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C H A P T E R  2



It never ceases to surprise me at the infinite capacity of the human mind to resist the introduction of useful knowledge." Thomas Raynesford


Thales, Anaximander, and Anaximenes



(624-545 BCE)
The Abyss



1.         Water is the basic nature of reality. (material monism)

2.         All things are full of gods.



1.       He was the first to ask: what is the basic nature of reality?

He took the step from mythology to science and philosophy.


2.         In 1925 we thought everything was made of hydrogen which is two thirds water.





Born Phoenician

Miletus citizen

Slavery existed there.

The poor murdered the wives and children of the rich.

The rich burned the poor alive.


In May 28, 585 BCE Thales was the first to predicted a solar eclipse. It threw the war between the Lydeans and Persians into confusion.


This picture is the negative of the original photograph of the 1919 solar eclipse that  confirmed Einstein's theory of general relativity.

Thales diverted a river, so an army could pass.

Measured the Pyramids & distance of ships at sea.

Called the absentminded professor.

Cornered the olive market.


Arthur Koestler said, ‘‘The history of ideas is filled with barren truths and fertile errors.’’





     On Nature


1.      Fire cannot be explained by water.

2.      He was the first to ask: what is the cause of all things?

3.      The cause of all things cannot be a thing.

4.      The Apeiron is the cause of all things. (rationalism)

5.      The earth is an unsupported stationary sphere.

6.      There are unlimited worlds existing in unlimited time.

7.      The first creatures were generated in moisture.

8.      Humans evolved from lower animals.

9.      He invented the sundial.




3.      If the cause of all things were an element, it would contradict itself, and it would require a cause.

4.      To Apeiron is boundless, unlimited, one, eternal, and indestructible.


All things arise out of the Apeiron, and all things return to it. It is a reservoir of properties.


They return according to justice.

Absolute justice is living all possible scenarios.


7.       At one time, we resembled fish, and were cast ashore.


Freaks are cast aside, and form subspecies:

Heraclitus said, "The Ephesians would do well to hang themselves, ... for they have cast out Hermodorus, the best man among them, saying: 'We will have none who is best among us; if there be any such, let him be so elsewhere and among others,'"  from the History of Western Philosophy by Bertrard Russell.






1.         To Apeiron is not a thing.

2.         That which is not a thing is nothing.

3.         Something cannot arise out of nothing; therefore,

4.         To Apeiron cannot be the cause of all things.

5.         Air/soul is the basic nature of reality. (animism)

6.         Gases are expanding air. Solids are condensed air.

            Expansion causes heat. Condensing causes coldness.

7.         Diogenes of Apollonia was a student of Anaximenes.



 3.      We accepted the belief that reality can not be created out of nothing, and it cannot perish into nothing. This lead modern physics to the belief in the conservation of matter.




1.         To Apeiron is not a thing.

2.         That which is not a thing is nothing; therefore,

3.         To Apeiron is nothing.


1.         To Apeiron is nothing.

2.         Nothing cannot cause something to exist; therefore,

3.         To Apeiron cannot cause something to exist.


1.         To Apeiron cannot cause something to exist.

2.         What cannot cause something to exist cannot be the cause of all things; therefore,

 To Apeiron cannot be the cause of all things.

Perelman, CH.: 1966, An Introduction to Philosophical Thinking, New York, Random House, Inc., p9.






1.      Philosophy is the love of Wisdom.

2.      Math is the language of the Universe. (form over matter)

3.      The soul is immortal.

4.      We can only escape reincarnation  by purifying the soul.




Born on the Island of Samos.

He migrated to Croton Italy.

He founded a religious sect that took a vow of secrecy.

He discovered the Pythagoream theorem.

The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).






(570-478 BCE)



1.         There is no certainty. (the beginning of epistemology)

2.         God is one, unchanging, and eternal (monotheism).

3.         God is total mind and thought.

4.         God's awareness and knowledge are instantaneous.

5.         God thinks the universe into motion.




1.         We have probable knowledge.




Born in Colophon

Migrated to Italy 

Taught Parmenides

Banished to Sicily.

Lived to an old age. 


Philip Wheelwright, in The Presocratics p.31-39, tells us that Xenophanes was the first critical theologian in Greece. He believed that God is one, and God is completely different from humans. Weelwright declares that Xenophanes was interested in theology. He was not interested in metaphysics. He was a monotheist. He was not a metaphysical monist. Wheelwright says, "He does not say that all being is one and that plurality is impossible...; he confines himself to proclaiming the doctrine of God as single and transcendent," (31). Parmenides was a metaphysical monist.




Diogenes Laertius: 

Xenophanes holds that God is spherical in substance, and that he is unlike men; for the whole of him sees, the whole of him hears, he does not breath, he is totally mind and thought, and is eternal.


