The Presocratic
Philosophers
I.
The PreParmenideans
A. Myth,
Philosophy, and Natural Science
B. The Nature of
Explanation
C. ProtoScience
D. Thales, Anaximenes,
Heraclitus,
Xenophanes
E. Anaximander's
Embarrassing
Question
F. Pythagoras
G. Philosophical Issues
II.
The Eleatics
 A. Parmenides
 1. Appearance and
Reality
 2. Impossibility of
Change
 B. Parmenides
and Melissus: The
Attributes of Being
 C. Zeno
 1. Argument against
plurality
 2. Arguments against motion
III. The Response to
Parmenides
 A. The
Problematic
 B. The
Reductionist Response
 1. Empedocles
 2. The Atomists
(Democritus, Leucippus)
 C. Anaxagoras's
"Advance"
IA.
Myth, Philosophy and Natural Science
 Myth:
A communityforming narrative (story)
concerning
some
or all of the following "big questions" about being and goodness: the
origins
of the universe (cosmogony); the nature of the universe (cosmology) and
of the entities contained therein; the origin and nature of human
beings;
the good for human beings and the ways to attain it; the meaning (if
any) of suffering and death. Always involves a
"liturgical calendar" of feasts and celebrations that mark cycles in
nature and in the history of the community, and hence it always or
often
involves something like a "priesthood."
 Philosophy:
A systematic inquiry, proceeding (i)
by
way of dialectic
and, as it were, diagrammatic reasoning, from what is better known to
what
is less known concerning the "big questions", and then (ii) by way of
descent
from general principles to particular conclusions (wisdom). Does not by
its nature involve liturgical practice, though this can be grafted on
to it. It might nonetheless involve a "way of life" because of the
systematic doctrinal and moral formation given to the adherents of
particular philosophical communities.
(Note: Systematicity implies, among other things, (i) an emphasis on
internal consistency and overall coherence, (ii) careful ordering of
premises
and conclusions, proceeding from what is more evident to what is less
evident,
(iii) multiple conceptual distinctions, (iv) completeness, and (v) a
careful
account of the different types and degrees of epistemic warrant.)
 Natural
Science: A systematic
theoretical and
experimental inquiry
into the principles and operations of nature. It does not of itself
involve a full "way of life," though it can, as a practice, be embedded
in such a way of life. (Question: Does (or can) natural science address
all the questions that myth and philosophy have sought to answer? If
not, does this show the limitations of inquiry in the sciences, or does
it instead show that human beings should refrain from asking certain
questions, or what?)
How are myth, philosophy, and natural science related to one another?
Historically,
there have been three views about this:
 Progressive
replacement theory (August
Comte, the
"father of positivism" and his modernday successors, e.g., Richard
Dawkins and (perhaps) Stephen Hawking)
 Noninteractive
parallelism ("Twotruth" or
"many
truth" theories)
 Integrationism (some forms of
reductionism;
Plato;
Catholic intellectual
tradition)
IB.
The nature of explanation
(Warning: Everything to
be said here about the Presocratics
is a
reconstruction based on flimsy evidence. Still, the reconstruction may
be more interesting philosophically than some of the Presocratics
themselves
were!)
In the
Presocratics we find protoexplanations
of natural
phenomena
according to two sorts of principle, which we will call by the names
Aristotle
gives them:
 1. The material
principle: that which is really
real (ousia)
and is acted upon to produce effects.
 2. The efficient
(or effective
or moving or agent)
principle:
that which acts
to
produce effects.
IC.
Protoscience
Given these types of explanation, the first natural philosophers
generally
employed the following explanatory schema, each adding his own peculiar
twists:
 Material
principles: Given the
fundamental or
"primary" qualities,
which come in two pairs of opposites, viz., hot/cold and moist/dry,
there
are four elements out of which all minerals are composed, each having
its
own set proportion of elements; and from the minerals all other
corporeal
entities in general are formed:
The four elements are:
 fire
= hot + dry
 air
= hot + moist
 earth
= cold + dry
 water
= cold + moist
 Efficient
principles: Changes in the world
are
produced by two active
(or agent) forces, viz., an attractive
force (such as Love or
Condensation)
and a repelling
force (such as Strife or Rarefaction). (Later, Aristotle will
attribute active causal powers and agency to all substances, i.e.,
things with natures.)
ID.
