Like other philosophers of their generation such as Melissus and Empedocles, both Anaxagoras and Philolaus seem to have been responding to issues raised by Parmenides and Zeno - issues having to do with whether we can have a coherent account of what exists, or of anything, if we claim that multiple determinate (discrete, identifiable) things exist. Like Empedocles, Anaxagoras and Philolaus do think that it is possible to provide an account of the cosmos in familiar terms, that it is possible to explain what the cosmos is, how it got that way, how there could be multiple things of the types we say exist (rocks, trees, rain), how changes or apparent changes occur, and what goes on when things appear to be generated or destroyed.
Evidence of Parmenides' influence is that later philosophers thought it was of first importance to address the issue of whether there could be multiple things, and why or why not; we have no record of anyone before Parmenides who thought that he or she had to show that there could or could not be multiple things. That later philosophers also thought it crucial to provide evidence or arguments for at least some of their claims is additional testimony to the influence of Parmenides and Zeno.
Philolaus tried to show that multiple things have their source,
some sense, in "the One" or in
unity, and that "the One" or unity can itself be analyzed or
understood in some way.
Anaxagoras held that even that which appears to be one, or appears
be unified, is really in
some way multiple; that there is no smallest bit of anything
and that therefore the
problems noted by Parmenides, Zeno, and Melissus can be avoided.
More direct evidence that Anaxagoras is responding to Parmenides,
Zeno, and/or Melissus (and
maybe Heracleitus - note that A. is trying to explain
processes or phenomena we call "coming
to be" and "passing away", "change", "birth", "death", etc.; all
fundamental for H.) is the wording
of A.'s fragments 5, 6, 8, and 17(13.5, 13.6, 13.8, 13.17 in your
text); much is close or identical
to the Eleatics' wording. A. is evidently trying to meet them on
own terms in order to
overcome their objections.
Anaxagoras of Clazomenae.
Anaxagoras tries to provide a cosmogony, an account of the
development of the cosmos. Unlike Anaximander and
(and possibly Heracleitus),
who conceived of the development process as cyclical; and unlike
Anaximenes (and perhaps
Heracleitus), who describes change within the familiar arrangement
the cosmos as a continual
ebb and flow in a variety of directions at once; Anaxagoras
an apparently one-way
development of the cosmos as a whole. At least, we have
record of Anaxagoras saying
anything about the process reversing, stopping, or repeating. See
especially fr. 12 (=13.12),
where he speaks of an "outset" of change (what moves cyclically
beginning), and of how
what brings about the change "will spread further".
At the "outset" of this change (which will eventually result in
development of everyday
things, and maybe further development), what exist are evidently
(Nous) and "seeds"
(spermata) (fragments 4, 11-14 [=13.4, 13.11-13.14 in
your text; see also
13.26 and 13.27]). Mind "always
is" (fr. 14 [=13.14]); it's not clear whether A. thought that Mind
always was as well, but the
phrase he uses ('aei esti') can be understood
way. Also, he says that Mind is infinite or
unlimited (apeiron) and self-ruling (autokrates);
might be plausibly be taken to mean that it
is not limited by anything else (such as having started at a
time, or having had to be
generated by something else), and that it is in no sense dependent
anything else. A. may also
have thought that the seeds always existed; there's nothing
in the fragments to indicate
that they came into existence at one point or another.
In A.'s time, the Greek language was often written without
letters (except at the beginning
of proper names). Thus it is not clear whether 'Noos'
is supposed to start with a capital.
Your text does capitalize, probably to call attention to the
point that A. is not saying
that an individual human mind is responsible for the generation of
familiar cosmos. Rather,
he seems to mean some sort of cosmic mind, something that pervades
cosmos (frr. 11, 12, 13, 14
[=13.11-13.14; see also 13.28-30]). Individual living things have
"in" them (frr. 11, 14),
though presumably none of these individual living things contain
it (none of them can
initiate the generation of the cosmos, and they can die,
whereas Mind "always is").
Mind brings about the development of familiar things in the following way. It initiates a sort of whirling or revolving which spreads through the mass of seeds, and the seeds collect into various forms, possibly as in a whirlpool or centrifuge (frr. 4, 5, 9, 12, 15-17[=13.4, 13.5, 13.9, 13.12, 13.15-13.17]). To see how that idea might seem plausible, consider what happens if you put food in a blender or food processor and let it run too long: liquid collects at one level, large particles at another level, small ones at another; or denser things go to one level and less dense ones to another; etc.
