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Sophia on the web A Resource Guide for Philosophy Students Created by Jennifer Leslie
Torgerson, MA Visiting Associate Professor of Philosophy, CCBC This
page last modified: September 6, 2012 ©
copyright, 1997 - 2012 ~ Jennifer Leslie Torgerson
The Pre-Socratics The Pre-Socratics: and the Problem of the One and the
Many Bibliography F.
M. Cornford.
Plato and Parmenides. (Indianapolis, IN: Bobbs-Merrill
Company, no date). __________,
Before and After Socrates. (Cambridge, UK: Cambridge University Press, 1999 [1932]). __________,
From Religion to Philosophy: A Study in the Origins of Western
Speculation. (Mineola, NY: Dover Books, 2004 [1912]). Frederick
Copleston, S.J., A History of Philosophy: Book
One. (New York, NY: Doubleday, 1985 [1944]). Walter Kaufmann, Philosophical Classics Volume I: Thales to Ockham, 2nd
Edition. (Englewood Cliffs, NJ: Prentice Hall, 1968 [1961]). The majority
of the primary source quotes were taken from this text. A. A. Long, Editor; The Cambridge Companion to Early Greek
Philosophy. (Cambridge, UK: Cambridge University Press, 1999). Merrill Ring, Beginning with the Pre-Socratics. (Mountain View, CA: Mayfield Publishing, 1987).
(N/A means
not answerable in this form. For example, Pythagoras was a dualist?) There are three groups of Pre-Socratics: (1) The Ionians, (2) The Italians, and (3) The Pluralists. Other divisions, or groups can be made such as: The Milesians are those Ionian Pre-Socratics
from Miletus. (1) The Ionians: Thales, Anaximander, Anaximenes,
Xenophanes, and Heraclitus. (2) The Italians: Pythagoras, Parmenides, and Zeno. (3) The Pluralists: Empedocles, Anaxgoras,
Democritus, and Leucippus. Ancient Greek concept of the cycling of the elements: Elements were thought to change from one to another, earth to water to
air, but it is unclear how fire comes from air (since fire is mystical and
air invisible) and it is unclear how fire comes from the earth (also
mysterious). Some key terms to know: (1) substance: (or essence), what a thing is opposed to
the way it appears to be. (Lockian definition or
Modern definition) (2) monist: one who believes that there is one kind of
basic stuff or substance to the universe, from which everything is composed. (3) pluralist: one who believes that there is more than
one basic stuff, or many substances in the universe, from which everything is
composed. (4) apeiron:
indefinite, or boundless (infinite). (5) ousia: ‘primary substance’ or being in the
Classical sense; the character, or a thing’s nature; it is what it is, in and
of itself: meaning it is what it is and its’ nature is independent of any
other nature (can be explained only in terms of itself). (6) arche: stuff (material cause or basic
stuff). Some Fragments (if
possible): Thales: NO FRAGMENTS Anaximander: ONLY FRAGMENT: “Existing
things perish into those things out of which they have come to be; for they
pay reparation to each other for their injustice according to the ordinance
of time.” Anaximenes: ONLY ONE FRAGMENT remains- one line of a
text which is now lost. The fragment is: "As our soul, which
is air, holds us together, so do breathe and air encompass the whole
world." Heraclitus: MANY MORE FRAGMENTS
REMAIN- 120+: Here are a few: #55: “The things of which there is
seeing and hearing and perception, these I prefer.” #50: “Listening
not to me but to the Logos it is wise to agree that all things are one.” #7:
“If all things turned to smoke, the nose would be the discriminating
organ.” #10: “I sought myself.” #118: “A dry soul is wisest and
best.” #93: “The lord whose oracle is in Delphi neither speaks out nor
conceals, but gives a sign.” #41: “Wisdom is One, knowing the thought
by which it steers all things through all things.” and the most quoted: #12:
Upon those who step into the same river, different and again different waters
flow.” #91: “It is not possible to step into the same river twice.” #60: “The
path up and the path down are one in the same.” #119: “Character is a
man’s fate.” #49: “One man to me is ten thousand if he is best.” #110:
“It is not good for men to obtain all they wish.” #112: “Sane thinking
is the greatest virtue, and wisdom is speaking the truth and acting according
to nature, paying heed.” #42: “Homer deserves to be thrown out of the
contests and whipped, and Archilochus too.” #62:
“Immortals are mortals, mortals immortal, each other’s death, dying each
other’s life.” Pythagoras: ALL OF HIS IDEAS COME
FROM UNDERSTANDING HIS BROTHERHOOD- and it is hard to separate his ideas from