Simplicious Commentaria:

Theophrastus says that Xenophanes of Colophon, teacher of Parmenides, declared that the first principle is one, and that What Is is one and all-embracing, that it is neither limited nor unlimited, and neither moving nor at rest.




Xenophanes ... had skeptical doubts about everything except his own dogma that all things are one, and that this One is God, who is limited, rational, and immovable.

Pseudo-Plutrarch Stomata:


Xenophanes ... denied that there is any coming-to-be or perishing, declaring that All is always the same. For if it had come-to-be it could not have existed before that moment when the coming-to-be occurred; but on the other hand not-being could not have come-to-be, because not-being has no power to bring anything about. Declaring that our senses are deceptive he even challenges the authority of reason itself.  




Xenophanes ... was the first to declare that nothing can be grasped with certainty, arguing: "Even if someone happened by chance to say what is true, he still could not know [whether he was right or not]; yet all men have the illusion of knowing" [Fr. 10]. He says that nothing comes-to-be or perishes, that nothing is moved, and that the universe is one and changeless. God is eternal and one, homogeneous throughout, limited, spherical, and with the power of perception in all his parts. 






     On Nature


1.         Knowledge comes from experience.

2.         Fire is the basic nature of reality.

3.         Everything is in motion.

4.         Permanence is an illusion.

5.         There are no separately existing things.

6.         Things that change cannot be known.

7.         The universe is all being and all touching.

8.         all things are one - Logos.

9.         Only God has wisdom.



3. "Nothing ever is, everything is always in a state of becoming," (Plato).

"Everything flows and nothing abides; everything gives way and nothing stays   fixed, (70).

"You cannot step twice into the same river ... ," (71).
"It is in changing that things find repose," (71).

"[If strife were to perish] ... all things would cease to exist," (71).

"War is the father of all ... ."             (The Naked Ape)

7. There is no place were there is nonbeing.

8. From out of all the many particulars comes oneness, and out of oneness come all the many particulars, (78).

The one is God, and it has more reality than the many.

"The Logos is common to all. Yet ... men live as if each of them had a private intelligence of his own," (69).

"Although intimately connected with the Logos, men keep setting themselves against it," (74)

Everything is composed out of soul. It is in a constant state of flux. (72)


9.      Pythagoras (6th century B. C. E.) argued; since only God possesses true Wisdom, we can only hope to be lovers of Wisdom. He is the first to define philosophy as the love of Wisdom.


"Wisdom is one ... ," (79).

"Much learning does not teach understanding ... ," (69) 

"Human nature has no real understanding," (74).

"Man is not rational," (74)




Born in Ephesus.

He was a misanthropist.






 Parmenides by Plato


1.         Reason is the proper guide to truth.

2.         What is is.

3.         What is not is not.

4.         Being is one.

5.         Being is unchanging.




2.         Only Being exists; nothingness does not exist.


4.         Is reality one or many?

  Does reality change, or is it static?


The whole is like (not is) a limited sphere. All of its exterior points are equi distant from its center point.  

His student Melissus argued that Being cannot be a sphere because nothingness would have to surround it. Being must be infinite in time and space.




1.       If there is a plurality of things, then nothingness exists.

2.       Nothingness cannot exist; therefore

There is no plurality of things.


1.       If there is movement, then nothingness exists.

2.       Nothingness cannot exist; therefore

There is no movement.


1.            M > N

2.            ~N            /            ~M

3.            ~M                   1,2  mt



1.       If there is movement, then a void exists.

2.       There is movement; therefore

A void exists.


1.            M > V

2.            M             /            V

3.            V            1,2   mp


1.       If there is a plurality of things, then a void exists.

2.       There is a plurality of things; therefore

A void exists.


1.            P > V

2.            P             /            V

3.            V            1,2   mp





Elea was in southern Italy.

He was a pupil of Xenophanes.






(490-430 BCE)





He was 25 years younger than Parmenides.

He invented the reductio ad absurdum to prove Parmenidies' doctrine.

The argued that the belief that there is a plurality of things results in absurdities.



The Paradoxes of Motion


Edward Muybridge


Nude Descending a Staircase
Marcel Duchamp, 1912


The Arrow Paradox

“ If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. ”

—Aristotle, Physics VI:9, 239b5

Zeno abolishes motion, saying "What is in motion moves neither in the place it is nor in one in which it is not". (Diogenes Laertius Lives of Famous Philosophers, ix.72)

Imagine an arrow in flight. At any moment we can say that it is at rest, and it occupies some space. Then when does it move? In any instant of time there is no motion occurring because an instant is a snapshot.


Achilles and the Tortoise

“ In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. ”

—Aristotle, Physics VI:9, 239b15

Achilles gives the tortoise a head start. After some time, Achilles will reach the tortoise's starting point. During this time, the tortoise will have advanced some distance. It will then take Achilles some further time to run that distance. By that time the tortoise will have advanced farther, and then more time still to reach this third point while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.

