The Presocratic Philosophers

I. The Pre-Parmenideans

A. Myth, Philosophy, and Natural Science
B. The Nature of Explanation
C. Proto-Science
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

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 community-forming 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?)

• Progressive replacement theory (August Comte, the "father of positivism" and his modernday successors, e.g., Richard Dawkins and (perhaps) Stephen Hawking)
• Noninteractive parallelism ("Two-truth" 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 proto-explanations 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.

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 principle--the ousia--and 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 t₁ ..... Water (cold/moist) at p at t₂ ...... Air (hot/moist) at p at t₃ ...... Fire (hot/dry) at p at t₄

• 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 whatever-it-is 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.)
 

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 full-fledged 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 non-being 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 I--which 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.

Given the impossibility of change, Parmenides and Melissus infer the following attributes of Being (notice the differences):
 
• Parmenides: One, Uncreated, Imperishable, Timeless, Immutable, Perfect, Spherical
  
 
• Melissus: One, Ungenerated, Incorruptible, Everlasting, Immutable, Homogeneous, Unlimited in Extension

You might be wondering about the attribute "One" (as opposed to Many).  Stay tuned for Zeno.

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 large--which is absurd--and that, worse yet, there are many infinitely large real entities--which 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 magnitude--which 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 false--or (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 all--which 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 one-dimensional version of the argument according to which there is just one infinitely long line and not a plurality of finite line-segments.)  Sometimes student critics of Zeno have claimed that since the infinitely many equal and non-overlapping parts have 'only' infinitesimal magnitude, the putatively finite line-segment 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 re-formulating 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 anti-plurality argument:
  
  Take a putatively finite line segment AB.  Let a Zeno-division D of AB be a division of AB that results in n equal non-overlapping 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 Zeno-divisible is just to say that for any conceivable Zeno-division Dx of AB there is another conceivable Zeno-division Dy of AB which results in a greater finite number of parts with a smaller positive magnitude.
  
  Now notice that any conceivable Zeno-division yields a finite number of non-overlapping 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 non-overlapping 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 fine-grained 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 non-denumerable 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

Preliminary definitions:

• 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 half-units 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:
 
A-------------------------------------------------B

(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 space-units or time units.

• Scene 2: Now imagine them aligned thus at a later time t*:

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 unit--there 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 "macro-objects" 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 do not and (presumably) 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 else -- every non-basic entity -- is a mere aggregation (a heap, if you will) of really real entities having "accidental unity," with no intrinsic principles of unity or activity.

 

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 in its own right" or, as the Latin Scholastics put it, "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 "bottom-up."
  
  

• Empedocles:
 
• The four elements--i.e., instances of them--are 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 ("man-faced 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?)
  
  

•  The problem: Properties such as life, sentience, sensible qualities, intelligence, and various causal powers had by non-basic 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 macro-entities 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 macro-entity one or more particular kind of seed dominates.
• Oh, by the way, natural processes are governed by Nous. (See Phaedo 97B-98D)

 
(Shades of Augustine and Leibniz)