Mind is distinct from and not mixed with other things, nor does it contain a portion of anything else (frr. 11, 12, 14 [=13.11, 13.12, 13.14]). It can exist where other things are (13.14); A. may be saying that it does not take up space in the way that material things do; or he may be saying that since it is so "fine" (i.e. fine-grained; leptos, fr. 12 [=13.12]) it can infiltrate or be "in" other things without mixing them into itself.
The seeds must evidently be imagined as invisibly small
no seed quite the same as any
other seed (fr. 4 [=13.4]). Everything except Mind is said by A.
contain a "portion of
everything" (frr. 6, 11, 12 [=McKirahan 13.6, 13.11, 13.12). This
suggests that the seeds all contain
or are composed of the same
stuff, the same "kinds of things", but that each seed contains
different proportions of each
element or each kind of thing. Anaxagoras appears to be trying to
account in this way for certain
problematic observations: When we eat vegetables, we do not grow
or turn green; and we
do develop muscle, bone, flesh, hair, etc. - non-vegetable-like
entities. Where did the vegetables
and their qualities go? And we don't generally eat bones or hair,
somehow our bones and hair
grow: where did they get the material to do this? If, as
and others suggested, nothing
could be understood to come from nothing, then it seemed likely to
Greek thinkers that
things that grew had to have absorbed or accreted something that
previously been external to
them. Anaxagoras addresses this at fragments 10 and 17, =13.10,
13.17. Anaxagoras' response to these problems seems to
have been that taking in
any kind of seeds would allow a thing to grow. We can get taller
heavier (gain bones,
muscle, etc.) even from a vegetarian diet because each of the
and vegetables we eat is
composed of seeds, and the seeds each contain a portion of
including flesh, bone,
etc. Perhaps an apple, say, does not contain a very large
bone, but that might be
why we would have to eat large and varied servings of fruits and
vegetables in order to stay
healthy. (If this sounds odd, consider that we are told today that
should eat broccoli so as to
build strong bones. Bones are largely calcium, and broccoli
fair amount of calcium
despite the fact that broccoli doesn't look or taste like calcium,
less like bone.)
When the seeds were all together before the revolution started,
mass of seeds had no
discernible color, nor was it hot or cold or bright or dark - for
"mixing" of the seeds
prevented this (fr. 4 [=13.4]). Possibly what A. meant was that
are little bits of hot (or hot
stuff), cold [stuff], bright [stuff], etc. in each seed, none of
qualities predominated in the
mass as a whole or in any part of it; and each quality or kind of
was imperceptible because
there was very little of each in any location, and because near
bit was a different of
"opposite" bit. That is, no single color would be discernible
any location in the mass
would contain seeds of different compositions, and there would not
enough red portions in the
seeds in any given location for us to be able to see that the area
red color - and green, blue,
black, white, transparent, reflective, and other portions in seeds
would be present nearby.
Wherever there were bright portions there would also be dark
the mixture was such that
seeds with large bright portions or large dark portions did not
But once Mind got the revolution underway, hot, cold, stars, sun,
moon, aer, aither, rare, dense,
etc. "separated off" (13.4, 13.5, 13.12, 13.16, 13.17) from the
mass. That is,
apparently seeds where a certain
quality or kind of stuff predominated got together in various
perhaps by something akin to
centrifuging (13.12). Each familiar thing "is" that of which it
the most (13.12). What this
seems to mean is that what we call "wood" is predominantly wood;
we consider to be a
piece of wood is a group of seeds in each one of which
portions predominate. To see how
this seems to be supposed to work, let us consider what the seeds
supposed to be like. Recall
that A. holds that there is no smallest thing (13.6) - he is
apparently trying to avoid the problems
that Zeno showed arose from the supposition that each thing with
is comprised of
compounded units. A. also holds that each seed contains a portion
everything. What I would
suggest that this means is that A. is proposing that although
things are comprised of
seeds, there is no smallest portion of anything in any seed.
Let's look at a seed that would be included in what we call a piece of wood. It has portions of all kinds of stuff, but the largest portion in it is wood. (If it's dry wood, it would also have a good-sized share of the dry,etc.)
Now let's look at the portion of the seed that is wood. It's only
considered to be a "wood portion"
because wood predominates.(1)
also contains smaller portions of all other kinds of stuff.
