THE PYTHAGOREANS
[Sidenote: The Pythagorean school.]
138. We have seen (§ 40) how the Pythagoreans, after losing their
supremacy at Kroton, concentrated themselves at Rhegion; but the school
founded there was soon broken up. Archippos stayed behind in Italy; but
Philolaos and Lysis, the latter of whom had escaped as a young man from
the massacre of Kroton, betook themselves to continental Hellas,
settling finally at Thebes. We know from Plato that Philolaos was there
some time during the latter part of the fifth century, and Lysis was
afterwards the teacher of Epameinondas.[732] Some of the Pythagoreans,
however, were able to return to Italy later on. Philolaos certainly did
so, and Plato implies that he had left Thebes some time before 399 B.C.,
the year in which Sokrates was put to death. In the fourth century, the
chief seat of the school is at Taras, and we find the Pythagoreans
heading the opposition to Dionysios of Syracuse. It is to this period
that Archytas belongs. He was the friend of Plato, and almost realised,
if he did not suggest, the ideal of the philosopher king. He ruled Taras
for years, and Aristoxenos tells us that he was never defeated in the
field of battle.[733] He was also the inventor of mathematical
mechanics. At the same time, Pythagoreanism had taken root in Hellas.
Lysis, we have seen, remained at Thebes, where Simmias and Kebes had
heard Philolaos, and there was an important community of Pythagoreans at
Phleious. Aristoxenos was personally acquainted with the last generation
of the school, and mentioned by name Xenophilos the Chalkidian from
Thrace, with Phanton, Echekrates, Diokles, and Polymnestos of Phleious.
They were all, he said, disciples of Philolaos and Eurytos.[734] Plato
was on friendly terms with these men, and dedicated the _Phaedo_ to
them.[735] Xenophilos was the teacher of Aristoxenos, and lived in
perfect health at Athens till the age of a hundred and five.[736]
Footnote 732:
For Philolaos, see Plato, _Phd._ 61 d 7; e 7; and for Lysis,
Aristoxenos in Iambl. _V. Pyth._ 250 (R. P. 59 b).
Footnote 733:
Diog. viii. 79-83 (R. P. 61). Aristoxenos himself came from Taras. For
the political activity of the Tarentine Pythagoreans, see Meyer,
_Gesch. des Alterth._ v. § 824. The story of Damon and Phintias (told
by Aristoxenos) belongs to this time.
Footnote 734:
Diog. viii. 46 (R. P. 62).
Footnote 735:
Compare the way in which the _Theaetetus_ is dedicated to the school
of Megara.
Footnote 736:
See Aristoxenos _ap._ Val. Max. viii. 13, ext. 3; and Souidas _s.v._
[Sidenote: Philolaos.]
139. This generation of the school really belongs, however, to a later
period, and cannot be profitably studied apart from Plato; it is with
their master Philolaos we have now to deal. The facts we know about his
teaching from external sources are few in number. The doxographers,
indeed, ascribe to him an elaborate theory of the planetary system, but
Aristotle never mentions his name in connexion with this. He gives it as
the theory of “the Pythagoreans” or of “some Pythagoreans.”[737] It
seems natural to suppose, however, that the Pythagorean elements of
Plato’s _Phaedo_ and _Gorgias_ come mainly from Philolaos. Plato makes
Sokrates express surprise that Simmias and Kebes had not learnt from him
why it is unlawful for a man to take his life,[738] and it seems to be
implied that the Pythagoreans at Thebes used the word “philosopher” in
the special sense of a man who is seeking to find a way of release from
the burden of this life.[739] It is extremely probable that Philolaos
spoke of the body (σῶμα) as the tomb (σῆμα) of the soul.[740] In any
case, we seem to be justified in holding that he taught the old
Pythagorean religious doctrine in some form, and it is likely that he
laid special stress upon knowledge as a means of release. That is the
impression we get from Plato, and he is by far the best authority we
have on the subject.
Footnote 737:
See below, § 150–152.
Footnote 738:
Plato, _Phd._ 61 d 6.
Footnote 739:
This appears to follow at once from the remark of Simmias in _Phd._ 64
b. The whole passage would be pointless if the words φιλόσοφος,
φιλοσοφεῖν, φιλοσοφία had not in some way become familiar to the
ordinary Theban of the fifth century. Now Herakleides Pontikos made
Pythagoras invent the word, and expound it in a conversation with
Leon, tyrant of Sikyon _or Phleious_. Cf. Diog. i. 12 (R. P. 3), viii.
8; Cic. _Tusc._ v. 3. 8; Döring in _Arch._ v. pp. 505 sqq. It seems to
me that the way in which the term is introduced in the _Phaedo_ is
fatal to the view that this is a Sokratic idea transferred by
Herakleides to the Pythagoreans. Cf. also the remark of Alkidamas
quoted by Arist. _Rhet._ Β, 23. 1398 b 18, Θήβησιν ἅμα οἱ προστάται
φιλόσοφοι ἐγένοντο καὶ εὐδαιμόνησεν ἡ πόλις.
Footnote 740:
For reasons which will appear, I do not attach importance in this
connexion to Philolaos, fr. 14 Diels = 23 Mullach (R. P. 89), but it
does seem likely that the μυθολογῶν κομψὸς ἀνήρ of _Gorg._ 493 a 5 (R.
P. 89 b) is responsible for the whole theory there given. He is
certainly, in any case, the author of the τετρημένος πίθος, which
implies the same general view. Now he is called ἴσως Σικελός τις ἢ
Ἰταλικός, which means he was an Italian; for the Σικελός τις is merely
an allusion to the Σικελὸς κομψὸς ἀνὴρ ποτὶ τὰν ματέρ’ ἔφα of
Timokreon. We do not know of any Italian from whom Plato could have
learnt these views except Philolaos or one of his disciples. They may,
however, be originally Orphic for all that (cf. R. P. 89 a).
We know further that Philolaos wrote on “numbers”; for Speusippos
followed him in the account he gave of the Pythagorean theories on that
subject.[741] It is probable that he busied himself mainly with
arithmetic, and we can hardly doubt that his geometry was of the
primitive type described in an earlier chapter. Eurytos was his
disciple, and we have seen (§ 47) that his views were still very crude.
Footnote 741:
See above, Chap. II. p. 113, _n._ 236.
We also know now that Philolaos wrote on medicine,[742] and that, while
apparently influenced by the theories of the Sicilian school, he opposed
them from the Pythagorean standpoint. In particular, he said that our
bodies were composed only of the warm, and did not participate in the
cold. It was only after birth that the cold was introduced by
respiration. The connexion of this with the old Pythagorean theory is
obvious. Just as the Fire in the macrocosm draws in and limits the cold
dark breath which surrounds the world (§ 53), so do our bodies inhale
cold breath from outside. Philolaos made bile, blood, and phlegm the
causes of disease; and, in accordance with the theory just mentioned, he
had to deny that the phlegm was cold, as the Sicilian school held it
was. Its etymology proved that it was warm. As Diels says, Philolaos
strikes us as an “uninteresting eclectic” so far as his medical views
are concerned.[743] We shall see, however, that it was just this
preoccupation with the medicine of the Sicilian school that gave rise to
some of the most striking developments of later Pythagoreanism.
Footnote 742:
It is a good illustration of the defective character of our tradition
(Introd. § XIII.) that this was quite unknown till the publication of
the extracts from Menon’s _Iatrika_ contained in the Anonymus
Londinensis. The extract referring to Philolaos is given and discussed
by Diels in _Hermes_, xxviii. pp. 417 sqq.
Footnote 743:
_Hermes_, _loc. cit._
[Sidenote: Plato and the Pythagoreans.]
140. Such, so far as we can see, was the historical Philolaos, and he is
a sufficiently remarkable figure. He is usually, however, represented in
a different light, and has even been spoken of as a “precursor of
Copernicus.” To understand this, we shall have to consider for a little
the story of what can only be called a literary conspiracy. Not till
this has been exposed will it be possible to estimate the real
importance of Philolaos and his immediate disciples.
As we can see from the _Phaedo_ and the _Gorgias_, Plato was intimate
with these men and was deeply impressed by their religious teaching,
though it is plain too that he did not adopt it as his own faith. He was
still more attracted by the scientific side of Pythagoreanism, and to
the last this exercised a great influence on him. His own system in its
final form had many points of contact with it, as he is careful to mark
in the _Philebus_.[744] But, just because he stood so near it, he is apt
to develop Pythagoreanism on lines of his own, which may or may not have
commended themselves to Archytas, but are no guide to the views of
Philolaos and Eurytos. He is not careful, however, to claim the
authorship of his own improvements in the system. He did not believe
that cosmology could be an exact science, and he is therefore quite
willing to credit Timaios the Lokrian, or “ancient sages” generally,
with theories which certainly had their birth in the Academy.
Footnote 744:
Plato, _Phileb._ 16 c sqq.
Now Plato had many enemies and detractors, and this literary device
enabled them to bring against him the charge of plagiarism. Aristoxenos
was one of these enemies, and we know he made the extraordinary
statement that most of the _Republic_ was to be found in a work by
Protagoras.[745] He seems also to be the original source of the story
that Plato bought “three Pythagorean books” from Philolaos and copied
the _Timaeus_ out of them. According to this, the “three books” had come
into the possession of Philolaos; and, as he had fallen into great
poverty, Dion was able to buy them from him, or from his relatives, at
Plato’s request, for a hundred _minae_.[746] It is certain, at any rate,
that this story was already current in the third century; for the
sillographer Timon of Phleious addresses Plato thus: “And of thee too,
Plato, did the desire of discipleship lay hold. For many pieces of
silver thou didst get in exchange a small book, and starting from it
didst learn to write _Timaeus_.”[747] Hermippos, the pupil of
Kallimachos, said that “some writer” said that Plato himself bought the
books from the relatives of Philolaos for forty Alexandrian _minae_ and
copied the _Timaeus_ out of it; while Satyros, the Aristarchean, says he
got it through Dion for a hundred _minae_.[748] There is no suggestion
in any of these accounts that the book was by Philolaos himself; they
imply rather that what Plato bought was either a book by Pythagoras, or
at any rate authentic notes of his teaching, which had come into the
hands of Philolaos. In later times, it was generally supposed that the
work entitled _The Soul of the World_, by Timaios the Lokrian, was
meant;[749] but it has now been proved beyond a doubt that this cannot
have existed earlier than the first century A.D. We know nothing of
Timaios except what Plato tells us himself, and he may even be a
fictitious character like the Eleatic Stranger. His name does not occur
among the Lokrians in the Catalogue of Pythagoreans preserved by
Iamblichos.[750] Besides this, the work does not fulfil the most
important requirement, that of being in three books, which is always an
essential feature of the story.[751]
Footnote 745:
Diog. iii. 37. For similar charges, cf. Zeller, _Plato_, p. 429, n. 7.