those of others. The most important Pythagorean contribution to Philosophy is
the discovery of Form. Parmenides and Zeno: BOTH
WROTE AN ENTIRE BOOK- we have Parmenides’ poem, but must rely upon quote for
our knowledge of Zeno. Parmenides wrote a poem entitled “The Way of Seeming
and the Way of Truth”. Zeno, Parmenides’ student, logically argued against
pluralism to defend their shared view of monism. Parmenides: “Come, I will
tell you; hear my word and carry it away. These are the only ways of inquiry
that can be thought of [literally: that exist for thinking] one way, that it
is and cannot not be, is the path of persuasion, for it attends upon truth,
the other, that is-not and needs must not-be, that, I will tell you, is a
path all together unthinkable. For you could not know that which is-not (that
is impossible), nor utter it.” (Section, or fragment #2) Zeno’s
arguments come to us via Aristotle (in his Metaphysics) and Plato (in his
dialogue entitled Parmenides). Simplicius quoted a
great deal from Zeno’s book as well. Zeno employs the reductio
ad absurdum (to reduce to absurdity) form of argumentation to attack
pluralism. Xenophanes: 35+ FRAGMENTS REMAIN-
here are a few: #11: “Homer and Hesiod have attributed to the gods
everything that, among men, is shameful and reproachable: stealing, adultery,
mutual deceit.” #32 (about a rainbow) “She whom men call Iris, she too
is a cloud, purple, red, and yellow to sight.” #14: “Mortals think
that the gods are born and have clothes and speech and bodies like their
own.” #34: “No man knows or ever will know the truth about the gods
and about everything of which I speak. For even if someone were, by chance,
to speak the whole truth, he would not know it- in all things there is
opinion.” #18: “Not from the beginning have the gods revealed all
things to mortals, but by long seeking men find what is better.” #16: “The
Ethiopians consider the gods flat-nosed and black; the Thracians blue-eyed
and red-haired.” #27: “Everything comes from earth and returns to
earth in the end.” Empedocles: 136+ FRAGMENTS REMAIN-
here are a few: #8: “I shall tell you another thing: there is no
creation of substance in any one of mortal existences, nor any end in
execrable death, but only mixing and exchange of what has been mixed; and the
name “substance” (physis, “nature”) is applied to
them by mankind.” #27: “(The sphere under the dominion of love);
Therein are articulated neither the swift limbs of the sun, nor the shaggy might of earth, nor the sea: so firmly is
it (the whole) fixed in a close-set secrecy, a rounded sphere enjoying a
circular solitude.” #25: “For what is right can well be uttered even
twice.” #136: “Will ye not cease from this harsh sounding slaughter?
Do you not see that you are devouring one another in the thoughtlessness of
your minds?” Anaxagoras: WROTE ONE BOOK- still on
sale in Athens in the 1st century CE for one drachma- but only 21+ fragments
of it survive today- here are a few: #7: “So that number of the things
separated off cannot be known either in thought or in fact.” #8: The
things in one Cosmos are not separated off from another with an axe, neither
Hot from Cold, nor the Cold from the Hot.” #9: “Thus these things
circulate and are separated off by force and speed. Their speed is not the
speed of any of the Things now existing among mankind, but altogether many
times as fast.” #10: “How can hair come from not-hair, and flesh from
not-flesh?” #11: “In everything there is a portion of everything
except in Mind; and some things contain Mind also.” #17: “The Greeks
have an incorrect belief on Coming into Being and Passing Away. No Thing
comes into being or passes away, but is mixed together or separated from
existing Things. Thus they would be correct if they called coming in to being
“mixing” and passing away “separation-off”.” #18: “It is the sun that
endows the moon with its brilliance.” #21: “Through the weakness of
the sense perceptions, we cannot judge the truth.” Democritus (and Leucippus): ALL
LEUCIPPUS’ WRITINGS ARE LOST (or some of Democritus’ writings may be actually
Leucippus’ own words) BUT THERE ARE 294+ FRAGMENTS FROM DEMOCRITUS SURVIVING,
SOME FROM HIS TEXT CALLED “ON THE FORMS” He also wrote about Ethics and a
text he may have called Gnomae- which we have
complete- here are a few fragments: #7: “We know nothing about anything
really, but opinion is for all individuals an inflowing.” #8: “It will
be obvious that it is impossible to understand how in reality each thing is.”
