PYTHAGOREANISM, THE ELEATICS, EMPEDOCLES
I. The Italian Philosophers
A. Pythagoras and Pythagoreanism
1. General
a. While there is little reliable information on
Pythagoras, there is some substantial
information on 5th century Pythagoreans (who
consituted an organized community).
b. There are still people today who identify
themselves as Pythagoreans--in their minds it
is religious philosophy and is merged with
the religious side of Platonism. [Note: these
are not academic philosophers, at least
European/American ones.]
c. Pythagoras
(1) Despised by some, admired by others
(2) Emigrated from Samos to Croton in Italy
(3) Teaching on reincarnation--frag. 260
(4) Founded a cult
(5) His brotherhood exercised political
power in Croton (frag. 272)
(6) He worked miracles (frag. 273)
(7) "Acusmata" (frags. 275-6)
(8) Number and harmony--the tetractys
(pattern we know as the arrangement of
bowling pins) [frag. 277]
(9) Immortality, reincarnation, reward, and
punishment [frag. 284]
d. The Fifth Century Pythagoreans [discussed in
Chapter XI].
(1) Philolaus' belief in unlimiteds and
limiters as principles [frags. 424-26,
429]
(2) Aristotle's principal account--the
Pythagoreans believe that the substances
of things are numbers. [frag. 430]
(3) The limited and unlimited, square and
oblong numbers, and the table of
opposites [frags. 437-438]
B. The Eleatics--Parmenides and Zeno
1. Both appear as characters in Plato's Parmenides
2. The introduction to that dialogue is considered by
Schofield to be the most reliable evidence for
details of their lives--that Zeno was the student
and beloved of Parmenides and that he wrote a book
defending Parmenides' views.
3. Parmenides' poem
a. Division into what concerns objects of
knowledge vs. what concerns objects of
sensation
b. Argument of part concerning knowledge
(1) We may distinguish appearance and
reality--what seems to be and what is.
(2) What is known is; what is sensed seems
to be.
(3) What is is, and cannot not be.
(4) There are two ways of error--that what
is is not, and that what is both is and
is not--the latter way is that on which
"mortals wander, knowing nothing."
(5) What is is not what was, or it would not
now be--nor is it what is to come for
the same reason. [This seems to depend
on seeing the past tense as referring
only to the past as opposed to something
continuing into the present.]
(6) Undivided (i.e., one, not many) and
equally present wherever it is.
Otherwise it would be not itself or not
like itself.
(7) Immobile and changeless. Otherwise it
would differ from itself.
(8) Perfect. For imperfection implies a
negation of self.
c. Part concerning opinion: a cosmology similar
to that of the Ionians, which are based on
accounting for the cosmic distribution of
sense qualities--hot, cold, wet, dry, heavy,
light, etc.
d. Significance of Parmenides
(1) Plato and Aristotle accepted his sharp
division between the objects of
knowledge (thinking, or noesis) and the
objects of sensation. Descartes also
made much of this distinction,
asserting, as did Plato, that sensation
was unreliable.
(2) Most philosophers who thought they were
doing metaphysics (as opposed to the
"anti-metaphysicians") have felt that
Parmenides must be taken into account.
(3) Plato answered Parmenides' monism by
distinguishing absolute non-being from
difference (Sophist).
(4) Aristotle elaborated on this with his
theory of categories.
4. Zeno
a. Antinomies (paradoxes--a paradox is an
apparent contradiction)
(1) Regarding plurality
(a) The many are both limited and
unlimited. The many are just as
many as they are, and thus limited
(for what can be numbered is
limited). But since between any two
of them there is a difference,
which is something, and so between
this difference and the thing there
is another difference, etc., the
many are infinitely many.
(b) The many must be small and large
(as a totality). Since each is
self-identical, it can have no
parts, and thus is unextended. But
the totality of unextendeds is
likewise unextended. But likewise
each of the many must be extended
[possibly because otherwise they
could all be in the same place?].
But between each and the next there
must be a difference or boundary,
which is likewise extended. Thus
there are an infinity of extended
things, which form an infinitely
large totality.