Footnote 746:
Iambl. _V. Pyth._ 199. Diels is clearly right in ascribing the story
to Aristoxenos (_Arch._ iii. p. 461, n. 26).
Footnote 747:
Timon _ap._ Gell. iii. 17 (R. P. 60 a).
Footnote 748:
For Hermippos and Satyros, see Diog. iii. 9; viii. 84, 85.
Footnote 749:
So Iambl. _in Nicom._ p. 105, 11; Proclus, _in Tim._ p. 1, Diehl.
Footnote 750:
Diels, _Vors._ p. 269.
Footnote 751:
They are τὰ θρυλούμενα τρία βιβλία (Iambl. _V. Pyth._ 199), τὰ
διαβόητα τρία βιβλία (Diog. viii. 15).
Not one of the writers just mentioned professes to have seen the famous
“three books”;[752] but at a later date there were at least two works
which claimed to represent them. Diels has shown how a treatise in three
sections, entitled Παιδευτικόν, πολιτικόν, φυσικόν, was composed in the
Ionic dialect and attributed to Pythagoras. It was largely based on the
Πυθαγορικαὶ ἀποφάσεις of Aristoxenos, but its date is uncertain.[753] In
the first century B.C., Demetrios Magnes was able to quote the opening
words of the work published by Philolaos.[754] That, however, was
written in Doric. Demetrios does not actually say it was by Philolaos
himself, though it is no doubt the same work from which a number of
extracts are preserved under his name in Stobaios and later writers. If
it professed to be by Philolaos, that was not quite in accordance with
the original story; but it is easy to see how his name may have become
attached to it. We are told that the other book which passed under the
name of Pythagoras was really by Lysis.[755] Boeckh has shown that the
work ascribed to Philolaos probably consisted of three books also, and
Proclus referred to it as the _Bakchai_,[756] a fanciful title which
recalls the “Muses” of Herodotos. Two of the extracts in Stobaios bear
it. It must be confessed that the whole story is very suspicious; but,
as some of the best authorities still regard the fragments as partly
genuine, it is necessary to look at them more closely.
Footnote 752:
As Mr. Bywater says (_J. Phil._ i. p. 29), the history of this work
“reads like the history, not so much of a book, as of a literary
_ignis fatuus_ floating before the minds of imaginative writers.”
Footnote 753:
Diels, “Ein gefälschtes Pythagorasbuch” (_Arch._ iii. pp. 451 sqq.).
Footnote 754:
Diog. viii. 85 (R. P. 63 b). Diels reads πρῶτον ἐκδοῦναι τῶν
Πυθαγορικῶν <βιβλία καὶ ἐπιγράψαι Περὶ> Φύσεως.
Footnote 755:
Diog. viii. 7.
Footnote 756:
Proclus, _in Eucl._ p. 22, 15 (Friedlein). Cf. Boeckh, _Philolaos_,
pp. 36 sqq. Boeckh refers to a sculptured group of _three_ Bakchai,
whom he supposes to be Ino, Agaue, and Autonoe.
[Sidenote: The “Fragments of Philolaos.”]
141. Boeckh argued with great learning and skill that all the fragments
preserved under the name of Philolaos were genuine; but no one will now
go so far as this. The lengthy extract on the soul is given up even by
those who maintain the genuineness of the rest.[757] It cannot be said
that this position is plausible on the face of it. Boeckh saw there was
no ground for supposing that there ever was more than a single work, and
he drew the conclusion that we must accept all the remains as genuine or
reject all as spurious.[758] As, however, Zeller and Diels still
maintain the genuineness of most of the fragments, we cannot ignore them
altogether. Arguments based, on the doctrine contained in them would, it
is true, present the appearance of a vicious circle at this stage. It is
only in connexion with our other evidence that these can be introduced.
But there are two serious objections to the fragments which may be
mentioned at once. They are sufficiently strong to justify us in
refusing to use them till we have ascertained from other sources what
doctrines may fairly be attributed to the Pythagoreans of this date.
Footnote 757:
The passage is given in R. P. 68. For a full discussion of this and
the other fragments, see Bywater, “On the Fragments attributed to
Philolaus the Pythagorean” (_J. Phil._ i. pp. 21 sqq.).
Footnote 758:
Boeckh, _Philolaos_, p. 38. Diels (_Vors._ p. 246) distinguishes the
_Bakchai_ from the three books Περὶ φύσιος (_ib._ p. 239). As,
however, he identifies the latter with the “three books” bought from
Philolaos, and regards it as genuine, this does not seriously affect
the argument.
In the first place, we must ask a question which has not yet been faced.
Is it likely that Philolaos should have written in Doric? Ionic was the
dialect of all science and philosophy till the time of the Peloponnesian
War, and there is no reason to suppose that the early Pythagoreans used
any other.[759] Pythagoras was himself an Ionian, and it is by no means
clear that in his time the Achaian states in which he founded his Order
had already adopted the Dorian dialect.[760] Alkmaion of Kroton seems to
have written in Ionic.[761] Diels says, it is true, that Philolaos and
then Archytas were the first Pythagoreans to use the dialect of their
homes;[762] but Philolaos can hardly be said to have had a home,[763]
and the fragments of Archytas are not written in the dialect of Taras,
but in what may be called “common Doric.” Archytas may have found it
convenient to use that dialect; but he is at least a generation later
than Philolaos, which makes a great difference. There is evidence that,
in the time of Philolaos and later, Ionic was still used even by the
citizens of Dorian states for scientific purposes. Diogenes of Apollonia
in Crete and the Syracusan historian Antiochos wrote in Ionic, while the
medical writers of Dorian, Kos and Knidos, continue to use the same
dialect. The forged work of Pythagoras referred to above, which some
ascribed to Lysis, was in Ionic; and so was the work on the _Akousmata_
attributed to Androkydes,[764] which shows that, even down to
Alexandrian times, it was still believed that Ionic was the proper
dialect for Pythagorean writings.
Footnote 759:
See Diels in _Arch._ iii. pp. 460 sqq.
Footnote 760:
On the Achaian dialect, see O. Hoffmann in Collitz and Bechtel,
_Dialekt-Inschriften_, vol. ii. p. 151. How slowly Doric penetrated
into the Chalkidian states may be seen from the mixed dialect of the
inscription of Mikythos of Rhegion (_Dial.-Inschr._ iii. 2, p. 498),
which is later than 468-67 B.C. There is no reason to suppose that the
Achaian dialect of Kroton was less tenacious of life.
Footnote 761:
The scanty fragments contain one Doric form, ἔχοντι (fr. 1), but
Alkmaion calls himself Κροτωνιήτης, which is very significant; for
Κροτωνιάτας is the Achaian as well as the Doric form. He did not,
therefore, write a mixed dialect like that referred to in the last
note. It seems safest to assume with Wachtler, _De Alcmaeone
Crotoniata_, pp. 21 sqq., that he used Ionic.
Footnote 762:
_Arch._ iii. p. 460.
Footnote 763:
He is distinctly called a Krotoniate in the extracts from Menon’s
Ἰατρικά (cf. Diog. viii. 84). It is true that Aristoxenos called him
and Eurytos Tarentines (Diog. viii. 46), but this only means that he
settled at Taras after leaving Thebes. These variations are common in
the case of migratory philosophers. Eurytos is also called a
Krotoniate and a Metapontine (Iambl. _V. Pyth._ 148, 266). Cf. also p.
380, _n._ 921 on Leukippos, and p. 406, _n._ 988 on Hippon.
Footnote 764:
For Androkydes, see Diels, _Vors._ p. 281. As Diels points out
(_Arch._ iii. p. 461), even Lucian has sufficient sense of style to
make Pythagoras speak Ionic.
In the second place, there can be no doubt that one of the fragments
refers to the five regular solids, four of which are identified with the
elements of Empedokles.[765] Now Plato gives us to understand, in a
well-known passage of the _Republic_, that stereometry had not been
adequately investigated at the time he wrote,[766] and we have express
testimony that the five “Platonic figures,” as they were called, were
discovered in the Academy. In the Scholia to Euclid we read that the
Pythagoreans only knew the cube, the pyramid (tetrahedron), and the
dodecahedron, while the octahedron and the icosahedron were discovered
by Theaitetos.[767] This sufficiently justifies us in regarding the
“fragments of Philolaos” with something more than suspicion. We shall
find more anachronisms as we go on.
Footnote 765:
Cf. fr. 12 = 20 M. (R. P. 79), τὰ ἐν τᾷ σφαίρᾳ σώματα πέντε ἐντί.
Footnote 766:
Plato, _Rep._ 528 b.