#9: “Sweet exists by convention, bitter by convention, color by
convention; atoms and void (alone) exist in reality... We know nothing
accurately in reality, but (only) as it changes according to the bodily
condition, and the constitution of those things that flow upon it.” #10:
“It has often been demonstrated that we do not grasp how each thing is or is
not.” #39: “One must either be good, or imitate a good man.” #40: “Men
find happiness neither by means of the body nor through possessions, but
through uprightness and wisdom.” #41: “Refrain from crimes not from
fear but through duty.” #42: “It is a great thing, when one is in adversity,
to think of duty.” #44: “One should tell the truth, not speak at
length.” #47: “Well-ordered behavior consists in obedience to the law,
the ruler, and the man wiser (than oneself).” #49: “It is hard to be
governed by one’s inferior.” #74: “Accept no pleasure unless it is
beneficial.” #75: “Virtuous love consists in decorous desire for the
beautiful.” #105: “Physical beauty is (merely) animal unless
intelligence be present.” #110: “A woman must
not practice argument: this is dreadful.” #111: “To be ruled by a
woman is the ultimate outrage for a man.” #115: “It is better to be
praised by another than by oneself. #208: “The self-control of the
father is the greatest example for the children.” #210: “A rich table
is provided by luck, but a sufficient one by wisdom.” #200: “People
are fools who live without enjoyment of life.” #226: “Freedom of
speech is the sign of freedom; but the danger lies in discerning the right
occasion #236: “It is hard to fight desire; but to control it is the
sign of a reasonable man.” Diagrams- Empedocles: Empedocles’ Cosmic cycle from love- to the richest possible world- to
strife- to the richest possible world- .... (ad
infinitum) Elements (earth, air, fire, water) under the force of strife/hate are
separated. Elements (earth, air, fire, water) under the force of love are mixed
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figure one |
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A1 |
A2 |
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<B1 |
B2 |
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C2 |
C1> |
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and in one minute the train cars look like the following:
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figure two |
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A1 |
A2 |
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B1 |
B2 |
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C2 |
C1 |
Zeno asked, essentially, “what distance Train B has moved in that
minute?” Car B1 has moved precisely opposite car A1, and each car is 10 units
long, B has covered 10 units in that minute. But notice that B1 has also
completely passed car C1 and come precisely opposite car C2. As each of those
is just 10 units long, B has covered 20 units in the same minute. SO B has
moved 10 units and 20 units during the same minute. In general, a moving
thing will cover both n and 2n units of distance at one and the same time.
Yet this is contradictory. Hence the concept of motion is reduced to absurdity
(reductio ad absurdum).
(2) The arrow: Consider an arrow in flight. As is true of all
objects, at every moment it must be in the place where it is and in no other.
Yet a moving arrow, as with all objects in motion, in order to be moving,
must be going from place to place. So at every moment it must be in a place
and going from place to place at the same time. This is a contradictory state
of affairs, and is absurd.
(3) Achilles example: You cannot transverse an infinity of
points. Motion is impossible
Pythagorean Diagrams
Clockwise from left to right-
Chart 1: Natural Number Series (1 is a point [no
dimension], 2 points are a line [1 dimension], 3 points are a triangle [2
dimensions], 4 points are a pyramid [3 dimensions]);
Chart 2: Even Number Series 2-4-6-8-10 (rectangle);
Chart 3: Odd Number Series 1-3-5-7 (square);
Chart 4: Natural Number Series 1, 2, 3, 4 (triangle).
The dots also represent an octave (ratio 2:1), a fifth (3:2), and a seventh
(4:3); and if you add those together you get part of the odd number series:
3, 5, and 7.