(Similarly, each of these smaller portions of other stuff contains
little bit of everything,
including wood; the smaller "iron portion" that would be in the
predominantly wood seed is only
considered to be "iron" because iron predominates in that
And again, in the "wood portion" of the "wood portion" of the "wood seed", wood predominates, but other ingredients are present also, in smaller quantities. This process of division (or apparent division) within the portions would seem to go on forever - hence there is no smallest bit of wood; each thing that seems to be a small bit of wood, or a portion of a portion of a portion....of a seed will be divisible into smaller portions.(2)
If a bunch of predominantly-wood seeds come together, A.
you get a piece of wood. If
this agglomeration of seeds gets a bit of Mind caught in it, you
tree that grows, reproduces,
etc. When the tree "dies", the piece of wood decomposes, falls
and mixes in with the soil
(or, if an animal eats the wood, it mixes with the animal's body,
the bone portions build
bone, etc.) Thus, A. says, beliefs in "coming into being" and
away" are incorrect (17
[=13.17]): things form when seeds "separate off" from the mass (or
later processes in
which the early things were involved result in rearrangements);
things change or cease to be
what they were when the separated-off pieces decompose and their
go into new mixtures.
This ingenious scheme is not without its problems, at least some
which were discovered
during or shortly after Anaxagoras' time. One problem is that if
is no pure wood - since all
"wood portions" contain sub-portions of other kinds of stuff -
what does it mean to say that
something is predominantly wood? That is, in virtue of being
predominantly what do we call
something "wood"? What exactly makes wood different from other
what is it to be wood?
Something like a paradox of Zeno's, pertaining to what we would
qualities rather than to
what we'd call quantities, would seem to arise if we tried to
or determine what wood was
on Anaxagoras' conception.
Another problem was raised by Socrates in Plato's Phaedo.
(We don't know whether the
historical Socrates actually did this, or whether Plato is using
dramatic license.) Socrates
says that he initially thought it was a terrific idea on
part to give Mind a central role
in determining how the universe will be, for this would seem to
promising way to account
for why things are one way rather than another, for what
processes and events have
taken, and for why at least some aspects of existence seem
regular (recall that A.
says that Mind understands or grasps all, fr. 12 [=13.12]). But,
complains, A. doesn't really make
his "Mind" sound like a mind. For "minds" make decisions, based on
preferences, goals, or values; minds understand things through the
things' relevance to an order,
and ordering reflects priorities. According to Socrates (and this
consistent with the
surviving fragments of A.), A. does not address these issues, does
say anything about why
Mind does what it does, how and why its decisions (to make things
way rather than another)
were made, why it finds one way to be better than another, and so
These questions would also
be important in determining what it would be best for a human to
any given situation; after
all, these matters too are features of what exists. Socrates
for acknowledging the issue
of purpose or value, but criticizes him for failing to address it
adequately (or at all).
1. As your text notes, it is not immediately clear what Anaxagoras means when he says that there is a portion of "everything" in every thing (Philosophy Before Socrates 208-216, especially 208-210). McKirahan suggests that Anaxagoras might have meant that there is a portion of each "Basic Thing" (McKirahan's term), each "basic" kind of stuff, in every thing. This is a reasonable suggestion, but the question arises as to what is "basic." Certainly there are certain kinds of stuff that Anaxagoras mentions repeatedly as being present in the seeds that compose everyday things: kinds of stuff such as flesh, bone, hot, cold, bright, dark, etc. There may of course have been others. We do not know the criteria he would have used to determine which kinds of stuff are basic and which ones are derived from them.
Also, there is nothing in the extant fragments that would explain why, or whether, some sort of thing must predominate in each seed. Perhaps in fact Anaxagoras thought that there could be seeds in which no one sort of thing predominated; in those cases, the seed could not be said to be a seed of one standardly named sort of thing or another. This type of seed might be found at what we would call interfaces between different things - in a riverbed, for example, we might find seeds that had significant portions of earth, water, chlorophyll, and fish parts, but with none of these predominating and perhaps none even forming a plurality in a seed.