Footnote 767:
Heiberg’s Euclid, vol. v. p. 654, 1, Ἐν τούτῳ τῷ βιβλίῳ, τουτέστι τῷ
ιγ’, γράφεται τὰ λεγόμενα Πλάτωνος ε̄ σχήματα, ἃ αὐτοῦ μὲν οὐκ ἔστιν,
τρία δὲ τῶν προειρημένων ε̄ σχημάτων τῶν Πυθαγορείων ἐστίν, ὅ τε κύβος
καὶ ἡ πυραμὶς καὶ τὸ δωδεκάεδρον, Θεαιτήτου δὲ τό τε ὀκτάεδρον καὶ τὸ
εἰκοσάεδρον. It is no objection to this that, as Newbold points out
(_Arch._ xix. p. 204), the inscription of the dodecahedron is more
difficult than that of the octahedron and icosahedron. The
Pythagoreans were not confined to strict Euclidean methods. It may
further be noted that Tannery comes to a similar conclusion with
regard to the musical scale described in the fragment of Philolaos. He
says: “Il n’y a jamais eu, pour la division du tétracorde, une
tradition pythagoricienne; on ne peut pas avec sûreté remonter plus
haut que Platon ou qu’Archytas” (_Rev. de Philologie_, 1904, p. 244).
[Sidenote: The Problem.]
142. We must look, then, for other evidence. From what has been said, it
will be clear that we cannot safely take Plato as our guide to the
original meaning of the Pythagorean theory, though it is certainly from
him alone that we can learn to regard it sympathetically. Aristotle, on
the other hand, was quite out of sympathy with Pythagorean ways of
thinking, but took a great deal of pains to understand them. This was
just because they played so great a part in the philosophy of Plato and
his successors, and he had to make the relation of the two doctrines as
clear as he could to himself and his disciples. What we have to do,
then, is to interpret what Aristotle tells us in the spirit of Plato,
and then to consider how the doctrine we arrive at in this way is
related to the systems which had preceded it. It is a delicate
operation, no doubt, but it has been made much safer by recent
discoveries in the early history of mathematics and medicine.
Zeller has cleared the ground by eliminating the purely Platonic
elements which have crept into later accounts of the system. These are
of two kinds. First of all, we have genuine Academic formulae, such as
the identification of the Limit and the Unlimited with the One and the
Indeterminate Dyad;[768] and secondly, there is the Neoplatonic doctrine
which represents it as an opposition between God and Matter.[769] It is
not necessary to repeat Zeller’s arguments here, as no one will any
longer attribute these doctrines to the Pythagoreans of the fifth
century.
Footnote 768:
Aristotle says distinctly (_Met._ Α, 6. 987 b 25) that “to set up a
dyad instead of the unlimited regarded as one, and to make the
unlimited consist of the great and small, is distinctive of Plato.”
Zeller seems to make an unnecessary concession with regard to this
passage (p. 368, n. 2; Eng. trans. p. 396, n. 1).
Footnote 769:
Zeller, p. 369 sqq. (Eng. trans. p. 397 sqq.).
This simplifies the problem very considerably, but it is still extremely
difficult. According to Aristotle, the Pythagoreans said _Things are
numbers_, though that does not appear to be the doctrine of the
fragments of “Philolaos.” According to them, things _have_ number, which
make them knowable, while their real essence is something
unknowable.[770] That would be intelligible enough, but the formula that
things _are_ numbers seems meaningless. We have seen reason for
believing that it is due to Pythagoras himself (§ 52), though we did not
feel able to say very clearly what he meant by it. There is no such
doubt as to his school. Aristotle says they used the formula in a
cosmological sense. The world, according to them, was made of numbers in
the same sense as others had said it was made of “four roots” or
“innumerable seeds.” It will not do to dismiss this as mysticism.
Whatever we may think of Pythagoras, the Pythagoreans of the fifth
century were scientific men, and they must have meant something quite
definite. We shall, no doubt, have to say that they used the words
_Things are numbers_ in a somewhat non-natural sense, but there is no
difficulty in such a supposition. We have seen already how the friends
of Aristoxenos reinterpreted the old _Akousmata_ (§ 44). The
Pythagoreans had certainly a great veneration for the actual words of
the Master (αὐτὸς ἔφα); but such veneration is often accompanied by a
singular licence of interpretation. We shall start, then, from what
Aristotle tells us about the numbers.
Footnote 770:
For the doctrine of “Philolaos,” cf. fr. 1 = 2 Ch. (R. P. 64); and for
the unknowable ἐστὼ τῶν πραγμάτων, see fr. 3 = 4 Ch. (R. P. 67). It
has a suspicious resemblance to the later ὕλη, which Aristotle would
hardly have failed to note if he had ever seen the passage. He is
always on the lookout for anticipations of ὕλη.
[Sidenote: Aristotle on the Numbers.]
143. In the first place, Aristotle is quite decided in his opinion that
Pythagoreanism was intended to be a cosmological system like the others.
“Though the Pythagoreans,” he tells us, “made use of less obvious first
principles and elements than the rest, seeing that they did not derive
them from sensible objects, yet all their discussions and studies had
reference to nature alone. They describe the origin of the heavens, and
they observe the phenomena of its parts, all that happens to it and all
it does.”[771] They apply their first principles entirely to these
things, “agreeing apparently with the other natural philosophers in
holding that reality was just what could be perceived by the senses, and
is contained within the compass of the heavens,”[772] though “the first
principles and causes of which they made use were really adequate to
explain realities of a higher order than the sensible.”[773]
Footnote 771:
Arist. _Met._ Α, 8. 989 b 29 (R. P. 92 a).
Footnote 772:
Arist. _Met._ Α, 8. 990 a 3, ὁμολογοῦντες τοῖς ἄλλοις φυσιολόγοις ὅτι
τό γ’ ὂν τοῦτ’ ἐστὶν ὅσον αἰσθητόν ἐστὶ καὶ περιείληφεν ὁ καλούμενος
οὐρανός.
Footnote 773:
_Met. ib._ 990 a 5, τὰς δ’ αἰτίας καὶ τὰς ἀρχάς, ὥσπερ εἴπομεν, ἱκανὰς
λέγουσιν ἐπαναβῆναι καὶ ἐπὶ τὰ ἀνωτέρω τῶν ὄντων, καὶ μᾶλλον ἢ τοῖς
περὶ φύσεως λόγοις ἁρμοττούσας.
The doctrine is more precisely stated by Aristotle to be that the
elements of numbers are the elements of things, and that therefore
things are numbers.[774] He is equally positive that these “things” are
sensible things,[775] and indeed that they are bodies,[776] the bodies
of which the world is constructed.[777] This construction of the world
out of numbers was a real process in time, which the Pythagoreans
described in detail.[778]
Footnote 774:
_Met._ Α, 5. 986 a 1, τὰ τῶν ἀριθμῶν στοιχεῖα τῶν ὄντων στοιχεῖα
πάντων ὑπέλαβον εἶναι; Ν, 3. 1090 a 22, εἶναι μὲν ἀριθμοὺς ἐποίησαν τὰ
ὄντα, οὐ χωριστοὺς δέ, ἀλλ’ ἐξ ἀριθμῶν τὰ ὄντα.
Footnote 775:
_Met._ Μ, 6. 1080 b 2, ὡς ἐκ τῶν ἀριθμῶν ἐνυπαρχόντων ὄντα τὰ αἰσθητά;
_ib._ 1080 b 17, ἐκ τούτου (τοῦ μαθηματικοῦ ἀριθμοῦ) τὰς αἰσθητὰς
οὐσίας συνεστάναι φασίν.
Footnote 776:
_Met._ Μ, 8. 1083 b 11, τὰ σώματα ἐξ ἀριθμῶν εἶναι συγκείμενα; _ib._ b
17, ἐκεῖνοι δὲ τὸν ἀριθμὸν τὰ ὄντα λέγουσιν· τὰ γοῦν θεωρήματα
προσάπτουσι τοῖς σώμασιν ὡς ἐξ ἐκείνων ὄντων τῶν ἀριθμῶν; Ν, 3. 1090 a
32, κατὰ μέντοι τὸ ποιεῖν ἐξ ἀριθμῶν τὰ φυσικὰ σώματα, ἐκ μὴ ἐχόντων
βάρος μηδὲ κουφότητα ἔχοντα κουφότητα καὶ βάρος.
Footnote 777:
_Met._ Α, 5. 986 a 2, τὸν ὅλον οὐρανὸν ἁρμονίαν εἶναι καὶ ἀριθμόν; Α,
8. 990 a 21, τὸν ἀριθμὸν τοῦτον ἐξ οὗ συνέστηκεν ὁ κόσμος; Μ, 6. 1080
b 18, τὸν γὰρ ὅλον οὐρανὸν κατασκευάζουσιν ἐξ ἀριθμῶν; _de Caelo_, Γ,
1. 300 a 15, τοῖς ἐξ ἀριθμῶν συνιστᾶσι τὸν οὐρανόν· ἔνιοι γὰρ τὴν
φύσιν ἐξ ἀριθμῶν συνιστᾶσιν, ὥσπερ τῶν Πυθαγορείων τινές.
Footnote 778:
_Met._ Ν, 3. 1091 a 18, κοσμοποιοῦσι καὶ φυσικῶς βούλονται λέγειν.
Further, the numbers were intended to be mathematical numbers, though
they were not separated from the things of sense.[779] On the other
hand, they were not mere predicates of something else, but had an
independent reality of their own. “They did not hold that the limited
and the unlimited and the one were certain other substances, such as
fire, water, or anything else of that sort; but that the unlimited
itself and the one itself were the reality of the things of which they
are predicated, and that is why they said that number was the reality of
everything.”[780] Accordingly the numbers are, in Aristotle’s own
language, not only the formal, but also the material, cause of
things.[781] According to the Pythagoreans, things are made of numbers
in the same sense as they were made of fire, air, or water in the
theories of their predecessors.
Footnote 779:
_Met._ Μ, 6. 1080 b 16; Ν, 3. 1090 a 20.
Lastly, Aristotle notes that the point in which the Pythagoreans agreed
with Plato was in giving numbers an independent reality of their own;
while Plato differed from the Pythagoreans in holding that this reality
was distinguishable from that of sensible things.[782] Let us consider
these statements in detail.
Footnote 780:
Arist. _Met._ Α, 5. 987 a 15.
Footnote 781:
_Met. ib._ 986 a 15 (R. P. 66).