Pyramidal Numbers
Pyramidal numbers have the same length on each side.
Examples of Pyramidal numbers:
3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171,
190, 210……
Corresponding side lengths: 2,
3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.. …
Sequence mathematically of Pyramidal numbers: (3/2) = x1R1; (6/3) = x2; (10/4) = x2R2;
(15/5) = x3; (21/6) = x3R3; (28/7) = x4; (36/8) = x4R4; (45/9) = x5; (55/10)
= x5R5; (66/11) = x6; (78/12) = x6R6; (91/13) = x7; (105/14) = x7R7; (120/15)
= x8; (136/16) = x8R8; (153/17) = x9; (171/18) = x9R9; (190/19) = x10; (210/20)
= x10R10.....
Here is a Pythagorean
Theorem Calculator:
Timeline of important events in ancient Greek history c. 1500 BCE Mionian culture (Crete). c. 1250 BCE Trojan war may have occurred. c. 1000 BCE Homer may have lived. 1000-600 BCE Dark Ages of Greece. c. 600 BCE Homer's epics written down. 585 BCE Thales predicts eclipse, battle of the river Halys. c. 550 BCE Anaximander, Anaximenes,
Pythagoras, Zenophanes wrote. c. 510 BCE Parmenides is born. 508 BCE Athenian Constitution written by Cleisthenes. c. 500 BCE Pythagoras died, Heraclitus and Anaxagoras
wrote. 499 BCE Persian War begins. c. 470 BCE Birth of Socrates. c. 460 BCE Democritus wrote. c. 450 BCE Empedocles wrote. 449 BCE End of the Persian War. 440 BCE Melissus wrote. 432 BCE Anaxagoras, a philosopher from Clazomenae, is tried for impiety. Anaxagoras was a
friend of Pericles, and was the first philosopher to be put on trial for
impiety. The trumped up charge was based on the fact that Anaxagoras taught
that the sun is a red hot stone and the moon is made of earth. (Apology, 26
d). Peloponnesian War begins. 427 or 428 BCE Plato is born. 423 BCE Aristophanes' The Clouds, a play which portrays
Socrates as a buffoon, was first performed in this year. 405 BCE The reign of the 30 Spartan tyrants in Athens
begins and lasts 8 months. 404 BCE Civil war ends of the reign of the 30 Spartan
tyrants and the re- establishment of democracy in Athens. The Peloponnesian
war is over. 399 BCE The trial and death of Socrates. 388 or 387 BCE Plato visits Italy, where he was, or
nearly was, (or it never even happened), sold into slavery by Dionysius,
because his outspokenness excited Dionysius; but Plato was ransomed by a
friend, and sent back to Athens. Plato founds the Academy, and writes Republic. Over the door of
the Academy read: "If you do not know geometry do not enter
these doors." 384 BCE Aristotle is born. 368 or 367 BCE Aristotle enters Plato's Academy in one of these
years at age 17. Plato goes to Syracuse, Italy because Dionysius had
died and Plato's friend Dion, (Dionysius' brother-in-law), invites Plato to
teach Dionysius II geometry. Plato was almost not able to leave
again due to a dispute between the two brothers-in-law (Dion and Dionysius
II); each wanted to be Master of Syracuse. Plato did return to Athens,
where he continued his correspondence with Dionysius II. 361/ 360 BCE Plato made another voyage to Syracuse. 360 BCE Plato returns to Athens. 357 BCE Dion finally becomes Master (Tyrant) of Syracuse
but was murdered in 353 to the grief of Plato who felt he had failed at his
dream of a philosopher-king. 348 or 347 BCE Plato wrote Laws just prior to death at 80.
Plato dies in one of these years. 343 BCE Aristotle was invited by Philip of Macedon to
undertake the teaching of Alexander the Great, his son of 13. Philip I had
conceived the idea of a Hellenic defeat of the Persians. 336 or 335 BCE Alexander the Great ascended the throne, and
Aristotle left Macedon, and returned to Athens and founded his own school,
the Lyceum 322-321 BCE Alexander the Great dies, and the Greek hate of
Macedonian rule force Aristotle to leave Athens, for the second time, and
he went to the estate of his dead mother in Euboea, where he died shortly
after of an illness.