Thales, Anaximenes, Heraclitus,
Xenophanes
According to the "popular" interpretation (due to Aristotle but not
to scholars), each of these philosophers tried to reduce the many
to
the
one by positing one of the "elements" as the
really real material
principlethe ousiaand
claiming that all the other elements are, appearances to the contrary,
simply permutations of that really real one. Interestingly, each chose
a different one of the four  or, at least, that's how Aristotle sees
it.
 Thales:
Water
is the really real.
("Everything
is
full of gods.")
 Anaximenes:
Air
is the really real.
(Permutations
result from condensation
and rarefaction) *(see note below)
 Heraclitus:
Fire
is the really real.
("Everything
flows.")
 Xenophanes:
Earth
is the really real.
(Protested
against theological
anthropomorphism.)
IE.
Anaximander's Embarrassing
Question
Anaximander asks: How in the
world can fire (hot + dry) be
water
(cold + moist)? Or how can fire come
from water if everything is water?!
 In a transformation
we might have a sequence such as:
Earth (cold/dry) at
place p at time t_{1}
.....
Water (cold/moist)
at p at t_{2}
...... Air (hot/moist) at p at t_{3}
......
Fire (hot/dry) at p at t_{4}
 But what is it that
perdures, at one time having the
qualities of water
and at a later time having the qualities of fire, so that we might call
this a genuine change? That
whateveritis would be the really
real,
which neither comes into nor passes out of existence, but receives and
loses the primary qualities. (Note: the primary qualities cannot
themselves
be the basic entities, since they cannot be the subjects of one
another,
and, in general, they themselves seem clearly to require some subject
to
inhere in and characterize.)
Anaximander's
solution: The really real, which
perdures through
every transformation and underlies the primary qualities, must be
wholly
indeterminate and must of itself lack all qualities. It is the Indeterminate,
the
Unlimited, the Apeiron.
*Note on Anaximenes:
In fairness to Anaximenes, he was historically a student of
Anaximander and so this raises the issue of how he might have thought
he escaped the latter's argument. Here's one way:
Abandon
the idea that each of the four elements is a permutation of the four
qualities hot/cold and dry/moist.
Instead, take air to be the primitive really real
stuff and just forget about the four qualities. Then, one
could
attribute a natural state to air and three nonnatural states,
differing from natural air by their denseness or rarity, that
correspond roughly to fire (less dense than air in its natural
state) and to water and earth (both more dense than air in its
natural state). This, of course, raises lots of other
questions
 Why choose air as basic? Does it come in basic spatial
units
(or, say, mass units) capable of participating in condensation and
rarefaction? And so on.
IF.
Pythagoras (some of this may derive primarily from Philolaus, a fifth
century BC Pythagorean)
Pythagoras posited two abstract and complementary material principles:
The Unlimited
(the many) and the Limited
(the one). All
entities
can be thought to result from the Unlimited's
being limited or
determined
to some definite shape. This is best thought of mathematically. Unity
limits
plurality and gives it determinate shape. (For instance, the soul is
the
harmony of the body.) Since each number is associated with a
determinate
shape, we can think of things as being numerical and of mathematics as
the key to understanding the world.
Note: With
the Pythagoreans we have the first known
philosophical
school or sect in the ancient world. Here we see philosophy
not
just
as a theoretical enterprise but as a
way of life to which
seekers
after wisdom attach themselves, at first as 'catechumens' and then as
fullfledged
members.
IG.
Philosophical Issues
 Naturalism and
Supernaturalism (Think of the Iliad.)
 Reductionism (Is
everything merely the manifestation of
some simple
sort of entity
or set of entities? What about your mother?)
 Process Metaphysics
vs. Substance Metaphysics (Are the
basic entities
perduring
continuants or events?)
 Reality and
Mathematics (Why should mathematics be the key
to
understanding
the physical world?)
 Anthropomorphism in
Theology (How do we get knowledge of
the divine?)
IIA.
Parmenides
 1. Appearance
and Reality
 The Poem: The Way of
Seeming vs. The Way of Truth
 The philosopher
challenges empirical science. (Is common
opinion a
constraint
on philosophical speculation?)
 The
unintelligibility of nonbeing or nothingness
 2. The
Impossibility of Change: An
argument
(1) During interval I
Socrates changed from being pale
to being tanned. (assumption
for reductio ad absurdum)
(2) If (1)
is true, then before I,
tanned
Socrates was
either (a) something or (b) nothing. (obviously
true exclusive
disjunction)
(3) If (a),
then there was no change during I.