Footnote 782:
_Met._ Α, 6. 987 b 27, ὁ μὲν (Πλάτων) τοὺς ἀριθμοὺς παρὰ τὰ αἰσθητά,
οἱ δ’ (οἱ Πυθαγόρειοι) ἀριθμοὺς εἶναί φασιν αὐτὰ τὰ αἰσθητά.
[Sidenote: The elements of numbers.]
144. Aristotle speaks of certain “elements” (στοιχεῖα) of numbers, which
were also the elements of things. That, of course, is only his own way
of putting the matter; but it is clearly the key to the problem, if we
can discover what it means. Primarily, the “elements of number” are the
Odd and the Even, but that does not seem to help us much. We find,
however, that the Odd and Even were identified in a somewhat violent way
with the Limit and the Unlimited, which we have seen reason to regard as
the original principles of the Pythagorean cosmology. Aristotle tells us
that it is the Even which gives things their unlimited character when it
is contained in them and limited by the Odd,[783] and the commentators
are at one in understanding this to mean that the Even is in some way
the cause of infinite divisibility. They get into great difficulties,
however, when they try to show how this can be. Simplicius has preserved
an explanation, in all probability Alexander’s, to the effect that they
called the even number unlimited “because every even is divided into
equal parts, and what is divided into equal parts is unlimited in
respect of bipartition; for division into equals and halves goes on _ad
infinitum_. But, when the odd is added, it limits it; for it prevents
its division into equal parts.”[784] Now it is plain that we must not
impute to the Pythagoreans the view that even numbers can be halved
indefinitely. They had carefully studied the properties of the decad,
and they must have known that the even numbers 6 and 10 do not admit of
this. The explanation is really to be found in a fragment of
Aristoxenos, where we read that “even numbers are those which are
divided into equal parts, while odd numbers are divided into unequal
parts and have a middle term.”[785] This is still further elucidated by
a passage which is quoted in Stobaios and ultimately goes back to
Poseidonios. It runs: “When the odd is divided into two equal parts, a
unit is left over in the middle; but when the even is so divided, an
empty field is left, without a master and without a number, showing that
it is defective and incomplete.”[786] Again, Plutarch says: “In the
division of numbers, the even, when parted in any direction, leaves as
it were within itself ... a field; but, when the same thing is done to
the odd, there is always a middle left over from the division.”[787] It
is clear that all these passages refer to the same thing, and that can
hardly be anything else than those arrangements of “terms” in patterns
with which we are already familiar (§ 47). If we think of these, we
shall see in what sense it is true that bipartition goes on _ad
infinitum_. However high the number may be, the number of ways in which
it can be equally divided will also increase.
Footnote 783:
__Met.__ Α, 5. 986 a 17 (R. P. 66); _Phys._ Γ, 4. 203 a 10 (R. P. 66
a).
Footnote 784:
Simpl. _Phys._ p. 455, 20 (R. P. 66 a). I owe the passages which I
have used in illustration of this subject to W. A. Heidel, “Πέρας and
ἄπειρον in the Pythagorean Philosophy” (_Arch._ xiv. pp. 384 sqq.).
The general principle of my interpretation is also the same as his,
though I think that, by bringing the passage into connexion with the
numerical figures, I have avoided the necessity of regarding the words
ἡ γὰρ εἰς ἴσα καὶ ἡμίση διαίρεσις ἐπ’ ἄπειρον as “an attempted
elucidation added by Simplicius.”
Footnote 785:
Aristoxenos, fr. 81, _ap._ Stob. i. p. 20, 1, ἐκ τῶν Ἀριστοξένου Περὶ
ἀριθμητικῆς ... τῶν δὲ ἀριθμῶν ἄρτιοι μέν εἰσιν οἱ εἰς ἴσα
διαιρούμενοι, περισσοὶ δὲ οἱ εἰς ἄνισα καὶ μέσον ἔχοντες.
Footnote 786:
[Plut.] _ap._ Stob. i. p. 22, 19, καὶ μὴν εἰς δύο διαιρουμένων ἴσα τοῦ
μὲν περισσοῦ μονὰς ἐν μέσῳ περιέστι, τοῦ δὲ ἀρτίου κενὴ λείπεται χώρα
καὶ ἀδέσποτος καὶ ἀνάριθμος, ὡς ἂν ἐνδεοῦς καὶ ἀτελοῦς ὄντος.
Footnote 787:
Plut. _de E apud Delphos_, 388 a, ταῖς γὰρ εἰς ἴσα τομαῖς τῶν ἀριθμῶν,
ὁ μὲν ἄρτιος πάντῃ διϊστάμενος ὑπολείπει τινὰ δεκτικὴν ἀρχὴν οἷον ἐν
ἑαυτῷ καὶ χώραν, ἐν δὲ τῷ περιττῷ ταὐτὸ παθόντι μέσον ἀεὶ περίεστι τῆς
νεμήσεως γόνιμον. The words which I have omitted in translating refer
to the further identification of Odd and Even with Male and Female.
The passages quoted by Heidel might be added to. Cf., for instance,
what Nikomachos says (p. 13, 10, Hoche), ἔστι δὲ ἄρτιον μὲν ὃ οἷόν τε
εἰς δύο ἴσα διαιρεθῆναι μονάδος μέσον μὴ παρεμπιπτούσης, περιττὸν δὲ
τὸ μὴ δυνάμενον εἰς δύο ἴσα μερισθῆναι διὰ τὴν προειρημένην τῆς
μονάδος μεσιτείαν. He significantly adds that this definition is ἐκ
τῆς δημώδους ὑπολήψεως.
145. In this way, then, the Odd and the Even were identified with the
Limit and the Unlimited, and it is possible, though by no means certain,
that Pythagoras himself had taken this step. In any case, there can be
no doubt that by his Unlimited he meant something spatially extended,
and we have seen that he identified it with air, night, or the void, so
we are prepared to find that his followers also thought of the Unlimited
as extended. Aristotle certainly regarded it so. He argues that, if the
Unlimited is itself a reality, and not merely the predicate of some
other reality, then every part of it must be unlimited too, just as
every part of air is air.[788] The same thing is implied in his
statement that the Pythagorean Unlimited was outside the heavens.[789]
Further than this, it is hardly safe to go. Philolaos and his followers
cannot have regarded the Unlimited in the old Pythagorean way as Air;
for, as we shall see, they adopted the theory of Empedokles as to that
“element,” and accounted for it otherwise. On the other hand, they can
hardly have regarded it as an absolute void; for that conception was
introduced by the Atomists. It is enough to say that they meant by the
Unlimited the _res extensa_, without analysing that conception any
further.
Footnote 788:
Arist. _Phys._ Γ, 4. 204 a 20 sqq., especially a 26, ἀλλὰ μὴν ὥσπερ
ἀέρος ἀὴρ μέρος, οὕτω καὶ ἄπειρον ἀπείρου, εἴ γε οὐσία ἐστὶ καὶ ἀρχή.
Footnote 789:
See Chap. II. § 53.
As the Unlimited is spatial, the Limit must be spatial too, and we
should naturally expect to find that the point, the line, and the
surface were regarded as all forms of the Limit. That was the later
doctrine; but the characteristic feature of Pythagoreanism is just that
the point was not regarded as a limit, but as the first product of the
Limit and the Unlimited, and was identified with the arithmetical unit.
According to this view, then, the point has one dimension, the line two,
the surface three, and the solid four.[790] In other words, the
Pythagorean points have magnitude, their lines breadth, and their
surfaces thickness. The whole theory, in short, turns on the definition
of the point as a unit “having position.”[791] It was out of such
elements that it seemed possible to construct a world.
Footnote 790:
Cf. Speusippos in the extract preserved in the _Theologumena
arithmetica_, p. 61 (Diels, _Vors._ p. 235), τὸ μὴν γὰρ ᾱ στιγμή, τὸ
δὲ β̄ γραμμή, τὸ δὲ τρία τρίγωνον, τὸ δὲ δ̄ πυραμίς. We know that
Speusippos is following Philolaos here. Arist. _Met._ Ζ, 11. 1036 b
12, καὶ ἀνάγουσι πάντα εἰς τοὺς ἀριθμούς, καὶ γραμμῆς τὸν λόγον τὸν
τῶν δύο εἶναί φασιν. The matter is clearly put in the Scholia on
Euclid (p. 78, 19, Heiberg), οἱ δὲ Πυθαγόρειοι τὸ μὲν σημεῖον ἀνάλογον
ἐλάμβανον μονάδι, δυάδι δὲ τὴν γραμμήν, καὶ τριάδι τὸ ἐπίπεδον,
τετράδι δὲ τὸ σῶμα. καίτοι Ἀριστοτέλης τριαδικῶς προσεληλυθέναι φησὶ
τὸ σῶμα, ὡς διάστημα πρῶτον λαμβάνων τὴν γραμμήν.
Footnote 791:
The identification of the point with the unit is referred to by
Aristotle, _Phys._ Ε, 3. 227 a 27.
[Sidenote: The numbers as magnitudes.]
146. It is clear that this way of regarding the point, the line, and the
surface is closely bound up with the practice of representing numbers by
dots arranged in symmetrical patterns, which we have seen reason for
attributing to the Pythagoreans (§ 47). The science of geometry had
already made considerable advances, but the old view of quantity as a
sum of units had not been revised, and so a doctrine such as we have
indicated was inevitable. This is the true answer to Zeller’s contention
that to regard the Pythagorean numbers as spatial is to ignore the fact
that the doctrine was originally arithmetical rather than geometrical.
Our interpretation takes full account of that fact, and indeed makes the
peculiarities of the whole system depend upon it. Aristotle is very
decided as to the Pythagorean points having magnitude. “They construct
the whole world out of numbers,” he tells us, “but they suppose the
units have magnitude. As to how the first unit with magnitude arose,
they appear to be at a loss.”[792] Zeller holds that this is only an
inference of Aristotle’s,[793] and he is probably right in this sense,
that the Pythagoreans never felt the need of saying in so many words
that points had magnitude. It does seem probable, however, that they
called them ὄγκοι.[794]
Footnote 792:
Arist. _Met._ Μ, 6. 1080 b 18 sqq., 1083 b 8 sqq.; _de Caelo_, Γ, 1.