(2) Regarding motion
(a) The Stadium. A stadium cannot be
traversed, because that would
require an infinity of tasks--
reaching the halafway point, but
before that, reaching the halfway
point to that, etc.
(b) The Achilles (the most famous). A
variant on the Stadium. Suppose a
race between (the proverbially
swift) Achilles and a (proverbially
slow) tortoise. Suppose that the
tortoise is given a head start.
Then Achilles can never catch the
tortoise because he would have to
accomplish an infinity of tasks--
reach the tortoise's starting
position, reach the position the
toroise had reached at that point,
etc.
(c) The Arrow. The moving arrow is at
rest. The arrow occupies a space
equal to itself in extent, and
whatever does so is at rest.
(d) The Moving Rows. In the same time,
the row of B's advance twice as far
among the C's as omong the A's (the
A's are at rest, the B's and C's
are in motion). The interpretation
of this is difficult (see below).
b. A comprehensive interpretation of the four
antinomies of motion which Schofield rejects-
-
(1) Either space is infinitely divisible or
not
(2) If so, then the Stadium and the Achilles
prove that motion is impossible
(3) If not, then the Arrow and Moving Rows
show that motion is impossible--
interpretaion of the Moving Rows on this
view (with terminology borrowed from the
Islamic occasionalists): if the A's
represent space atoms, and the B's and
C's are both moving at a velocity of one
space atom/time atom, then the first C
passes the first B without ever having
been at the first B. [Note: the Islamic
occasionalists accepted such paradoxical
conclusions.]
c. Schofield's interpretation of the Moving
Rows--it casts doubt on the distinction
between motion and rest by showing motion
(velocity) to be relative.
C. Empedocles of Acragas
1. General
a. Associate of Parmenides and the Pythagoreans
b. Wrote books On Nature, Purifications, and
Medicine
2. On Nature
a. Knowledge
(1) Sense knowledge is limited, but possible
(Frags 342-43)
(2) Knowledge is powerful (Frag. 345)
b. Cosmic cycle
(1) The four roots (Frags 346-7) with Gods
correlated with elements a la
Theophrastus
(a) Zeus (fire?)
(b) Hera (air?)
(c) Hades (Aidoneus) (earth?)
(d) Nestis (water)
(2) Eternal cycle of separation (i. e., like
collected with like) by Strife
alternating with combination (like being
mixed with unlike) by Love (Frags. 348-
9; 355-56)
(3) Generation and destruction are nothing
but combination and separation (Frags.
350-354)
(4) The complete dominance of Love: the
cosmos is a uniform, completely mixed
Sphere
(5) The arising of living things: when
Strife has gained complete victory and
the four world-masses are completely
separated, then Love begins to grow and
things begin to become mixed again.
(6) (According to Schofield's
interpretation) the cosmos comes to be
at the end of the cycle of Strife and
the beginning of the cycle of Love. The
world-masses arise as Strife moves
toward complete dominance; the heavenly
bodies arise at the beginning of the
movement of Love (because they involve
mixture of the elements).
(a) Cosmogony Stage 1 (Frags. 365-67)
(b) Cosmogony Stage 2 (Frags. 368-72)
(7) Zoogony
(a) Blood, flesh, and bone arise from
the elements
(b) Evolution through natural selection
in four stages, beginning with
separate organs which then combine
in various unsuccessful and
successful combinations (Frags.
375-382)
(8) Various biological ideas and Aristotle's
attitude towards them
(a) Homologous functions and parts in
different creatures (Frags 383-5) -
- Aristotle approves
(b) Aristotle finds a dilemma in
Empedocles regarding whether Love
or Strife produces natural, as
opposed to unnatural motion
(9) Sense perception and thought
(a) The senses are distinguished by
having differently shaped openings
through which can come the
effluences of the different
sensibles (Frags. 390-1)
(b) Both sensation and thought are of
like by like (Frags. 392-4)
(10) God is not a being like ourselves, but
rather a being of pure thought