Thalesand Ο. As to the nature and extent of the mathematical
geomerY: knowledge brought back by Thales from Egypt, it
seems desirable to point out that many writers have
seriously misunderstood the character of the tradition.’
In his commentary on the First Book of Euclid,
Proclus enumerates, on the authority of Eudemos,
1 Aet. iv. 1. 1 (Dox. p. 384).
2 Dox. pp. 226-229. ‘The Latin epitome will be found in Rose’s edition of the Aristotelian fragments.
3 Hekataios, fr. 278 (7. 4.G. i. p. 19).
* See Cantor, Vorlesungen wiber Geschichte der Mathematik, vol. i. pp. 112 sqq.; Allman, “Greek Geometry from Thales to Euclid ” (Zermathena, ili. pp. 164-174).
; the Milesian School 45
certain propositions which he says were known to
Thales.’ One of the theorems with which he credits.
him is that two triangles are equal when they have one
side and the two adjacent angles equal. This he must
have known, said Eudemos, as otherwise he could not
have measured the distances of ships at sea from a
watch-tower in the way he was said to have done?
Here we see how all these statements arose. Certain
remarkable feats in the way of measurement were
traditionally ascribed to Thales, and it was assumed
that he must have known all the propositions which
these imply. But this is quite an illusory method of
inference. Both the measurement of the distance of
ships at sea, and that of the height of the pyramids,
which is also ascribed to him,’ are easy applications of
~1 Proclus, zz Eucl. pp. 65, 73 157, 103 250, 20; 299, I; 352, 143 (Friedlein). _Eudemos wrote the first histories of astronomy and mathematics, just as Theophrastos wrote the first history of philosophy.
2 Proclus, p. 352, 14, Εὔδημος δὲ ἐν ταῖς γεωμετρικαῖς ἱστορίαις εἰς Θαλῆν τοῦτο ἀνάγει τὸ θεώρημα (πεῖ, i. 26) τὴν γὰρ τῶν ἐν θαλάττῃ πλοίων ἀπόστασιν δι’ οὗ τρόπου φασὶν αὐτὸν δεικνύναι τούτῳ προσχρῆσθαί φησιν ἀναγκαῖον. For [Π6 method adopted by Thales, see Tannery, Géomeétrie grecque, p. 90. I agree, however, with Dr. Gow (Short History of Greek Mathematics, § 84) that it is very unlikely Thales reproduced and measured on land the enormous triangle which he had constructed in a perpendicular plane over the sea. Such a method would be too cumbrous to be of use. It is much simpler to suppose that he made use of the Egyptian seg?.
3 The oldest version of this story is given in Diog. i. 27, ὁ δὲ Ἱερώνυμος καὶ ἐκμετρῆσαί φησιν αὐτὸν τὰς πυραμίδας, ἐκ τῆς σκιᾶς παρατηρήσαντα ὅτε
ἡμῖν. ἰσομεγέθης ἐστίν. Cf. Pliny, H. Wat. xxxvi. 82, mensuram altt-
tudinis earum deprehendere invenit Thales Milesius umbram metiendo qua hora par esse corport solet. (Hieronymos of Rhodes was contemporary with Eudemos.) This need imply no more than the simple reflexion that the shadows of all objects will probably be equal to the objects at the same hour. Plutarch (Conv. sept. sap. 147 a) gives a more elaborate method, τὴν βακτηρίαν στήσας ἐπὶ τῷ πέρατι τῆς σκιᾶς ἣν ἡ πυραμὶς ἐποίει, γενομένων τῇ ἐπαφῇ τῆς ἀκτῖνος δυοῖν τριγώνων, ἔδειξας ὃν ἡ σκιὰ πρὸς τὴν σκιὰν λόγον εἶχε, τὴν πυραμίδα πρὸς τὴν βακτηρίαν ἔχουσαν. This, as Dr. Gow points. out, is only another calculation of seg¢, and may very well have been the method of Thales.