300 a 16 (R. P. 76 a).
Footnote 793:
Zeller, p. 381.
Footnote 794:
We learn from Plato, _Theaet._ 148 b 1, that Theaitetos called surds,
what Euclid calls δυνάμει σύμμετρα, by the name of δυνάμεις, while
rational square roots were called μήκη. Now in _Tim._ 31 c 4 we find a
division of numbers into ὄγκοι and δυνάμεις, which seem to mean
rational and irrational quantities. Cf. also the use of ὄγκοι in
_Parm._ 164 d. Zeno in his fourth argument about motion, which, we
shall see (§ 163), was directed against the Pythagoreans, used ὄγκοι
for points. Aetios, i. 3, 19 (R. P. 76 b), says that Ekphantos of
Syracuse was the first of the Pythagoreans to say that their units
were corporeal. Probably, however, “Ekphantos” was a personage in a
dialogue of Herakleides (Tannery, _Arch._ xi. pp. 263 sqq.), and
Herakleides called the monads ἄναρμοι ὄγκοι (Galen, _Hist. Phil._ 18;
_Dox._ p. 610).
Nor is Zeller’s other argument against the view that the Pythagorean
numbers were spatial any more inconsistent with the way in which we have
now stated it. He himself allows, and indeed insists, that in the
Pythagorean cosmology the numbers were spatial, but he raises
difficulties about the other parts of the system. There are other
things, such as the Soul and Justice and Opportunity, which are said to
be numbers, and which cannot be regarded as constructed of points,
lines, and surfaces.[795] Now it appears to me that this is just the
meaning of a passage in which Aristotle criticises the Pythagoreans.
They held, he says, that in one part of the world Opinion prevailed,
while a little above it or below it were to be found Injustice or
Separation or Mixture, each of which was, according to them, a number.
But in the very same regions of the heavens were to be found things
having magnitude which were also numbers. How can this be, since Justice
has no magnitude?[796] This means surely that the Pythagoreans had
failed to give any clear account of the relation between these more or
less fanciful analogies and their quasi-geometrical construction of the
universe. And this is, after all, really Zeller’s own view. He has shown
that in the Pythagorean cosmology the numbers were regarded as
spatial,[797] and he has also shown that the cosmology was the whole of
the system.[798] We have only to bring these two things together to
arrive at the interpretation given above.
Footnote 795:
Zeller, p. 382.
Footnote 796:
Arist. _Met._ Α, 8. 990 a 22 (R. P. 81 e). I read and interpret thus:
“For, seeing that, according to them, Opinion and Opportunity are in a
given part of the world, and a little above or below them Injustice
and Separation and Mixture,—in proof of which they allege that each of
these is a number,—and seeing that it is also the case (reading
συμβαίνῃ with Bonitz) that there is already in that part of the world
a number of composite magnitudes (_i.e._ composed of the Limit and the
Unlimited), because those affections (of number) are attached to their
respective regions;—(seeing that they hold these two things), the
question arises whether the number which we are to understand each of
these things (Opinion, etc.) to be is the same as the number in the
world (_i.e._ the cosmological number) or a different one.” I cannot
doubt that these are the extended numbers which are composed
(συνίσταται) of the elements of number, the limited and the unlimited,
or, as Aristotle here says, the “affections of number,” the odd and
the even. Zeller’s view that “celestial bodies” are meant comes near
this, but the application is too narrow. Nor is it the number (πλῆθος)
of those bodies that is in question, but their magnitude (μέγεθος).
For other views of the passage, see Zeller, p. 391, n. 1.
Footnote 797:
Zeller, p. 404.
Footnote 798:
_Ibid._ pp. 467 sqq.
[Sidenote: The numbers and the elements.]
147. When we come to details, we seem to see that what distinguished the
Pythagoreanism of this period from its earlier form was that it sought
to adapt itself to the new theory of “elements.” It is just this which
makes it necessary for us to take up the consideration of the system
once more in connexion with the pluralists. When the Pythagoreans
returned to Southern Italy, they must have found views prevalent there
which imperatively demanded a partial reconstruction of their own
system. We do not know that Empedokles founded a philosophical society,
but there can be no doubt of his influence on the medical school of
these regions; and we also know now that Philolaos played a part in the
history of medicine.[799] This discovery gives us the clue to the
historical connexion, which formerly seemed obscure. The tradition is
that the Pythagoreans explained the elements as built up of geometrical
figures, a theory which we can study for ourselves in the more developed
form which it attained in Plato’s _Timaeus_.[800] If they were to retain
their position as the leaders of medical study in Italy, they were bound
to account for the elements.
Footnote 799:
All this has been put in its true light by the publication of the
extract from Menon’s Ἰατρικά, on which see p. 322, _n._ 742.
Footnote 800:
In Aet. ii. 6, 5 (R. P. 80) the theory is ascribed to Pythagoras,
which is an anachronism, as the mention of “elements” shows it must be
later than Empedokles. In his extract from the same source, Achilles
says οἱ Πυθαγόρειοι, which doubtless represents Theophrastos better.
There is a fragment of “Philolaos” bearing on the subject (R. P. 79),
where the regular solids must be meant by τὰ ἐν τᾷ σφαίρᾳ σώματα.
We must not take it for granted, however, that the Pythagorean
construction of the elements was exactly the same as that which we find
in Plato’s _Timaeus_. It has been mentioned already that there is good
reason for believing they only knew three of the regular solids, the
cube, the pyramid (tetrahedron), and the dodecahedron.[801] Now it is
very significant that Plato starts from fire and earth,[802] and in the
construction of the elements proceeds in such a way that the octahedron
and the icosahedron can easily be transformed into pyramids, while the
cube and the dodecahedron cannot. From this it follows that, while air
and water pass readily into fire, earth cannot do so,[803] and the
dodecahedron is reserved for another purpose, which we shall consider
presently. This would exactly suit the Pythagorean system; for it would
leave room for a dualism of the kind outlined in the Second Part of the
poem of Parmenides. We know that Hippasos made Fire the first principle,
and we see from the _Timaeus_ how it would be possible to represent air
and water as forms of fire. The other element is, however, earth, not
air, as we have seen reason to believe that it was in early
Pythagoreanism. That would be a natural result of the discovery of
atmospheric air by Empedokles and of his general theory of the elements.
It would also explain the puzzling fact, which we had to leave
unexplained above, that Aristotle identifies the two “forms” spoken of
by Parmenides with Fire and Earth.[804] All this is, of course,
problematical; but it will not be found easy to account otherwise for
the facts.
Footnote 801:
See above, p. 329, _n._ 767.
Footnote 802:
Plato, _Tim._ 31 b 5.
Footnote 803:
Plato, _Tim._ 54 c 4. It is to be observed that in _Tim._ 48 b 5 Plato
says of the construction of the elements οὐδείς πω γένεσιν αὐτῶν
μεμήνυκεν, which implies that there is some novelty in the theory as
he makes Timaios state it. If we read the passage in the light of what
has been said in § 141, we shall be inclined to believe that Plato is
working out the Pythagorean doctrine on the lines of the discovery of
Theaitetos. There is another indication of the same thing in Arist.
_Gen. Corr._ Β, 3. 330 b 16, where we are told that, in the
Διαιρέσεις, Plato assumed three elements, but made the middle one a
mixture. This is stated in close connexion with the ascription of Fire
and Earth to Parmenides.
Footnote 804:
See above, Chap. IV. p. 213, _n._ 462.
[Sidenote: The dodecahedron.]
148. The most interesting point in the theory is, perhaps, the use made
of the dodecahedron. It was identified, we are told, with the “sphere of
the universe,” or, as it is put in the Philolaic fragment, with the
“hull of the sphere.”[805] Whatever we may think of the authenticity of
the fragments, there is no reason to doubt that this is a genuine
Pythagorean expression, and it must be taken in close connexion with the
word “keel” applied to the central fire.[806] The structure of the world
was compared to the building of a ship, an idea of which there are other
traces.[807] The key to what we are told of the dodecahedron is given by
Plato. In the _Phaedo_ we read that the “true earth,” if looked at from
above, is “many-coloured like the balls that are made of twelve pieces
of leather.”[808] In the _Timaeus_ the same thing is referred to in
these words: “Further, as there is still one construction left, the
fifth, God made use of it for the universe when he painted it.”[809] The
point is that the dodecahedron approaches more nearly to the sphere than
any other of the regular solids. The twelve pieces of leather used to
make a ball would all be regular pentagons; and, if the material were
not flexible like leather, we should have a dodecahedron instead of a
sphere. This points to the Pythagoreans having had at least the
rudiments of the “method of exhaustion” formulated later by Eudoxos.
They must have studied the properties of circles by means of inscribed
polygons and those of spheres by means of inscribed solids.[810] That
gives us a high idea of their mathematical attainments; but that it is
not too high, is shown by the fact that the famous lunules of
Hippokrates date from the middle of the fifth century. The inclusion of
_straight_ and _curved_ in the “table of opposites” under the head of
Limit and Unlimited points in the same direction.[811]
Footnote 805:
Aet. ii. 6, 5 (R. P. 80); “Philolaos,” fr. 12 (= 20 M.; R. P. 79). On
the ὁλκάς, see Gundermann in _Rhein. Mus._ 1904, pp. 145 sqq. I agree
with him in holding that the reading is sound, and that the word means
“ship,” but I think that it is the structure, not the motion, of a
ship which is the point of comparison.
Footnote 806:
Aet. ii. 4, 15, ὅπερ τρόπεως δίκην προϋπεβάλετο τῇ τοῦ παντὸς <σφαίρᾳ>
ὁ δημιουργὸς θεός.