2. In the representations of seeds and portions that I have provided here, the sections are meant to represent percentages. That is, Anaxagoras may or may not have meant that the wood portion or main wood portion of a seed (or of a portion) was located in a certain spatial part of the seed (or portion), the iron portion or main iron portion in another, and so on. Perhaps he did not conceive of the portions (and sub-portions) as being distinguished spatially. He could for example have thought that the various portions found in a seed were composed of little bits (each with its own similarly distributed sub-portions, etc.) distributed all around the seed in the way that little bits of ice, air, milk, sugar, and flavoring are distributed around a milkshake.
Philolaus of Croton.
(Also known as Philolaus of Tarentum; what is clear is that he was
member of one or both of the main Pythagorean communities.)
seems to have had
among his concerns the implicit challenge raised by the Eleatics
regarding the basis on which
knowledge would be possible. He seemed to want to account for the
relationship between what
exists and our knowledge of it; he apparently wanted to try to
for what is believed to
exist in such a way as to show that we can have knowledge of that
exists. He tried to do
this by fleshing out the Pythagorean ideas of number as a
or regulatory feature of
what exists, and of the importance of numerical or other
relationships as the key to
understanding. Crucially, he seems to want to claim that we can
that what exists is at least
in some respects the way we say it is, on the grounds that (as he
it) there are fundamental
stable features (number, limiting, non-limited(1),
etc.) that account for the way things are and that
can be recognized by us. That is, Philolaus holds that numbers
certain other related stable
features of the universe) exist "in" and account for the universe
general. Numbers and these
other fundamental stable features account for the way things are,
provide principles that can even
explain changing phenomena, and can be recognized by us. If we
(in appropriate ways)
about things in terms of number, what we think and what is will be
same, and knowledge will
be possible, on Philolaus' view.
The question of whether there were stable underlying recognizable
features of the universe that
accounted for the way things were (or appeared) was of great
to Plato and to
Aristotle, as well as to later thinkers such as the Stoics, the
Skeptics, and the neo-Platonists.
There was also some concern about whether there could be other
conditions under which
knowledge or understanding (whatever these might be conceived to
was possible, and about
whether or how we can tell that such conditions were fulfilled.
According to Philolaus' conception, the conditions under which knowledge would be possible were fulfilled. His conception sees to have worked in the following way.
1. The ultimate component features of the cosmos are the limiting and the non-limited (fr. 1 [=18.1]; see below for a translation of these fragments).
All things are comprised of the limiting and the non-limited; they need both aspects in order to be determinate things (fr. 3 [=18.3]). (The idea seems to be that if anything was thought to have only a non-limited element it would not be a determinate thing; and that the limiting has to limit something - which would have to be non-limited or else the limiting would not be limiting - in order to be in effect.)
2. Number takes or has three forms: the odd, the even, and the even-odd (the number one, or the unit: the number one was taken to be the unit out of which all other counting numbers were built). (fr. 5 [=18.5])
Odd numbers are seen as limiting; even numbers are seen as non-limited (see the Burkert reserve reading, or see McKirahan, pages 93-96 and 9.26). The number one, or the unit, is seen as containing both limiting and non-limited (and both odd and even), or as containing the sources of both.
3. The One (the number one? unity?) is the source of everything (fr. 8; not in McKirahan's Philolaus chapter, but compare 9.26, where Aristotle reports something similar as a position espoused by some Pythagoreans). The One is also the source of all other numbers. (If you are interested in this, start with Heath's A History of Greek Mathematics and Nussbaum's article "Eleatic Conventionalism and Philolaus on the Conditions of Thought" in Harvard Studies in Classical Philology 83 (1979).)
4. The nature of number is the cause of recognition (fr. 11), and is related to harmony (frr. 6 [=18.6], 11). Recognition requires the limiting and the non-limited (fr. 6 [=18.6]).
5. Thus numbers involve exactly what things involve, in some way
another, so grasping
numbers and their relations can (or does) tell us about other
and their relations. Note too
that numbers are a feature of human thought and speech (though not
of human thought and
speech, the Pythagoreans would warn); they are not visible or
or audible in themselves
(you can see or touch what you count to be four objects, and you
see or touch or hear a
symbol for the number four, but you don't see or touch or hear
itself), yet they enable us to
understand and recognize what is visible or tangible or audible.
A question that arises is whether the limiting and the
or the odd and the even, or
numbers, really have the status P. says they do; and whether or
can tell. On the other
hand, if one is not convinced by P.'s account of things (and many
ancient Greece were not),
one is left with the interesting questions of why mathematical
relations "work" (why proofs are
possible; why for any two numbers a and b, a+b=b+a; etc.), and of
at least some observable
phenomena in the universe (tides, planetary motions, fulcrums,
pendulums) seem to function in
ways that are describable mathematically.