46 Early Greek Philosophy
what Aahmes calls the seg¢. These rules of mensura-
tion may well have been brought from Egypt by
Thales, but we have no ground for supposing that he
knew any more about their vationale than did the
author of the Rhind papyrus. Perhaps, indeed, he
gave them a wider application than the Egyptians had
done. Still, mathematics, properly so called, did not
come into existence till some time after Thales. |
Thalesasa 7. Thales appears once more in the pages of
politician. “Herodotos some time before the fall of the Lydian empire. He is said to have urged the Ionian Greeks to unite in a federal state with its capital at Teos.’ We shall have occasion to notice more than once in the sequel that the early schools of philosophy were in the habit of trying to influence the course of political events; and there are many things, for instance the part played by. Hekataios in the Ionian revolt, which point to the conclusion that the scientific men of Miletos took up a very decided position in the stirring times that followed the death of Thales. It is this political action which has gained the founder of the Milesian school his undisputed place among the Seven Wise Men; and it is owing mainly to his inclusion among those worthies that the numerous anecdotes which were told of him in later days attached themselves to his name.”
Uncertain 8. If Thales ever wrote anything, it soon was lost,
character of
Bee te ρὰ, and the works which were written in his name did
not, as a rule, deceive even the ancients.® Aristotle
1 Herod. i. 170 (R. P. 9 d).
* The story of Thales falling into a well (Plato, Z%¢. 174 a) is nothing but a fable teaching the uselessness of σοφία; the anecdote about the **corner” in oil (Ar. Pol. A, 11. 1259 a 6) is intended to inculcate the opposite lesson. - § See R.XP. oe.
; THE MILESIAN SCHOOL 49
professes to know something about the views of Thales ;
but he does not pretend to know how they were arrived
at, nor the arguments by which they were supported.
He does, indeed, make certain suggestions, which are
repeated by later writers as statements of fact; but he
himself simply gives them for what they are worth.’
There is another difficulty in connexion with the
tradition. Many a precise-looking statement in the
Placita has no other foundation than the habit of
ascribing any doctrine which was, roughly speaking,
characteristic of the whole Ionic “Succession” to
“Thales and his followers,’ and so producing the
appearance of a definite statement about Thales. “But,
in spite of all this, we need not doubt that Aristotle
was correctly informed with regard to the leading
points. We have seen traces of reference to Thales in
Hekataios, and nothing can be more likely than that
later writers of the school should have quoted the
views of its founder. We may venture, therefore, upon
a conjectural restoration of his cosmology, in which we
shall be guided by what we know for certain of the
subsequent development of the Milesian school; for
we should naturally expect to find its characteristic
doctrines at least foreshadowed in the teaching of its
earliest representative. But all this must be taken for
just what it is worth; speaking strictly, we do not
know anything about the teaching of Thales at all.
9. The statements of Aristotle may be reduced to Conjectural account of the
three : cosmology of
᾿ Thales.
(1) The earth floats on the water.
ΒΡ δ |
2 Arist. 2222. A, 3. 983 Ὁ 21 (Ε. P. 10) ; de Caelo, B, 13. 294 a 28 (R. Ρ. 11). Later writers add that he gave this as an explanation of earthquakes (so Aet. iii. 15, 1); but this is probably due to a “" Homeric allegorist ?
Water.
46 Early Greek Philosophy
(2) Water is the material cause’ of all things.
(3) All things are full of gods. The magnet is
alive ; for it has the power of moving iron.’
The first of these statements must be understood in
the light of the second, which is expressed in Aristotelian
terminology, but would undoubtedly mean that Thales
had said water was the fundamental or primary thing,
of which all other things were mere transient forms.
It was, we shall see, just such a primary substance
that the Milesian school as a whole was seeking, and
it is unlikely that the earliest answer to the great
question of the day should have been the comparatively
subtle one given by Anaximander. We are, perhaps,
justified in holding that the greatness of Thales con-
ow
sisted in this, that he was the first to ask, not what
was the original thing, but what zs the primary thing
now ; or, more simply still, “What is the world made
of?” The answer he gave to this question was: Water.
10. Aristotle and Theophratos, followed by Sim-
plicius and the doxographers, suggest several explana-
tions of this answer. By Aristotle these explanations
are given as conjectural ; it is only later writers that
repeat them as if they were quite certain.? The most
(Appendix, ὃ 11}, who wished to explain the epithet ἐννοσίγαιος. Cf. Diels, Dox. p. 225.
1 Met. A, 3. 983 Ὁ 20 (R. P. 10). I have said ‘‘ material cause,” because τῆς τοιαύτης ἀρχῆς (Ὁ 19) means τῆς ἐν ὕλης εἴδει ἀρχῆς (Ὁ 7).
