of Aristotle's Metaphysics:
Contemporaneously with these philosophers, and even earlier, the
so-called Pythagoreans, who were the first to take up mathematics, not
only advanced this study, but also having been brought up in it, they
thought its principles were the principles of everything. Since of
these principles numbers are by nature the first, and in numbers they
seemed to see many resemblances to the things that exist and come into
being – more than in fire and earth and water … since, again, they saw
that the properties and the ratios of the musical scales were
expressible in numbers; – since, then, all other things seemed in
their whole nature to be modeled on numbers, and numbers seemed to be
the ultimate things in the whole of nature, they supposed the elements
of numbers to be the elements of everything, and the whole universe to
be a harmony (or proportion) and a number. [985b-986a]
Aristotle's explanation seems to contain some difficult inconsistency.
It is not one and the same to say that individual things "are
numbers," or the whole cosmos to be a number — because of difference
between the singularities and the universals. Further, different
sources sometimes ascribe to Pythagoreans the idea that things "are
numbers," or sometimes that they are "like numbers." Furthermore, it
is not so difficult to admit geometric figures or musical scales
depending on numbers; more difficult is to imagine, for example, a
fire made of numbers; and it is almost incomprehensible, how justice
(say) "was four." Indeed, the very Pythagorean doctrine of numbers was
full of contradictions. Were really "all things" (everything) numbers
— or only some of them? Were the things really numbers, or "like
numbers?" Were the numbers elements of the things, or "the elements of
numbers to be the elements of everything?" Were the things "made of
numbers," or "to be modeled on numbers," i.e. they were made
"according to numbers?" It is not so easy to reconcile such
discrepancy of ill-assorted opinions.
We have still to consider a view, also attributed to Pythagoreans,
that the First Principle (arkhe) is Unity (monas): "The beginning of
all is unity…" [DL, VIII, 25]. Late Pythagoreans erected altars and
temples for the Unity (i.e. One), and worshipped it as God. They
deified Unity, rather than numbers. A reason is that the numbers
themselves consist of, or originated from the units. But in what sense
did the Pythagoreans speak of the Unity as the First Principle — as a
unity of singular things? or hidden unity, being the basis of
everything? or the unity of opposites? and if so, then either opposite
philosophical categories (finite and infinite, one and many, rest and
motion, etc.), or opposing characteristics and qualities of singular
things (as, for example, white-black, sweet-bitter, and similar)? As
we can see, the Pythagorean concept of the Unity is no clearer than
their doctrine of numbers.
So, what was the First Principle? Was it the Number, or the Unity? It
is hard to see how the Pythagoreans could reconcile the two. If the
Number was the beginning of all, then we must regard the numbers as
resulting from the units; and, then, the Universe originated from the
Unity, rather than numbers. Even we could exclude numbers at all,
because any thing is some entire wholeness and a unit (not "two", or
"three", or "number"). Then, we have to consider the numbers as
secondary qualities or external characteristics of things, proceeding
from the Unity.
However, Pythagorean teaching of the Unity also maintains a
contradiction — between really existing things and some underlying,
invisible and 'mystical' Unity. So, singular things, gathered
together, become not a unity, but a plurality. If we want to dig
anything out of the depth of things, why was it unity, rather than
duality (say), or plurality again? Consequently, we accept a unity of
singular, finite, separate things in themselves (as "units") — but we
couldn't realize their unity as One (monas). Thus, the Pythagorean
principle of the Unity is inconsistent with the doctrine that things
are numbers.
There is no doubt, however, that the Pythagoreans asserted that
"things were like numbers", and this was the original doctrine, going
back to Pythagoras himself. Valuable comments are to be found in
W.K.C. Guthrie:
The earlier of them (i.e. the Pythagoreans) maintained, that the
"things were numbers." To demonstrate it they said: "Look! 1 is a
point, 2 a line, 3 a surface, and 4 a solid. Thus you have solid
bodies generated from numbers." We may call this an unwarrantable and
indeed incomprehensible leap from the abstract intellectual
conceptions of mathematics to the solid realities of nature. The
pyramid, which they have made of the number 4, is not a pyramid of
stone or wood, but non-material, a mere concept of the mind. Aristotle
was already too far removed from their mentality to understand it, and
complained that they "made weightless entities the elements of
entities which had weight." [Guthrie 1960, pp.14-15. Cf. Aristotle,
Metaphysics 1090a32-34]
Consequently, the above question — whether Pythagoreans acknowledged
as the First Principle the Number, or the Unity — we also have to
reconcile with matter. To understand the origin of the Universe, it is
necessary to explain how material things proceeded either from
(non-material) Number, or from (non-material) Unity, or how "entities
which had weight" originated from "weightless entities." It was an
irresolvable yet important problem for the whole Ancient philosophy.
The outstanding importance and exclusive difficulties of this problem
were stressed in Aristotle's criticism of theory of ideas and numbers
as independent entities and first principles of the things (in books
13 and 14 of Metaphysics). The final conclusion is that that to
explain the origin of numbers is tortuous, and it is impossible here
to make ends meet; thus, it gives evidence of impossibility — in spite
of Pythagorean statements — to separate mathematical objects from
sensibly acceptable things, and that they are not the First Principles
of these things. [Metaphysics 1093b25f.]
Perhaps a suitable historical approach to the question is the one
proposed by the famous Russian philosopher Alexey Losev, in his
Ancient Cosmos and Contemporary Science:
As it is known, the Neo-Pythagoreanism developed into two
different directions: the first didn't put forward the concept of the
number (Timaeus Locrus, Ocellos, Pseudo-Architos); the second
proceeded from the philosophy of number — here are the Pythagoreans
Alexander Polyhistor, and also Moderatus, Nichomachos, Numenius and
some others. The study of this second direction in the
Neo-Pythagoreanism is especially important for understanding of
Plotinus' (say, Neo-Platonic) teaching of matter. [Losev 1993, p. 464]
Thus, the main doctrine of Old Pythagoreanism was that of numbers as
the First Principles. The main difficulty of this doctrine was the
impossibility of explaining how material things originated from
non-material beginnings. Neo-Pythagoreanism divided into two streams;
and some Pythagoreans simply didn't put forward the concept of the
number; others strived to retain original doctrine of numbers,
arranging it with some teachings about matter, and thus moving toward
Neo-Platonism.
At last, we could consider the fragment of Polyhistor (quoted above)
as a quite successful attempt to reconcile Pythagorean concepts of the
unity, their doctrine of numbers as the beginning of all things, and
simultaneously to include matter in the Pythagorean explanation of the
origin of the sensibly acceptable world. It was a great deed, even
more amazing with regard to the fact that we haven't sufficient
grounds to consider Alexander Polyhistor himself exactly as
Pythagorean. In the same time, by his felicitous reconciliation of
main Pythagorean ideas — just in one paraphrase — Polyhistor provided
us with some integrated philosophical account of Pythagoreanism from
a doctrinal perspective, and perhaps he is, for this reason, a better
Pythagorean than Pythagoras himself. Generally speaking, from what we
know of Polyhistor's ideas, we could gather that this "unknown
philosopher" was an outstanding historian of philosophy, and an
important thinker of his era, somewhat along the lines of Posidonius.
Indeed, the almost absolute loss of his writings is one of the
irrecoverable and unbearable tragedies of the history of philosophy!
4. References and Further Reading
* Guthrie, W.K.C. The Greek Philosophers: From Thales to Aristotle
(New York: Evanston 1960)
* Losev, A.F. Ancient Cosmos and Contemporary Science in Being –
Name – Cosmos (Moscow: Thought 1993 – published in Russian)
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