Footnote 807:
Cf. the ὑποζώματα of Plato, _Rep._ 616 c 3. As ὕλη generally means
“timber” for shipbuilding (when it does not mean firewood), I suggest
that we should look in this direction for an explanation of the
technical use of the word in later philosophy. Cf. Plato, _Phileb._ 54
c 1, γενέσεως ... ἕνεκα ... πᾶσαν ὕλην παρατίθεσθαι πᾶσιν, which is
part of the answer to the question πότερα πλοίων ναυπηγίαν ἕνεκα φῂς
γίγνεσθαι μᾶλλον ἢ πλοῖα ἕνεκα ναυπηγίας; (_ib._ b 2); _Tim._ 69 a 6,
οἷα τέκτοσιν ἡμῖν ὕλη παράκειται.
Footnote 808:
Plato, _Phd._ 110 b 6, ὥσπερ οἱ δωδεκάσκυτοι σφαῖραι with Wyttenbach’s
note.
Footnote 809:
Plato, _Tim._ 55 c 4. Neither this passage nor the last can refer to
the Zodiac, which would be described by a dodecagon, not a
dodecahedron. What is implied is the division of the heavens into
twelve pentagonal fields.
Footnote 810:
Gow, _Short History of Greek Mathematics_, pp. 164 sqq.
Footnote 811:
This is pointed out by Kinkel, _Gesch. der Phil._ vol. i. p. 121.
The tradition confirms in an interesting way the importance of the
dodecahedron in the Pythagorean system. According to one account,
Hippasos was drowned at sea for revealing its construction and claiming
the discovery as his own.[812] What that construction was, we may
partially infer from the fact that the Pythagoreans adopted the
pentagram or _pentalpha_ as their symbol. The use of this figure in
later magic is well known; and Paracelsus still employed it as a symbol
of health, which is exactly what the Pythagoreans called it.[813]
Footnote 812:
Iambl. _V. Pyth._ 247. Cf. above, Chap. II. p. 117, _n._ 247.
Footnote 813:
See Gow, _Short History of Greek Mathematics_, p. 151, and the
passages there referred to, adding Schol. Luc. p. 234, 21, Rabe, τὸ
πεντάγραμμον] ὅτι τὸ ἐν τῇ συνθείᾳ λεγόμενον πένταλφα σύμβολον ἦν πρὸς
ἀλλήλους Πυθαγορείων ἀναγνωριστικὸν καὶ τούτῳ ἐν ταῖς ἐπιστολαῖς
ἐχρῶντο.
[Sidenote: The Soul a “Harmony.”]
149. The view that the soul is a “harmony,” or rather an attunement, is
intimately connected with the theory of the four elements. It cannot
have belonged to the earliest form of Pythagoreanism; for, as shown in
Plato’s _Phaedo_, it is quite inconsistent with the idea that the soul
can exist independently of the body. It is the very opposite of the
belief that “any soul can enter any body.”[814] On the other hand, we
know also from the _Phaedo_ that it was accepted by Simmias and Kebes,
who had heard Philolaos at Thebes, and by Echekrates of Phleious, who
was the disciple of Philolaos and Eurytos.[815] The account of the
doctrine given by Plato is quite in accordance with the view that it was
of medical origin. Simmias says: “Our body being, as it were, strung and
held together by the warm and the cold, the dry and the moist, and
things of that sort, our soul is a sort of temperament and attunement of
these, when they are mingled with one another well and in due
proportion. If, then, our soul is an attunement, it is clear that, when
the body has been relaxed or strung up out of measure by diseases and
other ills, the soul must necessarily perish at once.”[816] This is
clearly an application of the theory of Alkmaion (§ 96), and is in
accordance with the views of the Sicilian school of medicine. It
completes the evidence that the Pythagoreanism of the end of the fifth
century was an adaptation of the old doctrine to the new principles
introduced by Empedokles.
Footnote 814:
Arist. _de An._ Α, 3. 407 b 20 (R. P. 86 c).
Footnote 815:
Plato, _Phd._ 85 e sqq.; and for Echekrates, _ib._ 88 d.
Footnote 816:
Plato, _Phd._ 86 b 7-c 5.
[Sidenote: The central fire.]
150. The planetary system which Aristotle attributes to “the
Pythagoreans” and Aetios to Philolaos is sufficiently remarkable.[817]
The earth is no longer in the middle of the world; its place is taken by
a central fire, which is not to be identified with the sun. Round this
fire revolve ten bodies. First comes the _Antichthon_ or Counter-earth,
and next the earth, which thus becomes one of the planets. After the
earth comes the moon, then the sun, the five planets, and the heaven of
the fixed stars. We do not see the central fire and the _antichthon_
because the side of the earth on which we live is always turned away
from them. This is to be explained by the analogy of the moon. That body
always presents the same face to us; and men living on the other side of
it would never see the earth. This implies, of course, that all these
bodies rotate on their axes in the same time as they revolve round the
central fire.[818]
Footnote 817:
For the authorities, see R. P. 81-83. The attribution of the theory to
Philolaos is perhaps due to Poseidonios. The “three books” were
doubtless in existence by his time.
Footnote 818:
Plato attributes an axial rotation to the heavenly bodies (_Tim._ 40 a
7), which must be of this kind. It is quite likely that the
Pythagoreans already did so, though Aristotle was unable to see the
point. He says (_de Caelo_, Β, 8. 290 a 24), ἀλλὰ μὴν ὅτι οὐδὲ
κυλίεται τὰ ἄστρα, φανερόν· τὸ μὲν γὰρ κυλιόμενον στρέφεσθαι ἀνάγκη,
τῆς δὲ σελήνης ἀεὶ δηλόν ἐστι τὸ καλούμενον πρόσωπον. This, of course,
is just what proves it does rotate.
It is not very easy to accept the view that this system was taught by
Philolaos. Aristotle nowhere mentions him in connexion with it, and in
the _Phaedo_ Plato gives a description of the earth and its position in
the world which is entirely opposed to it, but is accepted without demur
by Simmias the disciple of Philolaos.[819] It is undoubtedly a
Pythagorean theory, however, and marks a noticeable advance on the
Ionian views then current at Athens. It is clear too that Plato states
it as something of a novelty that the earth does not require the support
of air or anything of the sort to keep it in its place. Even Anaxagoras
had not been able to shake himself free of that idea, and Demokritos
still held it.[820] The natural inference from the _Phaedo_ would
certainly be that the theory of a spherical earth, kept in the middle of
the world by its equilibrium, was that of Philolaos himself. If so, the
doctrine of the central fire would belong to a somewhat later generation
of the school, and Plato may have learnt it from Archytas and his
friends after he had written the _Phaedo_. However that may be, it is of
such importance that it cannot be omitted here.
Footnote 819:
Plato, _Phd._ 108 e 4 sqq. Simmias assents to this doctrine in the
emphatic words Καὶ ὀρθῶς γε.
Footnote 820:
The primitive character of the astronomy taught by Demokritos as
compared with that of Plato is the best evidence of the value of the
Pythagorean researches.
It is commonly supposed that the revolution of the earth round the
central fire was intended to account for the alternation of day and
night, and it is clear that an orbital motion of the kind just described
would have the same effect as the rotation of the earth on its axis. As
the same side of the earth is always turned to the central fire, the
side upon which we live will be turned towards the sun when the earth is
on the same side of the central fire, and turned away from it when the
earth and sun are on opposite sides. This view appears to derive some
support from the statement of Aristotle that the earth “being in motion
round the centre, produces day and night.”[821] That remark, however,
would prove too much; for in the _Timaeus_ Plato calls the earth “the
guardian and artificer of night and day,” while at the same time he
declares that the alternation of day and night is caused by the diurnal
revolution of the heavens.[822] That is explained, no doubt quite
rightly, by saying that, even if the earth were regarded as at rest, it
could still be said to produce day and night; for night is due to the
intervention of the earth between the sun and the hemisphere opposite to
it. If we remember how recent was the discovery that night was the
shadow of the earth, we shall see how it may have been worth while to
say this explicitly.
Footnote 821:
Arist. _de Caelo_, Β, 13. 293 a 18 sqq. (R. P. 83).
Footnote 822:
Plato, _Tim._ 40 c 1, (γῆν) φύλακα καὶ δημιουργὸν νυκτός τε καὶ ἡμέρας
ἐμηχανήσατο. On the other hand, νὺξ μὲν οὖν ἡμέρα τε γέγονεν οὕτως καὶ
διὰ ταῦτα, ἡ τῆς μιᾶς καὶ φρονιμωτάτης κυκλήσεως περίοδος (39 c 1).
In any case, it is wholly incredible that the heaven of the fixed stars
should have been regarded as stationary. That would have been the most
startling paradox that any scientific man had yet propounded, and we
should have expected the comic poets and popular literature generally to
raise the cry of atheism at once. Above all, we should have expected
Aristotle to say something about it. He made the circular motion of the
heavens the very keystone of his system, and would have regarded the
theory of a stationary heaven as blasphemous. Now he argues against
those who, like the Pythagoreans and Plato, regarded the earth as in
motion;[823] but he does not attribute the view that the heavens are
stationary to any one. There is no necessary connexion between the two
ideas. All the heavenly bodies may be moving as rapidly as we please,
provided that their relative motions are such as to account for the
phenomena.[824]
Footnote 823:
Arist. _de Caelo_, Β, 13. 293 b 15 sqq.
Footnote 824:
Boeckh admitted a very slow motion of the heaven of the fixed stars,
which he at first supposed to account for the precession of the
equinoxes, though he afterwards abandoned that hypothesis
(_Untersuchungen_, p. 93). But, as Dreyer admits (_Planetary Systems_,
p. 49), it is “not ... necessary with Boeckh to suppose the motion of
the starry sphere to have been an exceedingly slow one, as it might in
any case escape direct observation.”