Relevant Fragments of Philolaus (tr. Cherubin)
(for a complete listing, see K. Freeman, Ancilla to the Pre-Socratic Philosophers)
fr. 1. Nature in the kosmos was fitted together from limiting and non-limited, both the kosmos as a whole and everything in it.
fr. 2. All things that are must necessarily be either limiting [things] or non-limited [things], or both limiting and non-limited [things]. But they could not be merely limiting, nor merely non-limited. Since however it appears that they are neither all from limiting nor all from non-limited, it is clear that the kosmos and the things in it were fitted together from both limiting and non-limited. Things in actions (deeds, works, facts) also show this. For those of them that are from limiting limit, and those that are both from limiting and from non-limited limit and also do not limit, and those that are from non-limited appear non-limited.
fr. 3. For there will not be anything that knows (OR: anything that is known) in the first place if all things are non-limited.
fr. 4. And indeed all things that are known/recognized have number, for it is not possible for anything to be conceived of or known/recognized without this.
fr. 5. Number, indeed, has two kinds (OR: forms) specific to it, odd and even, and a third that comes from (OR: is made out of) mixture of the two, even-odd. Each of the two kinds has many forms, which [forms] each thing in itself indicates.
fr. 6. Concerning nature and harmony this holds: The being of the things (OR: matters, affairs) is eternal and nature itself admits of divine and not human knowledge (OR: recognition), except that it was not possible for any of the things that are and [that] are known/recognized by us to have come to be without there being initially the being of the things from wich the kosmos is composed, both the limiting [things] and the non-limited [things]. And since these principles made the beginning being neither alike (OR: like, same) nor of the same kind, it would have been impossible for them to be ordered (i.e. put into an order), if harmony did not come follow, in whatever way this came to be. The things that were alike/like/same and of the same kind, on the one hand, did not have any need of harmony, but the things that were unlike and not of the same kind and not of equal order, on the other hand - it was necessary for those things to be enclosed together by harmony, if they are to be held together in a kosmos.
(The rest of fr. 6 gives numerical principles for musical harmony, as at McKirahan pp. 92-93.)
fr. 8. The one is the beginning of all things.
fr. 11. (The first few lines of this fragment concern the "decad" or group of the first ten numbers; see McKirahan 93 for the basic idea.) Philolaus goes on:
For the nature of number is able to give (OR: suited to, related to) recognition/judgment and able to lead and to teach to everyone in what is puzzling and unknown/unrecognized. For none of the things (matters, affairs) would be clear to anyone either in/of itself or in how they are [related] to one another, if there were not number and its being (OR: what is proper to it). Now this (i.e., number) fitting (accommodating? attuning?) all things throughout (OR: in accordance with) soul by means of sense-perception, makes all things known (OR: knowable) and agreeable with one another according to the nature of the gnomon(2), making them corporeal (? bodies?) and dividing each of the things, both the limiting and the non-limited, separately with respect to their accounts (OR: proportions, measures).
And you may see the nature and power/capability of number prevailing not only in superhuman (daimon-related) and divine matters/affairs/things, but also in all human deeds and words/accounts everywhere, throughout arts and crafts/skills and music.
The nature of number and harmony does not admit of the false at all; for it is not proper (related) to them. The false and ill-will are of a nature to belong to the non-limited and unconceiving (unconceived) and non-rational (unreasoning, unreasoned).
The false does not in any way breathe on (favor? inspire?)
for the false is opposed and
hostile to the nature of number, and truth is proper (related) to
of the same nature as the
family of number.
Philolaus' account of what is might be represented something like this:
1. Your text focuses on Aristotle's reports about Pythagoreans, reports where Aristotle gives the Pythagoreans' opposing principles as "limited" (peperasmenon) and "unlimited" or "non-limited" (apeiron). But the diverse sources for Philolaus give Philolaus' opposing principles as "limiting" (perainonton) and "unlimited"/ "non-limited" (apeiron). Possibly there were differences among Pythagoreans, or possibly Aristotle has made some unannounced inference.
2. Remember the gnomon from our
halcyon days with Thales and Anaximander? Right. The
gnomon was a device that marks off right angles, like a
carpenter's square; it was used in
building, astronomy, time-keeping (one can set it up as a
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