MWilson: I have lifted this from HHTP and excerpted texts appropriate
for our class.
Pythagoras and the Pythagoreans,
Fragments and Commentary
Arthur Fairbanks, ed. and trans.
The First Philosophers of Greece
(London: K. Paul, Trench, Trubner, 1898), 132-156.
Hanover Historical Texts Project
Scanned and proofread by Aaron Gulyas, May 1998.
Proofread and pages added by Jonathan Perry, March 2001.
Fairbanks's Introduction
Passages in Plato referring to the Pythagoreans
Passages in Aristotle referring to the Pythagoreans
Pythagoras and the Pythagoreans: Passages in the Doxographists
Fairbanks's Introduction
[Page 132] Pythagoras, son of Mnesarchos, a native of Samos, left his
fatherland to escape the tyranny of Polykrates (533/2 or 529/8 B.C.).
He made his home for many years in Kroton in southern Italy, where his
political views gained control in the city. At length he and his
followers were banished by an opposing party, and he died at
Metapontum. Many stories are told of his travels into Egypt and more
widely, but there is no evidence on which the stories can be accepted.
He was a mystic thinker and religious reformer quite as much as a
philosopher, but there is no reason for denying that the doctrines of
the school originated with him. Of his disciples, Archytas, in southern
Italy, and Philolaos and Lysis, at Thebes, are the best known. It is
the doctrine of the school, not the teaching of Pythagoras himself,
which is known to us through the writings of Aristotle.
(Some very old (MWilson)) Literature: :-On Pythagoras: Krische, De
societatis a Pythagora conditae scopo politico, 1830; E.
Rohde, Rhein. Mus. xxvi. 565 sqq. ; xxvii. 23 sqq.; Diels,
Rhein. Mus. xxxi. 25 sq. ; Zeller, Sitz. d. kgl. preus. Akad.
1889, 45, p. 985 sqq.; Chaignet, Pythagore, 1873, and the
excellent account in Burnett.
Philolaos : Boeckh, Philolaos Lehren, nebst den
Bruchstiicken seines Werkes, 1819 ; V. Rose, Comment. de Arist.
libr. ord. et auct. Berlin 1854 Schaarschmidt, Die angebliche
Schriftstellerei des Phil. Bonn 18C,4; Zeller, Gesch. d. griech.
Phil. 4 Auf. 261, 341, 386 ; Hermes x. 178 ; Bywater, ,Journal of
Philol. i. 21 sqq.
MWilson: Walter Burkert, Lore and Science in Ancient Pythagoreanism has
a fine discussion of the sources of Pythagoras and their value.
Passages in Plato referring to the Pythagoreans
[Page 133] Phaedo 62 B. The saying that is uttered in secret
rites, to the effect that we men are in a sort of prison, and that one
ought not to loose himself from it nor yet to run away, seems to me
something great and not easy to see through; but this at least I think
is well said, that it is the gods who care for us, and we men are one
of the possessions of the gods.
Kratyl. 400 B. For some say that it (the body) is the tomb of the
soul-I think it was the followers of Orpheus in particular who
introduced this word-which has this enclosure like a prison in order
that it may be kept safe.
Gorg. 493 A. I once heard one of the wise men say that now we are dead
and the body is our tomb, and that that part of the soul where desires
are, it so happens, is open to persuasion, and moves upward or
downward. And, indeed, a clever man-perhaps some inhabitant of Sicily
or Italy-speaking allegorically, and taking the word from credible' and
'persuadable' called this a jar; and he called those without
intelligence uninitiated, and that part of the soul of uninitiated
persons where the desires are, he called its intemperateness, and said
it was not water tight, as a jar might be pierced with holes-using the
simile because of its insatiate desires.