It seems probable that the theory of the earth’s revolution round the
central fire really originated in the account given by Empedokles of the
sun’s light. The two things are brought into close connexion by Aetios,
who says that Empedokles believed in two suns, while Philolaos believed
in two or even in three.[825] The theory of Empedokles is unsatisfactory
in so far as it gives two inconsistent explanations of night. It is, we
have seen, the shadow of the earth; but at the same time Empedokles
recognised a fiery diurnal hemisphere and a nocturnal hemisphere with
only a little fire in it.[826] All this could be simplified by the
hypothesis of a central fire which is the true source of light. Such a
theory would, in fact, be the natural issue of the recent discoveries as
to the moon’s light and the cause of eclipses, if that theory were
extended so as to include the sun.
Footnote 825:
Aet. ii. 20, 13 (Chap. IV. p. 275, _n._ 609); cf. _ib._ 12 (of
Philolaos), ὥστε τρόπον τινὰ διττοὺς ἡλίους γίγνεσθαι, τό τε ἐν τῷ
οὐρανῷ πυρῶδες καὶ τὸ ἀπ’ αὐτοῦ πυροειδὲς κατὰ τὸ ἐσοπτροειδές· εἰ μή
τις καὶ τρίτον λέξει τὴν ἀπὸ τοῦ ἐνόπτρου κατ’ ἀνάκλασιν
διασπειρομένην πρὸς ἡμᾶς αὐγήν. Here τὸ ἐν τῷ οὐρανῷ πυρῶδες is the
central fire, in accordance with the use of the word οὐρανός explained
in another passage of Aetios, Stob. _Ecl._ i. p. 196, 18 (R. P. 81).
It seems to me that these strange notices must be fragments of an
attempt to show how the heliocentric hypothesis arose from the theory
of Empedokles as to the sun’s light. The meaning is that the central
fire really was the sun, but that Philolaos unnecessarily duplicated
it by supposing the visible sun to be its reflexion.
Footnote 826:
Chap. VI. § 113.
The central fire received a number of mythological names. It was called
the Hestia or “hearth of the universe,” the “house” or “watch-tower” of
Zeus, and the “mother of the gods.”[827] That was in the manner of the
school; but these names must not blind us to the fact that we are
dealing with a real scientific hypothesis. It was a great thing to see
that the phenomena could best be “saved” by a central luminary, and that
the earth must therefore be a revolving sphere like the planets. Indeed,
we are almost tempted to say that the identification of the central fire
with the sun, which was suggested for the first time in the Academy, is
a mere detail in comparison. The great thing was that the earth should
definitely take its place among the planets; for once it has done so, we
can proceed to search for the true “hearth” of the planetary system at
our leisure. It is probable, at any rate, that it was this theory which
made it possible for Herakleides of Pontos and Aristarchos of Samos to
reach the heliocentric hypothesis,[828] and it was certainly Aristotle’s
reversion to the geocentric theory which made it necessary for
Copernicus to discover the truth afresh. We have his own word for it
that the Pythagorean theory put him on the right track.[829]
Footnote 827:
Aet. i. 7, 7 (R. P. 81). Procl. _in Tim._ p. 106, 22, Diehl (R. P. 83
e).
Footnote 828:
On these points, see Staigmüller, _Beiträge zur Gesch. der
Naturwissenschaften im klassichen Altertume_ (Progr., Stuttgart,
1899); and “Herakleides Pontikos und das heliokentrische System”
(_Arch._ xv. pp. 141 sqq.). Though, for reasons which will partly
appear from the following pages, I should not put the matter exactly
as Staigmüller does, I have no doubt that he is substantially right.
Diels had already expressed his adhesion to the view that Herakleides
was the real author of the heliocentric hypothesis (_Berl. Sitzb._,
1893, P. 18).
Footnote 829:
In his letter to Pope Paul III., Copernicus quotes Plut. _Plac._ iii.
13, 2-3 (R. P. 83 a), and adds “Inde igitur occasionem nactus, coepi
et ego de terrae mobilitate cogitare.” The whole passage is
paraphrased by Dreyer, _Planetary Systems_, p. 311. Cf. also the
passage from the original MS., which was first printed in the edition
of 1873, translated by Dreyer, _ib._ pp. 314 sqq.
[Sidenote: The _antichthon_.]
151. The existence of the _antichthon_ was also a hypothesis intended to
account for the phenomena of eclipses. In one place, indeed, Aristotle
says that the Pythagoreans invented it in order to bring the number of
revolving bodies up to ten;[830] but that is a mere sally, and Aristotle
really knew better. In his work on the Pythagoreans, we are told, he
said that eclipses of the moon were caused sometimes by the intervention
of the earth and sometimes by that of the _antichthon_; and the same
statement was made by Philip of Opous, a very competent authority on the
matter.[831] Indeed, Aristotle shows in another passage exactly how the
theory originated. He tells us that some thought there might be a
considerable number of bodies revolving round the centre, though
invisible to us because of the intervention of the earth, and that they
accounted in this way for there being more eclipses of the moon than of
the sun.[832] This is mentioned in close connexion with the
_antichthon_, so there is no doubt that Aristotle regarded the two
hypotheses as of the same nature. The history of the theory seems to be
this. Anaximenes had assumed the existence of dark planets to account
for the frequency of lunar eclipses (§ 29), and Anaxagoras had revived
that view (§ 135). Certain Pythagoreans[833] had placed these dark
planets between the earth and the central fire in order to account for
their invisibility, and the next stage was to reduce them to a single
body. Here again we see how the Pythagoreans tried to simplify the
hypotheses of their predecessors.
Footnote 830:
Arist. _Met._ Α, 5. 986 a 3 (R. P. 83 b).
Footnote 831:
Aet. ii. 29, 4, τῶν Πυθαγορείων τινὲς κατὰ τὴν Ἀριστοτέλειον ἱστορίαν
καὶ τὴν Φιλίππου τοῦ Ὀπουντίου ἀπόφασιν ἀνταυγείᾳ καὶ ἀντιφράξει τοτὲ
μὲν τῆς γῆς, τοτὲ δὲ τῆς ἀντίχθονος (ἐκλείπειν τὴν σελήνην).
Footnote 832:
Arist. _de Caelo_, Β, 13. 293 b 21, ἐνίοις δὲ δοκεῖ καὶ πλείω σώματα
τοιαῦτα ἐνδέχεσθαι φέρεσθαι περὶ τὸ μέσον ἡμῖν ἄδηλα διὰ τὴν
ἐπιπρόσθησιν τῆς γῆς. διὸ καὶ τὰς τῆς σελήνης ἐκλείψεις πλείους ἢ τὰς
τοῦ ἡλίου γίγνεσθαί φασιν· τῶν γὰρ φερομένων ἕκαστον ἀντιφράττειν
αὐτήν, ἀλλ’ οὐ μόνον τὴν γῆν.
Footnote 833:
It is not expressly stated that they were Pythagoreans, but it is
natural to suppose so. Such, at least, was Alexander’s opinion (Simpl.
_de Caelo_, P. 515, 25).
[Sidenote: Planetary motions.]
152. We must not assume that even the later Pythagoreans made the sun,
moon, and planets, including the earth, revolve in the opposite
direction to the heaven of the fixed stars. It is true that Alkmaion is
said to have agreed with “some of the mathematicians”[834] in holding
this view, but it is never ascribed to Pythagoras or even to Philolaos.
The old theory was, as we have seen (§ 54), that all the heavenly bodies
revolved in the same direction, from east to west, but that the planets
revolved more slowly the further they were removed from the heavens, so
that those which are nearest the earth are “overtaken” by those that are
further away. This view was still maintained by Demokritos, and that it
was also Pythagorean, seems to follow from what we are told about the
“harmony of the spheres.” We have seen (§ 54) that we cannot attribute
this theory in its later form to the Pythagoreans of the fifth century,
but we have the express testimony of Aristotle to the fact that those
Pythagoreans whose doctrine he knew believed that the heavenly bodies
produced musical notes in their courses. Further, the velocities of
these bodies depended on the distances between them, and these
corresponded to the intervals of the octave. He distinctly implies that
the heaven of the fixed stars takes part in the concert; for he mentions
“the sun, the moon, and the stars, so great in magnitude and in number
as they are,” a phrase which cannot refer solely or chiefly to the
remaining five planets.[835] Further, we are told that the slower bodies
give out a deep note and the swifter a high note.[836] Now the
prevailing tradition gives the high note of the octave to the heaven of
the fixed stars,[837] from which it follows that all the heavenly bodies
revolve in the same direction, and that their velocity increases in
proportion to their distance from the centre.
Footnote 834:
The term οἱ μαθηματικοί is that used by Poseidonios for the Chaldæan
astrologers (Berossos). Diels, _Elementum_, p. 11, n. 3. As we have
seen, the Babylonians knew the planets better than the Greeks.
Footnote 835:
Arist. _de Caelo_, Β, 9. 290 b 12 sqq. (R. P. 82).
Footnote 836:
Alexander, _in Met._ p. 39, 24 (from Aristotle’s work on the
Pythagoreans), τῶν γὰρ σωμάτων τῶν περὶ τὸ μέσον φερομένων ἐν ἀναλογίᾳ
τὰς ἀποστάσεις ἐχόντων ... ποιούντων δὲ καὶ ψόφον ἐν τῷ κινεῖσθαι τῶν
μὲν βραδυτέρων βαρύν, τῶν δὲ ταχυτέρων ὀξύν. We must not attribute the
identification of the seven planets with the seven strings of the
heptachord to the Pythagoreans of this date. Mercury and Venus have in
the long run the same velocity as the sun, and we must take in the
earth and the fixed stars. We can even find room for the _antichthon_
as προσλαμβανόμενος.
Footnote 837:
For the various systems, see Boeckh, _Kleine Schriften_, vol. iii. pp.
169 sqq., and Carl v. Jan, “Die Harmonie der Sphären” (_Philol._ 1893,
pp. 13 sqq.). They vary with the astronomy of their authors, but they
bear witness to the fact stated in the text. Many give the highest
note to Saturn and the lowest to the Moon, while others reverse this.