The Dichotomy Paradox

The argument is called the Dichotomy because it involves repeatedly splitting a distance into two parts. Suppose you want to catch a stationary bus. Before you can get there, you must get halfway there - to its halfway point. Before you can get halfway there, you must get a quarter of the way there. Before traveling a fourth, you must travel one-eighth; before an eighth, one-sixteenth; and so on. This requires that you complete an infinite number of tasks - which is impossible.

This sequence also presents a second problem in that it contains no first distance to run, for any possible (finite) first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even begin. The paradoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, and so motion is an illusion.

Paradox of Place:

"… if everything that exists has a place, place too will have a place, and so on ad infinitum."

Paradox of the Grain of Millet:

Suppose you drop a sack of millet. When it hits the floor, it will make a sound, but if you drop a single grain, it will not make a sound. It could be that the notion of primary and secondary substances was a proposed solution to this paradox.

The Moving Rows:

For an expanded account of Zeno's arguments as presented by Aristotle, see Simplicius' commentary On Aristotle's Physics.

Proposed Solutions:

Aristotle (384 BC−322 BC) remarked that as the distance decreases, the time needed to cover those distances also decreases, so that the time needed also becomes increasingly small. Aristotle's proposed solution for the paradoxes involves distinguishing "things infinite in respect of divisibility" (such as a unit of space that can be mentally divided into ever smaller units while remaining spatially the same) from things (or distances) that are infinite in extension ("with respect to their extremities").

Saint Thomas Aquinas offered the following solution to the arrow paradox: " Instants are not parts of time, for time is not made up of instants any more than a magnitude is made of points, as we have already proved. Hence it does not follow that a thing is not in motion in a given time, just because it is not in motion in any instant of that time."

Peter Lynds argues that instants in time do not exist. An object in relative motion cannot have a determined position. If it did, it could not be in motion.

Another possible solution is to reject the idea that between any two points in space or time there is always another point. Without this assumption there are only a finite number of distances between two points.

Reichenbach points out that the paradox arises from considering space and time as separate entities. Einstein's theory of general relativity states a single space-time continuum.







1.     Perception is the result of particles bouncing, or flying, of of objects, and striking our sense organs. Blue is the result of blue particles.

2.     Empty space, or a void, does not exist.

3.     Reality is a sea of undulating toughing particles.

4.     Life goes through random variations. Advantageous variations survive.








1.         Mind (Nous) is the basic nature of reality.

2.         Nothing comes into being out of nothing.

3.         Objects have a share of everything in them.

4.         All things are present.

5.         Things are infinite in number.

6.         Things are infinite in size.

7.         Stars are distant suns.

8.         The sun is molten stone.

9.         The moon is made of earth, and reflects the sun's light.





He was a teacher and friend or Pericles.

The enemies of Pericles charged, tried, and convicted Anaxagoras for impiety.

He escaped, and returned to Ionia.




1.         The world order was produced by reason.

3.         Since there are many things in the world, and nothing comes into being out of nothing, everything that comes into existence must be present in the things that they come out of.









1.  Everything is composed of atoms moving in a void.

2. Atoms are eternal, unchanging, and inseparable.

3. The void is infinite, eternal, and unchanging.




1. I movement exists, then a void must exist.

2. Movement does exist / Therefore a void exists


1. M > V

2. M   /  V

3. V           1,2 mp




He was an Ionian - probably born in Miletus. The dates are unknown.

Leucippus was the first to formulated the atomic theory for reality.

He was the teacher of Democritus.

His lost works were Megas Diakosmos (The Great Order of the Universe) and Peri Nou (On mind). A single fragment survived:

Nothing happens at random, but everything from reason and necessity.
—Leucippus, Diels-Kranz 67 B2

This sentence is the first expression of the Principle of Sufficient Reason.







1.      Something cannot arise from nothing.

2.      Change is real; it's not an illusion.

3.      Everything is made of atoms moving in a void. (There is no soul)

        Atoms are indivisible, unchanging, eternal, and infinite.

        The void is infinite empty space.

4.     Atoms have different shapes. Solids are interlocked atoms.

        Liquids are made of smooth round atoms.

5.     Atoms lack color, smell, taste, odor, and temperature.
        Sweetness is caused by smooth atoms - bitterness by sharp atoms.

6.     The senses provide indirect subjective knowledge.

7.     Moderation produces calmness and pleasure.

8.     Excess causes agitation and pain.

9.     Pleasure is the only value.
        Calmness is the highest pleasure. (prudent hedonism)








Born in Abdera.

The pupil of Leucippus. 

He traveled to Asia, India, Egypt, and Ethiopia.








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