Gorg. 507 A. And the wise men say that one community embraces heaven
and earth and gods and men and friendship and order and temperance and
righteousness, and for that reason they call this whole a
universe, [Page 134] my friend, for it is not without order
nor yet is there excess. It seems to me that you do not pay attention
to these things, though you are wise in regard to them. But it has
escaped your notice that geometrical equality prevails widely among
both gods and men.
Passages in Aristotle referring to the Pythagoreans
Phys. iii. 4; 203 a 1. For all who think they have worthily applied
themselves to such philosophy, have discoursed concerning the infinite,
and they all have asserted some first principle of things-some, like
the Pythagoreans and Plato, a first principle existing by itself, not
connected with anything else, but being itself the infinite in its
essence. Only the Pythagoreans found it among things perceived by sense
(for they say that number is not an abstraction), and they held that it
was the infinite outside the heavens.
iii. 4; 204 a 33. (The Pythagoreans) both hold that the infinite
is being, and divide it. iv. 6; 213 b 22. And the Pythagoreans
say that there is a void, and that it enters into the heaven itself
from the infinite air, as though it (the heaven) were breathing; and
this void defines the natures of things, inasmuch as it is a certain
separation and definition of things that lie and this is true first in
the case of numbers, for the void defines the nature of these.
De coel. i. ; 268 a 10. For as the Pythagoreans say, the all and
all things are defined by threes; for end and middle and beginning
constitute the number of the all, and also the number of the triad.
de Caelo iii.1; 300 a 15. The same holds true for those who
construct the heaven out of numbers; for some construct nature out of
numbers, as do certain of the Pythagoreans.
Metaphys. i. 5 ; 985 b 23-986 b 8. With these and before them
(Anaxagoras, Empedokles, Atomists) those called Pythagoreans applying
themselves to the sciences, first developed them ; and being brought up
in them they thought that the first principles of these (i.e. numbers)
were the first principles of all things. And since of these (sciences)
numbers are by nature the first, in numbers rather than in fire and
earth and water they thought they saw many likenesses to things that
are and that are coming to be, as, for instance, justice is such a
property of numbers, and soul and mind are [Page 137] such a
property, and another is opportunity, and of other things one may say
the same of each one.
And further, discerning in numbers the conditions and reasons of
harmonies also; since, moreover, other things seemed to be like numbers
in their entire nature, and numbers were the first of every nature,
they assumed that the elements of numbers were the elements of all
things, and that the whole heavens were harmony and number. And
whatever characteristics in numbers and harmonics they could show were
in agreement with the properties of the heavens and its parts and with
its whole arrangement, these they collected and adapted; and if there
chanced to be any gap anywhere, they eagerly sought that the whole
system might be connected with these (stray phenomena). To give an
example of my meaning: inasmuch as ten seemed to be the perfect number
and to embrace the whole nature of numbers, they asserted that the
number of bodies moving through the heavens were ten, and when only
nine were visible, for the reason just stated they postulated the
counter-earth as the tenth. We have given a more definite account of
these thinkers in other parts of our writings. But we have referred to
them here with this purpose in view, that we might ascertain from them
what they asserted as the first principles and in what manner they came
upon the causes that have been enumerated. They certainly seem to
consider number as the first principle and as it were the matter in
things and in their conditions and states; and the odd and the even are
elements of number, and of these the one is infinite and the other
finite, and unity is the product of both of them, for it is both odd
and even, and number arises from unity, and the whole heaven, as has
been said, is numbers.
A different party in this same school say that the [Page
138] first principles are ten, named according to the following
table: -finite and infinite, even and odd, one and many, right and
left, male and female, rest and motion, straight and crooked, light and
darkness, good and bad, square and oblong. After this manner Alkmaeon
of Kroton seems to have conceived them, and either he received this
doctrine from them or they from him ; for Alkmaeon arrived at maturity
when Pythagoras was an old man, and his teachings resembled theirs. For
he says that most human affairs are twofold, not meaning opposites
reached by definition, as did the former party, but opposites by chance
- as, for example, white-black, sweet-bitter, good-bad, small-great.