The system which corresponds best, however, with the Pythagorean
planetary system must include the heaven of the fixed stars and the
earth. It is that upon which the verses of Alexander of Ephesos quoted
by Theon of Smyrna, p. 140, 4, are based:
γαῖα μὲν οὖν ὑπάτη τε βαρεῖά τε μέσσοθι ναίει·
ἀπλανέων δὲ σφαῖρα συνημμένη ἔπλετο νήτη, κ.τ.λ.
The “base of Heaven’s deep Organ” in Milton’s “ninefold harmony”
(_Hymn on the Nativity_, xiii.) implies the reverse of this.
The theory that the proper motion of the sun, moon, and planets is from
west to east, and that they also share in the motion from east to west
of the heaven of the fixed stars, makes its first appearance in the Myth
of Er in Plato’s _Republic_, and is fully worked out in the _Timaeus_.
In the _Republic_ it is still associated with the “harmony of the
spheres,” though we are not told how it is reconciled with that theory
in detail.[838] In the _Timaeus_ we read that the slowest of the
heavenly bodies appear the fastest and _vice versa_; and, as this
statement is put into the mouth of a Pythagorean, we might suppose the
theory of a composite movement to have been anticipated by some members
at least of that school.[839] That is, of course, possible; for the
Pythagoreans were singularly open to new ideas. At the same time, we
must note that the theory is even more emphatically expressed by the
Athenian Stranger in the _Laws_, who is in a special sense Plato
himself. If we were to praise the runners who come in last in the race,
we should not do what is pleasing to the competitors; and in the same
way it cannot be pleasing to the gods when we suppose the slowest of the
heavenly bodies to be the fastest. The passage undoubtedly conveys the
impression that Plato is expounding a novel theory.[840]
Footnote 838:
The difficulty appears clearly in Adam’s note on _Republic_, 617 b
(vol. ii. p. 452). There the ἀπλανής appears rightly as the νήτη,
while Saturn, which comes next to it, is the ὑπάτη. It is
inconceivable that this should have been the original scale. Aristotle
touches upon the point (_de Caelo_, Β, 10. 291 a 29 sqq.); and
Simplicius sensibly observes (_de Caelo_, p. 476, 11), οἱ δὲ πάσας τὰς
σφαίρας τὴν αὐτὴν λέγοντες κίνησιν τὴν ἀπ’ ἀνατολῶν κινεῖσθαι καθ’
ὑπόληψιν (ought not the reading to be ὑπόλειψιν?), ὥστε τὴν μὲν
Κρονίαν σφαῖραν συναποκαθίστασθαι καθ’ ἡμέραν τῇ ἀπλανεῖ παρ’ ὀλίγον,
τὴν δὲ τοῦ Διὸς παρὰ πλέον καὶ ἐφεξῆς οὕτως, οὗτοι πολλὰς μὲν ἄλλας
ἀπορίας ἐκφεύγουσι, but their ὑπόθεσις is ἀδύνατος. This is what led
to the return to the geocentric hypothesis and the exclusion of earth
and ἀπλανὴς from the ἁρμονία. The only solution would have been to
make the earth rotate on its axis or revolve round the central fire in
twenty-four hours, leaving only precession for the ἀπλανής. As we have
seen, Boeckh attributed this to Philolaos, but without evidence. If he
had thought of it, these difficulties would not have arisen.
Footnote 839:
_Tim._ 39 a 5-b 2, especially the words τὰ τάχιστα περιιόντα ὑπὸ τῶν
βραδυτέρων ἐφαίνετο καταλαμβάνοντα καταλαμβάνεσθαι (“they appear to be
overtaken, though they overtake”).
Footnote 840:
Plato, _Laws_, 822 a 4 sqq. The Athenian says of the theory that he
had not heard of it in his youth nor long before (821 e 3). If so, it
can hardly have been taught by Philolaos, though it may have been by
Archytas.
[Sidenote: Things likenesses of numbers.]
153. We have still to consider a view, which Aristotle sometimes
attributes to the Pythagoreans, that things were “like numbers.” He does
not appear to regard this as inconsistent with the doctrine that things
_are_ numbers, though it is hard to see how he could reconcile the
two.[841] There is no doubt, however, that Aristoxenos represented the
Pythagoreans as teaching that things were _like_ numbers,[842] and there
are other traces of an attempt to make out that this was the original
doctrine. A letter was produced, purporting to be by Theano, the wife of
Pythagoras, in which she says that she hears many of the Hellenes think
Pythagoras said things were made _of_ number, whereas he really said
they were made _according to_ number.[843] It is amusing to notice that
this fourth-century theory had to be explained away in its turn later
on, and Iamblichos actually tells us that it was Hippasos who said
number was the exemplar of things.[844]
Footnote 841:
Cf. especially _Met._ Α, 6. 787 b 10 (R. P. 65 d). It is not quite the
same thing when he says, as in Α, 5. 985 b 23 sqq. (R. P. _ib._), that
they perceived many likenesses in things to numbers. That refers to
the numerical analogies of Justice, Opportunity, etc.
Footnote 842:
Aristoxenos _ap._ Stob. i. pr. 6 (p. 20), Πυθαγόρας ... πάντα τὰ
πράγματα ἀπεικάζων τοῖς ἀριθμοῖς.
Footnote 843:
Stob. _Ecl._ i. p. 125, 19 (R. P. 65 d).
Footnote 844:
Iambl. _in Nicom._ p. 10, 20 (R. P. 56 c).
When this view is uppermost in his mind, Aristotle seems to find only a
verbal difference between Plato and the Pythagoreans. The metaphor of
“participation” was merely substituted for that of “imitation.” This is
not the place to discuss the meaning of Plato’s so-called “theory of
ideas”; but it must be pointed out that Aristotle’s ascription of the
doctrine of “imitation” to the Pythagoreans is abundantly justified by
the _Phaedo_. The arguments for immortality given in the early part of
that dialogue come from various sources. Those derived from the doctrine
of Reminiscence, which has sometimes been supposed to be Pythagorean,
are only known to the Pythagoreans by hearsay, and Simmias requires to
have the whole psychology of the subject explained to him.[845] When,
however, we come to the question what it is that our sensations remind
us of, his attitude changes. The view that the equal itself is alone
real, and that what we call equal things are imperfect imitations of it,
is quite familiar to him.[846] He requires no proof of it, and is
finally convinced of the immortality of the soul just because Sokrates
makes him see that the theory of forms implies it.
Footnote 845:
Plato, _Phd._ 73 a sqq.
Footnote 846:
_Ibid._ 74 a sqq.
It is also to be observed that Sokrates does not introduce the theory as
a novelty. The reality of the “ideas” is the sort of reality “we are
always talking about,” and they are explained in a peculiar vocabulary
which is represented as that of a school. The technical terms are
introduced by such formulas as “we say.”[847] Whose theory is it? It is
usually supposed to be Plato’s own, though nowadays it is the fashion to
call it his “early theory of ideas,” and to say that he modified it
profoundly in later life. But there are serious difficulties in this
view. Plato is very careful to tell us that he was not present at the
conversation recorded in the _Phaedo_. Did any philosopher ever propound
a new theory of his own by representing it as already familiar to a
number of distinguished living contemporaries? It is not easy to believe
that. It would be rash, on the other hand, to ascribe the theory to
Sokrates, and there seems nothing for it but to suppose that the
doctrine of “forms” (εἴδη, ἰδέαι) originally took shape in Pythagorean
circles, perhaps under Sokratic influence. There is nothing startling in
this. It is a historical fact that Simmias and Kebes were not only
Pythagoreans but disciples of Sokrates; for, by a happy chance, the good
Xenophon has included them in his list of true Sokratics.[848] We have
also sufficient ground for believing that the Megarians had adopted a
like theory under similar influences, and Plato states expressly that
Eukleides and Terpsion of Megara were present at the conversation
recorded in the _Phaedo_. There were, no doubt, more “friends of the
ideas”[849] than we generally recognise. It is certain, in any case,
that the use of the words εἴδη and ἰδέαι to express ultimate realities
is pre-Platonic, and it seems most natural to regard it as of
Pythagorean origin.[850]
Footnote 847:
Cf. especially the words ὃ θρυλοῦμεν ἀεί (76 d 8). The phrases αὐτὸ ὃ
ἔστιν, αὐτὸ καθ’ αὑτό, and the like are assumed to be familiar. “We”
define reality by means of question and answer, in the course of which
“we” give an account of its being (ἧς λόγον δίδομεν τοῦ εἶναι, 78 d 1,
where λόγον ... τοῦ εἶναι is equivalent to λόγον τῆς οὐσίας). When we
have done this, “we” set the seal or stamp of αὐτὸ ὃ ἔστιν upon it (75
d 2). Technical terminology implies a school. As Diels puts it
(_Elementum_, p. 20), it is in a school that “the simile concentrates
into a metaphor, and the metaphor condenses into a term.”
Footnote 848:
Xen. _Mem._ i. 2, 48.
Footnote 849:
Plato, _Soph._ 248 a 4.
Footnote 850:
See Diels, _Elementum_, pp. 16 sqq. Parmenides had already called the
original Pythagorean “elements” μορφαί (§ 91), and Philistion called
the “elements” of Empedokles ἰδέαι. If the ascription of this
terminology to the Pythagoreans is correct, we may say that the
Pythagorean “forms” developed into the atoms of Leukippos and
Demokritos on the one hand (§ 174), and into the “ideas” of Plato on
the other.
We have really exceeded the limits of this work by tracing the history
of Pythagoreanism down to a point where it becomes practically
indistinguishable from the earliest form of Platonism; but it was
necessary to do so in order to put the statements of our authorities in
their true light. Aristoxenos is not likely to have been mistaken with
regard to the opinions of the men he had known personally, and
Aristotle’s statements must have had some foundation. We must assume,
then, a later form of Pythagoreanism which was closely akin to early
Platonism. That, however, is not the form of it which concerns us here,
and we shall see in the next chapter that the fifth-century doctrine was
of the more primitive type already described.