(Principle
of inference: What
already is cannot come to be.)
(4) So it
is not the case that before I
tanned Socrates
was something. (from 1 and 3)
(5) If (b),
then tanned Socrates was nothing before I
and
something after Iwhich
is absurd. (Principle of inference: Something
cannot come to be from nothing)
(6) So it
is not the case that before I
tanned Socrates
was nothing. (Whatever
entails an absurdity is itself absurd)
(7) So it
is not the case that before I
tanned Socrates
was something, and it is not the case that before I
tanned
Socrates
was nothing (from 3 and 6)
Therefore,
Socrates did not change during I.
(1, 2,
7, disjunctive modus tollens)
But this is a perfectly general argument that can be applied to any
putative
change. Therefore, there is no genuine change in the world. All
apparent
change is an illusion, a mere appearance.
IIB.
Parmenides and Melissus: The
Attributes
of Being
IIC.
Zeno
1. Argument
against plurality
(1) There are many (i.e., more than one) real entities or beings (ousiai).
(assumption
for reductio ad absurdum)
(2) If (1), then
either (a) each of the many
entities has positive
magnitude or (b) each of the many real entities lacks positive
magnitude
or (c) some real entities have positive magnitude and some lack
positive
magnitude. (exhaustive
disjunction, necessary truth)
(3) If (a), then each
real entity has two halves with
equal positive
magnitude, and each of these halves has two halves with equal positive
magnitude, and each of these halves has two halves with equal positive
magnitude ..... ad infinitum,
with the result that each real
entity
has infinitely many parts with equal positive magnitude, none of which
is part of another, and so is infinitely large. It follows that each
real entity is infinitely largewhich is absurdand that, worse yet,
there
are
many infinitely large real entitieswhich is obviously false, since
there
cannot be more than one infinitely large being (assuming that distinct
bodies cannot be in exactly the same place at the same time).
(4) So (a) is not the
case. (from 3 via modus tollens)
(5) If (b), then no
number of real entities will
constitute a thing
with magnitude, and so no being whatever has any positive
magnitudewhich
is false, since obviously some being has positive magnitude.
(6) So (b) is not the
case. (from 5 via
modus
tollens)
(7) If (c), then
either (i) there are many infinitely
large entities
(from 3)which is obviously falseor (ii) if there is just one real
entity with positive magnitude, then exactly one entity is infinitely
large
(from 3) and every other entity has no positive magnitude at
allwhich
is likewise obviously false (isn't it?).
(8) So (c) is not the
case. (from 7 via modus tollens)
(9) Therefore, the
consequent of (2) is false (from
4,
7, and 8)
(10) Therefore, the
antecedent of (2) is false, and it is
not the case
that there are many (i.e., more than one) real entities or beings. (2,
9, modus tollens)
(11) But, of course,
there is something. (obvious)
Therefore, there is
just one real entity. (from 10
and
11)
Possible
replies:
 The
response of just about everyone else:
The
problem is with premise (3). But just what is the problem?
(In what follows I'll use a onedimensional version of the
argument according to which there is just one infinitely long line and
not a plurality of finite linesegments.) Sometimes student
critics of Zeno have claimed that since the infinitely many equal and
nonoverlapping parts have 'only' infinitesimal magnitude, the
putatively finite linesegment we began with is indeed finite.
On
the surface, this seems like cheating. One wants to know
whether
each of these infinitesimal parts has positive magnitude or not.
If yes, then Zeno is right; if no, see premise (5), and Zeno
is
right again.
However, I
think I have a way of reformulating this reply
to Zeno that
allows one to use the language of infinitesimals as a sort of shorthand
and that counts as a sort of Aristotelian reply to the
antiplurality argument:
Take a putatively finite line segment AB. Let a Zenodivision
D of
AB be a division of AB that results in n equal
nonoverlapping parts of finite magnitude m (expressed as a
fraction of 1), where n
is finite and m
is positive and nm
= 1. To say that AB is infinitely Zenodivisible is just to
say that for any conceivable Zenodivision Dx of AB there is
another conceivable Zenodivision Dy
of AB which results in a greater finite number of parts with a smaller
positive magnitude.
Now notice that any conceivable Zenodivision yields a finite
number of nonoverlapping parts with equal positive
magnitude.