This philosopher let fall his opinions indefinitely about the rest, but
the Pythagoreans declared the number of the opposites and what they
were. From both one may learn this much, that opposites are the first
principles of things; but from the latter he may learn the number of
these, and what they are. But how it is possible to bring them into
relation with the causes of which we have spoken if they have not
clearly worked out; but they seem to range their elements under the
category of matter, for they say that being is compounded and formed
from them, and that they inhere in it.
i. 8; 989 b 32-990 a 32. Those, however, who carry on their
investigation with reference to all things, and divide things into what
are perceived and what are not perceived by sense, evidently examine
both classes, so [Page 140] one must delay a little longer over
what they say. They speak correctly and incorrectly in reference to the
questions now before us. Now those who are called Pythagoreans use
principles and elements yet stranger than those of the physicists, in
that they do not take them from the sphere of sense, for mathematical
objects are without motion, except in the case of astronomy. Still,
they discourse about everything in nature and study it they construct
the heaven, they observe what happens in its parts and their states and
motions; they apply to these their first principles and causes, as
though they agreed entirely with the other physicists that being is
only what is perceptible and what that which is called heaven includes.
But their causes and first principles, they say, are such as to lead up
to the higher parts of reality, and are in harmony with this rather
than with the doctrines of nature. In what manner motion will take
place when finite and infinite, odd and even, are the only underlying
realities, they do not say; nor how it is possible for genesis and
destruction to take place without motion and change, or for the
heavenly bodies to revolve. Farther, if one grant to them that
greatness arises from these principles, or if this could be proved,
nevertheless, how will it be that some bodies are light and some heavy
? For their postulates and statements apply no more to mathematical
objects than to things of sense; accordingly they have said nothing at
all about fire or earth or any such objects, because I think they have
no distinctive doctrine about things of sense. Farther, how is it
necessary to assume that number and states of number are the causes of
what is in the heavens and what is taking place there from the
beginning and now, and that there is no other number than that out of
which the world is composed? For when opinion and opportune time are at
a certain point in the heavens, [Page 141] and a little
farther up or down are injustice and judgment or a mixture of them, and
they bring forward as proof that each one of these is number, and the
result then is that at this place there is already a multitude of
compounded quantities because those states of number have each their
place-is this number in heaven the same which it is necessary to assume
that each of these things is, or is it something different? Plato says
it is different ; still, he thinks that both these things and the
causes of them are numbers; but the one class are ideal causes, and the
others are sense causes.
1036 b 17. So it turns out that many things of which the forms
appear different have one form, as the Pythagoreans discovered; and one
can say that there is one form for everything, and the others are not
forms; and thus all things will be one.
xii. 6; 1080 b 16. The Pythagoreans say that there is but one
number, the mathematical, but things of sense are not separated from
this, for they are composed of it; indeed, they construct the whole
heaven out of numbers, but not out of unit numbers, for they assume
that the unities have quantity; but how the first unity was so
constituted as to have quantity, they seem at a loss to say. b 31. All,
as many as regard the one as the element and first principle of things,
except the Pythagoreans, assert that numbers are based on the unit; but
the Pythagoreans assert, as has been remarked, that numbers have
quantity.
xii. 8; 1083 b 9. The Pythagorean standpoint has on the one hand
fewer difficulties than those that have been discussed, but it has new
difficulties of its own. The fact that they do not regard number as
separate, removes many of the contradictions ; but it is impossible
that bodies should consist of numbers, and that this number should be
mathematical. Nor is it true that indivisible elements have quantity;
but, granted that they have this quality of indivisibility, the units
have no quantity; for how can quantity be composed of indivisible
elements? but arithmetical number consists of units. But these say that
things are number; at least, they adapt their speculations to such
bodies as consist of elements which are numbers.