8 Arist. de An, A, 5. 411 a 7 (ΚΒ. P. 13); 2. 2. 405 a 19 (R. P. 13 a). Diog. i. 24 (R. P. 206.) adds amber. This comes from Hesychios of Miletos ; for it occurs in the scholium of Par. A on Plato, Ref. 600 a.
3 Met. A, 3. 983 Ὁ 22; Aet. i. 3, 1; Simpl. PAys. Ὁ. 36, 10 (R. P. 10, 12, 12a). The last of the explanations given by Aristotle, namely, that Thales was influenced by early cosmogonical theories about Okeanos and Tethys, has strangely been supposed to be more historical than the rest, whereas it is merely a fancy of Plato’s taken literally. Plato says more than once (Tht. 180 ἃ 2; Crat. 402 Ὁ 4) that Herakleitos and his predecessors (οἱ ῥέοντες) derived their philosophy from Homer (77. xiv. 201), and even
The Milesian School 49
probable view of them seems to be that Aristotle simply
ascribed to Thales the arguments used at a later date
by Hippon of Samos in support of a similar thesis.'
This would account for their physiological character.
' The rise of scientific medicine had made_ biological
arguments very popular in the fifth century ; but, in the
days of Thales, the prevailing interest was not physio-
logical, but rather what we should call meteorological,
and it is therefore from this point of view we must try
to understand the theory.
Now it is not very hard to see how considerations of
a meteorological kind may have led Thales to adopt
the view he did. Of all the things we know, water
#seems to take the most various shapes. It is familiar
to us in a solid, a liquid, and a vaporous form, and so
Thales may well have thought that he saw the world-
process from water and back to water again going on
before his very eyes. The phenomenon of evaporation
naturally suggests everywhere that the fire of the
heavenly bodies is kept up by the moisture which they
draw from the sea. Even at the present day, the
country people speak of the appearance of sunbeams as
“the sun drawing water.” Water comes down again in
the rain ; and lastly, so the early cosmologists thought,
earlier sources (Orph. frag. 2, Diels, Vors. 1st ed. p. 491). In quoting this suggestion, Aristotle refers it to ‘‘ some ”—a word which often means Plato —and he calls the originators of the theory παμπαλαίους, as Plato had done (Met. 983 Ὁ 28; cf. 721. 181 Ὁ 3). This is a characteristic example of the way in which Aristotle gets"history out of Plato. See Appendix, § 2.
1 Compare Arist. de An. A, 2. 405 Ὁ 2 (R. P. 220) with the passages referred to in the last note. The same suggestion is made in Zeller’s fifth edition (p. 188, n. 1), which I had not seen when the above was written. Doring, “ Thales” (Zschr. 7. Philos. 1896, pp. 179 sqq.), takes the same view. We now know that, though Aristotle declines to consider Hippon as a philosopher (ez. A, 3. 984 a 3; R. P. 219 a), he was discussed in the history of medicine known as Menon’s /atrika. See Diels in Hermes, xxviii. p. 420.
Theology.
50 Early Greek Philosophy
it turns toearth. This seems strange to us, but it may
have seemed natural enough to men who were familiar
with the river of Egypt which had formed the Delta,
and with the torrents of Asia Minor, which bring down
unusually large alluvial deposits. At the present day
the Gulf of Latmos, on which Miletos used to stand, is
completely filled up. Lastly, they thought, earth turns
once more to water—an idea derived from the obser-
vation of dew, night-mists, and subterranean springs.
For these last were not in early times supposed
to have anything at all to do with the rain. The
“waters under the earth” were regarded as an entirely
independent source of moisture.’
11. The third of the statements mentioned above
is supposed by Aristotle himself to imply that Thales
believed in a “soul of the world,” though he is careful
to mark this as no more than an inference.” The
doctrine of the world-soul is then attributed quite
positively to Thales by Aetios, who gives it in the
Stoic phraseology which he found in his immediate
source, and identifies the world-intellect with God;
Cicero found a similar account of the matter in the
Epicurean manual which he followed, but he goes a
step further. Eliminating the Stoic pantheism, he
turns the world-intellect into a Platonic demzourgos, and
says that Thales held there was a divine mind which
formed all things out of water.* All this is derived