That's the only sort of division there could be. (This is why I call
this reply 'Aristotelian'.) There is no conceivable division that
yields infinitely many parts of the sort in question. We
use language like 'infinitely
many parts of infinitesimal magnitude'
as simply shorthand for the fact that AB is infinitely divisible in the
sense defined above. So it is a mistake for me to ask you
whether
or not each of these infinitesimal parts has positive magnitude, since
you are not claiming that there are any conceivable parts that are
infinitesimal. Rather, all you are saying is this:
Divide
AB into equal nonoverlapping parts that are as small as you please;
the result of multiplying the number of parts by the magnitude of each
will still be 1 because, in effect, you will still have finitely many
such parts.
Zeno's
reply, presumably, is that there just is an actual infinity of parts of
the sort in question already actually present in any material whole.
So there! After all, after any conceivable division
you
make (either really or in your imagination), there's a more
finegrained division to be made. But the parts are always
already there; the division only makes them manifest to us.
In
addition, the Aristotelian gambit has potentially strong consequences
for the philosophy of mathematics, where it tends to steer one toward the
rejection of the actual infinite and hence to a denial of the
legitimacy of certain parts of mathematics dealing with infinities.
 Adolph
Grünbaum's response:
(3) is fine. That is, if you have infinitely many parts with
equal positive magnitude, then you have an infinitely long line and
Zeno wins. The problem with the argument is premise
(5).
Even though a denumerable
infinity
of parts without positive magnitude (in this case, points)
cannot
yield anything with positive magnitude, it's a different story with a nondenumerable infinity
of parts without positive magnitude.
Who's right? Anyone? Hmm, that's
a toughie. Each reply insists that the other is wrong, indeed
obviously
wrong.
 2. Two
arguments against motion
 Space (time) is dense
= Space (time) is
infinitely
divisible,
so that between any two points there are others.
 Space (time) is discrete
= Space (time)
consists of
basic
units with some (perhaps very small) minimal possible magnitude, and
each
basic unit is immediately adjacent to other basic units, with no basic
units in between them. (So there are no halfunits of space
and
time
among the basic units.)
a. The Stadium (aka The
Dichotomy)
We can take the first argument to be directed against the claim that
there is real motion or change in the world and that space and time are
dense.
Imagine a race course that stretches from point A to point B, thus:
AB
(1) To reach point B
from point A, a runner must
successively reach
(or pass over) infinitely many points (or finite lengths) ordered in
the sequence 1/2, 1/4,
1/8,
1/16, 1/32 ...... . (In other words, the runner must get halfway to B,
and so must first get halfway to halfway to B, and so must first get
halfway
to halfway to halfway to B, etc.)
(2) But it
is impossible to complete the task of
successively
reaching (or passing over) infinitely many points (or finite lengths),
ordered one after
another.
(3) Therefore,
the runner cannot reach B!!!
(4) But
this is so, no matter how small the distance
is between
A and B, for there are just as many points (or finite lengths) between
A and B no matter
how
far apart they are from one another.
Therefore, no runner
can traverse any space at all. In
fact, no corporeal
object can traverse any space at all. Therefore, there is no motion,
appearances  and
that's all they
are  to the contrary!!
Possible
replies:
How much time does the runner have to go
from A to
B? Isn't this time similarly infinitely divisible?
But
suppose it is; then Zeno has himself a neat little argument to show
that nothing can persist in existence through any length of time!
Does the runner have to 'rest'
at every point
(or after traversing every finite length) along the way? If
not,
are the points (or finite lengths) actual or only potential?
b. The Moving Rows (aka
The Stadium)
We can take
the second argument to be directed against
the claim
that there is real motion or change in the world and that space and
time
are discrete.
 Scene
1: Imagine that there are three
rows of
(teeny
weeny) chariots
aligned as below at a given time t,
that each of the chariots
occupies
one basic space unit, and that the (putative) motion of the B's and C's
is at the rate of one basic space unit per basic time unit. Remember:
There
are no half spaceunits or time units.
....AAAA....
BBBB>
<CCCC
 Scene
2: Now imagine them aligned thus
at a
later
time t*:
AAAA
BBBB
CCCC
Embarrassing question: How many
basic time
units
have elapsed
between t
and t*?
 The first obvious
answer is 2,
since the first
B and the first
C
have each passed two A's.
 The second, just
as obvious answer, is 4,
since
the first B has
passed 4 C's and vice versa.