Pythagoras and the Pythagoreans: Passages in the Doxographists
Aet. Plac. i. 3; `. 280. And again from another starting-point,
Pythagoras, son of Muesarchos, a Samian, who was the first to call this
matter by the name of philosophy, assumed as first principles the
numbers an [Page 144] the symmetries existing in them,
which he calls harmonies, and the elements compounded of both, that are
called geometrical. And again he includes the monad and the undefined
dyad among the first principles; and for him one of the first
principles tends toward the creative and form-giving cause, which is
intelligence, that is god, and the other tends toward the passive and
material cause, which is the visible universe. And he says that the
starting-point of number is the decad; for all Greeks and all
barbarians count as far as ten, and when they get as far as this they
return to the monad. And again, he says, the power of the ten is in the
four and the tetrad. And the reason is this: if any one returning from
the monad adds the numbers in a series as far as the four, he will fill
out the number ten (i.e. 1 + 2 + 3 + 4 10); but if he goes beyond the
number of the tetrad, he will exceed the ten. Just as if one should add
one and two and should add to these three and four, he will fill out
the number ten; so that according to the monad number is in the ten,
but potentially in the four. Wherefore the Pythagoreans were wont to
speak as though the greatest oath were the tetrad: 'By him that
transmitted to our soul the tetraktys, which has the spring and root of
ever-flowing nature.' And our soul, he says, is composed of the tetrad
; for it is intelligence, understanding, opinion, sense, from which
things come every art and science, and we ourselves become reasoning
beings. The monad, however, is intelligence, for intelligence sees
according to the monad. As for example, men are made up of many parts,
and part by part they are devoid of sense and comprehension and
experience, yet we perceive that man as one alone, whom no being
resembles, possesses these qualities; and we perceive that a horse is
one, but part by part it is without experience. [Page 145]
For these are all forms and classes according to monads. Wherefore,
assigning this limit with reference to each one of these, they speak of
a reasoning being and a neighing being. On this account the monad is
intelligence by which we perceive these things. And the undefined dyad
is science; fittingly, for all proof and all persuasion is part of
science, and farther every syllogism brings together what is questioned
out of some things that are agreed upon, and easily proves something
else; and science is the comprehension of these things, wherefore it
would be the dyad. And opinion as the result of comprehending them is
the triad; fittingly, for opinion has to do with many things; and the
triad is quantity, as 'The thrice-blessed Danaoi.' On this account then
he includes the triad. . . . And their sect is called Italic because
Pythagoras taught in Italy, for he removed from Samos, his fatherland,
because of dissatisfaction with the tyranny of Polykrates.
Number is the first principle, a thing which is undefined,
incomprehensible, having in itself all numbers which could reach
infinity in amount. And the first principle of numbers is in substance
the first monad, which is a male monad, begetting as a father all other
numbers. Secondly the dyad is female number, and the same is called by
the arithmeticians even. Thirdly the triad is male number; this the
arithmeticians have been wont to call odd. Finally the tetrad is a
female number, and the same is called even because it is female.
All numbers, then, taken by classes are fours (for number is
undefined in reference to class), of which is composed the perfect
number, the decad. For the series, one two three and four, becomes ten,
if its own name is kept in its essence by each of the numbers.
Pythagoras said that this sacred tetraktys is 'the spring having the
roots of ever-flowing nature in itself, and from this numbers have
their first principle. For the eleven and the twelve and the rest
derive from the ten the first principle of their being. The four parts
of the decad, this perfect number, are called number, monad, power, and
cube. And the interweavings and [Page 153] minglings of
these in the origin of growth are what naturally completes nascent
number; for when a power is multiplied upon itself, it is the power of
a power and when a power is multiplied on a cube, it is the power of a
cube ; and when a cube is multiplied on a cube, the cube of a cube;
thus all numbers, from which arises the genesis of what arises, are
seven: -number, monad, power, cube, power of a power, power of a cube,
cube of a cube.
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