 Therefore, 2
= 4!!!! So the assumption that
the
B's and the C's
are in motion leads to an incoherence. (And please do not tell me that
a B passes a C in 1/2 of a basic time unitthere
are no half basic
time units in discrete time!!!!)
Possible
replies:
So what? All this
argument shows is that motion in discrete space is quirky ..... After
the first moment, the first B is lined up with the second C
without ever having passed the first C, and after the second moment,
the first B is lined up with the fourth C without ever having passed
the third C! Hmmm .......
A pertinent question:
Suppose that you personally
cannot
refute Zeno's arguments, and that you know that commentators disagree
about
what, if anything, is wrong with the arguments. Should
you
stop believing in motion? Can
you stop believing in motion?
Should
philosophers, as is sometimes claimed, follow an argument wherever it
leads
them? A pertinent question is: What starting points
or
first
principles is it correct (or at least reasonable) to begin with?
IIIA.
The Problematic
 Qualified
vs. Unqualified Change: All the
respondents
we are looking
at here agree with Parmenides that there is no unqualified change. That
is, no basic or really real entities (ousiai)
either come into
existence
or pass out of existence. There is change, but all of it has to do with
changing arrangements of or relations among the basic
entities.
Familiar
"macroobjects" are thus not really real or basic entities.
 Pluralism
vs. Monism: All the respondents
agree
that
that there
is a plurality of basic or really real entities. (Here they disagree
with
Parmenides and Zeno, even though they cannot provide a really
convincing
reply to Zeno's argument.) These entities are eternal (or
everlasting),
ingenerable, incorruptible, etc.
 The basic entities, as
conceived by the respondents, are
thus little
Parmenidean
"one's"it's just that there are a lot of them. And everything
elseevery
nonbasic entityis a mere aggregation (a heap, if you will) of really
real entities having "accidental unity," with no intrinsic principles
of
unity or activity.
IIIB.
The Reductionist Response
Reductionism is (roughly) a position according to which:
 animals (including
human beings), plants, minerals and
any other
entities
distinct from the really real entities are mere aggregations of the
latter
without their own proper principles of unity or activity, and so they
would
not show up on a list of what "really exists" or "exists per
se";
 all the genuine
properties of the aggregates are either
properties of
the
basic entities or strictly reducible to the properties of the basic
entities;
and
 any putative
properties of the aggregates that are not
reducible to the
properties of the basic entities are merely appearances and not
real.
Another way to put this is: There are no "emergent"
properties, and all explanation is "bottomup."
 Empedocles:
 The four
elementsi.e., instances of themare the only
really real
entities
or ousiai.
 The eternal cycle of
change is due to the forces of love
and strife
randomly acting on the elements ("manfaced ox progeny").
 Question: Are genuine
mixtures possible on
Empedocles's theory?
Seemingly not, since a genuine mixture is a new entity in which the
composing
elements exist no longer in their own right but only through the powers
with which they endow the composite mixture.
 The
Atomists (Leucippus and Democritus):
 There are infinitely
many invisible particles (atoms),
and these are
the
really real entities.
 The atoms are
indivisible, imperishable, eternal,
homogeneous. (Sound
familiar?)
 The atoms have
shape, motion, and weight, and differ from
one another
in
these properties.
 Motion takes place
in the void.
 Sensible qualities
(color, taste, sound, etc.) are mere
appearances.
(What about mental properties?)
IIIC.
Anaxagoras's "Advance"
 The
problem: Properties such as
life,
sentience, sensible
qualities, intelligence, and various causal powers had by nonbasic
entities
are not
reducible to the properties of the elements or the
atoms
and are not
mere appearances.
 Two
possible solutions:
1. Acknowledge that animals, plants, etc. are really real and try to
show how unqualified change is after all possible. [Aristotle]
2. Retain reductionism, but conceive of the basic entities in such
a way that they have the above properties. [Anaxagoras]
 Anaxagoras's
solution:
 The really real
entities are the seeds.
 There are as many
kinds of seeds as there are natural
kinds (including,
e.g., armadillo seeds, red oak seeds, etc.), and the seeds have in some
way or other all the properties of the macroentities of which they are
seeds.
 Any given chunk of
the universe, no matter how small,
contains every
kind of seed ("Everything contains everything")and "matter" is
infinitely
divisible.
 In every
macroentity one or more particular kind of seed
dominates.
 Oh, by the way,
natural processes are governed by Nous.
(See Phaedo
97B98D)
(Shades of Augustine and Leibniz)
